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5.8: Averages and Probability (Part 1)

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    Learning Objectives
    • Calculate the mean of a set of numbers
    • Find the median of a set of numbers
    • Find the mode of a set of numbers
    • Apply the basic definition of probability
    be prepared!

    Before you get started, take this readiness quiz.

    1. Simplify: \(\dfrac{4 + 9 + 2}{3}\). If you missed this problem, review Example 4.6.12.
    2. Simplify: 4(8) + 6(3). If you missed this problem, review Example 2.2.8.
    3. Convert \(\dfrac{5}{2}\) to a decimal. If you missed this problem, review Example 5. 5.1.

    One application of decimals that arises often is finding the average of a set of numbers. What do you think of when you hear the word average? Is it your grade point average, the average rent for an apartment in your city, the batting average of a player on your favorite baseball team? The average is a typical value in a set of numerical data. Calculating an average sometimes involves working with decimal numbers. In this section, we will look at three different ways to calculate an average.

    Calculate the Mean of a Set of Numbers

    The mean is often called the arithmetic average. It is computed by dividing the sum of the values by the number of values. Students want to know the mean of their test scores. Climatologists report that the mean temperature has, or has not, changed. City planners are interested in the mean household size.

    Suppose Ethan’s first three test scores were 85, 88, and 94. To find the mean score, he would add them and divide by 3.

    \[\dfrac{85 + 88 + 94}{3}\]

    \[\dfrac{267}{3}\]

    \[89\]

    His mean test score is 89 points.

    Definition: The Mean

    The mean of a set of n numbers is the arithmetic average of the numbers.

    \[mean = \dfrac{sum\; of\; values\; in\; data\; set}{n}\]

    HOW TO: CALCULATE THE MEAN OF A SET OF NUMBERS

    Step 1. Write the formula for the mean\[mean = \dfrac{sum\; of\; values\; in\; data\; set}{n}\]

    Step 2. Find the sum of all the values in the set. Write the sum in the numerator.

    Step 3. Count the number, n, of values in the set. Write this number in the denominator.

    Step 4. Simplify the fraction.

    Step 5. Check to see that the mean is reasonable. It should be greater than the least number and less than the greatest number in the set.

    Example \(\PageIndex{1}\):

    Find the mean of the numbers 8, 12, 15, 9, and 6.

    Solution

    Write the formula for the mean. $$mean = \dfrac{sum\; of\; values\; in\; data\; set}{n}$$
    Write the sum of the numbers in the numerator. $$mean = \dfrac{8 + 12 + 15 + 9 + 6}{n}$$
    Count how many numbers are in the set. There are 5 numbers in the set, so n = 5. $$mean = \dfrac{8 + 12 + 15 + 9 + 6}{5}$$
    Add the numbers in the numerator. $$mean = \dfrac{50}{5}$$
    Then divide. mean = 10
    Check to see that the mean is ‘typical’: 10 is neither less than 6 nor greater than 15. The mean is 10.
    Exercise \(\PageIndex{1}\):

    Find the mean of the numbers: 8, 9, 7, 12, 10, 5.

    Answer

    \(8.5\)

    Exercise \(\PageIndex{2}\):

    Find the mean of the numbers: 9, 13, 11, 7, 5.

    Answer

    \(9\)

    Example \(\PageIndex{2}\):

    The ages of the members of a family who got together for a birthday celebration were 16, 26, 53, 56, 65, 70, 93, and 97 years. Find the mean age.

    Solution

    Write the formula for the mean. $$mean = \dfrac{sum\; of\; values\; in\; data\; set}{n}$$
    Write the sum of the numbers in the numerator. $$mean = \dfrac{16 + 26 + 53 + 56 + 65 + 70 + 93 + 97}{n}$$
    Count how many numbers are in the set. Call this n and write it in the denominator. $$mean = \dfrac{16 + 26 + 53 + 56 + 65 + 70 + 93 + 97}{8}$$
    Simplify the fraction. $$mean = \dfrac{476}{5}$$
      mean = 59.5

    Is 59.5 ‘typical’? Y es, it is neither less than 16 nor greater than 97. The mean age is 59.5 years.

    Exercise \(\PageIndex{3}\):

    The ages of the four students in Ben’s carpool are 25, 18, 21, and 22. Find the mean age of the students.

    Answer

    21. 5 years

    Exercise \(\PageIndex{4}\):

    Yen counted the number of emails she received last week. The numbers were 4, 9, 15, 12, 10, 12, and 8. Find the mean number of emails

    Answer

    10

    Did you notice that in the last example, while all the numbers were whole numbers, the mean was 59.5, a number with one decimal place? It is customary to report the mean to one more decimal place than the original numbers. In the next example, all the numbers represent money, and it will make sense to report the mean in dollars and cents.

    Example \(\PageIndex{3}\):

    For the past four months, Daisy’s cell phone bills were $42.75, $50.12, $41.54, $48.15. Find the mean cost of Daisy’s cell phone bills.

    Solution

    Write the formula for the mean. $$mean = \dfrac{sum\; of\; all\; the\; numbers}{n}$$
    Write the sum of the numbers in the numerator. $$mean = \dfrac{sum\; of\; all\; the\; numbers}{4}$$
    Count how many numbers are in the set. Call this n and write it in the denominator. $$mean = \dfrac{42.75 + 50.12 + 41.54 + 48.15}{4}$$
    Simplify the fraction. $$mean = \dfrac{182.56}{4}$$
      mean = 45.64

    Does $45.64 seem ‘typical’ of this set of numbers? Yes, it is neither less than $41.54 nor greater than $50.12. The mean cost of her cell phone bill was $45.64.

    Exercise \(\PageIndex{5}\):

    Last week Ray recorded how much he spent for lunch each workday. He spent $6.50, $7.25, $4.90, $5.30, and $12.00. Find the mean of how much he spent each day.

    Answer

    $7.19

    Exercise \(\PageIndex{6}\):

    Lisa has kept the receipts from the past four trips to the gas station. The receipts show the following amounts: $34. 87, $42.31, $38.04, and $43.26. Find the mean.

    Answer

    $39.62

    Find the Median of a Set of Numbers

    When Ann, Bianca, Dora, Eve, and Francine sing together on stage, they line up in order of their heights. Their heights, in inches, are shown in Table 5.70.

    Table 5.70

    Ann Bianca Dora Eve Francine
    59 60 65 68 70

    Dora is in the middle of the group. Her height, 65″, is the median of the girls’ heights. Half of the heights are less than or equal to Dora’s height, and half are greater than or equal. The median is the middle value.

    Definition: Median

    The median of a set of data values is the middle value.

    • Half the data values are less than or equal to the median.
    • Half the data values are greater than or equal to the median.

    What if Carmen, the pianist, joins the singing group on stage? Carmen is 62 inches tall, so she fits in the height order between Bianca and Dora. Now the data set looks like this:

    \[59, 60, 62, 65, 68, 70\]

    There is no single middle value. The heights of the six girls can be divided into two equal parts.

    \[\underbrace{59, 60, 62} \quad \underbrace{65, 68, 70}\]

    Statisticians have agreed that in cases like this the median is the mean of the two values closest to the middle. So the median is the mean of 62 and 65, \(\dfrac{62 + 65}{2}\). The median height is 63.5 inches.

    Notice that when the number of girls was 5, the median was the third height, but when the number of girls was 6, the median was the mean of the third and fourth heights. In general, when the number of values is odd, the median will be the one value in the middle, but when the number is even, the median is the mean of the two middle values.

    HOW TO: FIND THE MEDIAN OF A SET OF NUMBERS

    Step 1. List the numbers from smallest to largest.

    Step 2. Count how many numbers are in the set. Call this n.

    Step 3. Is n odd or even?

    • If n is an odd number, the median is the middle value.
    • If n is an even number, the median is the mean of the two middle values.
    Example \(\PageIndex{4}\):

    Find the median of 12, 13, 19, 9, 11, 15, and 18.

    Solution

    List the numbers in order from smallest to largest. 9, 11, 12, 13, 15, 18, 19
    Count how many numbers are in the set. Call this n. n = 7
    Is n odd or even? odd
    The median is the middle value.
    The middle is the number in the 4th position. So the median of the data is 13.
    Exercise \(\PageIndex{7}\):

    Find the median of the data set: 43, 38, 51, 40, 46.

    Answer

    43

    Exercise \(\PageIndex{8}\):

    Find the median of the data set: 15, 35, 20, 45, 50, 25, 30.

    Answer

    30

    Example \(\PageIndex{5}\):

    Kristen received the following scores on her weekly math quizzes: 83, 79, 85, 86, 92, 100, 76, 90, 88, and 64. Find her median score.

    Solution

    List the numbers in order from smallest to largest. 64, 76, 79, 83, 85, 86, 88, 90, 92, 100
    Count the number of data values in the set. Call this n. n = 10
    Is n odd or even? even
    The median is the mean of the two middle values, the 5th and 6th numbers.
    Find the mean of 85 and 86. mean = 85.5

    Kristen’s median score is 85.5.

    Exercise \(\PageIndex{9}\):

    Find the median of the data set: 8, 7, 5, 10, 9, 12.

    Answer

    8.5

    Exercise \(\PageIndex{10}\):

    Find the median of the data set: 21, 25, 19, 17, 22, 18, 20, 24.

    Answer

    20.5

    Identify the Mode of a Set of Numbers

    The average is one number in a set of numbers that is somehow typical of the whole set of numbers. The mean and median are both often called the average. Yes, it can be confusing when the word average refers to two different numbers, the mean and the median! In fact, there is a third number that is also an average. This average is the mode. The mode of a set of numbers is the number that occurs the most. The frequency, is the number of times a number occurs. So the mode of a set of numbers is the number with the highest frequency.

    Definition: mode

    The mode of a set of numbers is the number with the highest frequency.

    Suppose Jolene kept track of the number of miles she ran since the start of the month, as shown in Figure 5.7.

    Figure 5.7

    If we list the numbers in order it is easier to identify the one with the highest frequency.

    \[2, 3, 5, 8, 8, 8, 15\]

    Jolene ran 8 miles three times, and every other distance is listed only once. So the mode of the data is 8 miles.

    HOW TO: IDENTIFY THE MODE OF A SET OF NUMBERS

    Step 1. List the data values in numerical order.

    Step 2. Count the number of times each value appears.

    Step 3. The mode is the value with the highest frequency.

    Example \(\PageIndex{6}\):

    The ages of students in a college math class are listed below. Identify the mode.

    18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 22, 23, 24, 24, 25, 29, 30, 40, 44

    Solution

    The ages are already listed in order. We will make a table of frequencies to help identify the age with the highest frequency.

    Now look for the highest frequency. The highest frequency is 7, which corresponds to the age 20. So the mode of the ages in this class is 20 years.

    Exercise \(\PageIndex{11}\):

    The number of sick days employees used last year: 3, 6, 2, 3, 7, 5, 6, 2, 4, 2. Identify the mode.

    Answer

    2

    Exercise \(\PageIndex{12}\):

    The number of handbags owned by women in a book club: 5, 6, 3, 1, 5, 8, 1, 5, 8, 5. Identify the mode.

    Answer

    5

    Example \(\PageIndex{7}\):

    The data lists the heights (in inches) of students in a statistics class. Identify the mode.

    56 61 63 64 65 66 67 67
    60 62 63 64 65 66 67 70
    60 63 63 64 66 66 67 74
    61 63 64 65 66 67 67  

    Solution

    List each number with its frequency.

    Now look for the highest frequency. The highest frequency is 6, which corresponds to the height 67 inches. So the mode of this set of heights is 67 inches.

    Exercise \(\PageIndex{13}\):

    The ages of the students in a statistics class are listed here: 19, 20, 23, 23, 38, 21, 19, 21, 19, 21, 20, 43, 20, 23, 17, 21, 21, 20, 29, 18, 28. What is the mode?

    Answer

    21

    Exercise \(\PageIndex{14}\):

    Students listed the number of members in their household as follows: 6, 2, 5, 6, 3, 7, 5, 6, 5, 3, 4, 4, 5, 7, 6, 4, 5, 2, 1, 5. What is the mode?

    Answer

    5

    Some data sets do not have a mode because no value appears more than any other. And some data sets have more than one mode. In a given set, if two or more data values have the same highest frequency, we say they are all modes.

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    How to Find the Mean of a Set of Numbers: Formula and Examples

    Are you taking the SAT or ACT and want to make sure you know how to work with data sets? Or maybe you’re looking to refresh your memory for a high school or college math class. Whatever the case, it’s important you know how to find the mean of a data set.

    We’ll explain what the mean is used for in math, how to calculate the mean, and what problems about the mean can look like.

     

    What Is a Mean and What Is It Used For?

    The mean, or arithmetic mean, is the average value of a set of numbers. More specifically, it’s the measure of a «central» or typical tendency in a given set of data.

    Mean—often simply called the «average»—is a term used in statistics and data analysis. In addition, it’s not unusual to hear the words «mean» or «average» used with the terms «mode,» «median,» and «range,» which are other methods of calculating the patterns and common values in data sets.

    Briefly, here are the definitions of these terms:

    • Mode — the value that appears most frequently in a data set
    • Median — the middle value of a data set (when arranged from lowest value to highest)
    • Range — the difference between the highest and smallest values in a data set

    So what is the purpose of the mean exactly? If you have a data set with a wide range of numbers, knowing the mean can give you a general sense of how these numbers could essentially be put together into a single representative value.

    For example, if you’re a high school student getting ready to take the SAT, you might be interested to know the current mean SAT score. Knowing the mean score gives you a rough idea of how most students taking the SAT tend to score on it.

     

    How to Find the Mean: Overview

    To find the arithmetic mean of a data set, all you need to do is add up all the numbers in the data set and then divide the sum by the total number of values.

    Let’s look at an example. Say you’re given the following set of data:

    $$6, 10, 3, 27, 19, 2, 5, 14$$

    To find the mean, you’ll first need to add up all the values in the data set like this:

    $$6 + 10 + 3 + 27 + 19 + 2 + 5 + 14$$

    Note that you don’t need to rearrange the values here (though you may if you wish to) and can simply add them in the order in which they’ve been presented to you.

    Next, write down the sum of all the values:

    $$6 + 10 + 3 + 27 + 19 + 2 + 5 + 14 = \bo86$$

    The last step is to take this sum (86) and divide it by the number of values in the data set. Because there are eight different values (6, 10, 3, 27, 19, 2, 5, 14), we’ll be dividing 86 by 8:

    $$86 / 8 = 10. 75$$

    The mean, or average, for this set of data is 10.75.

     

     

    How to Calculate a Mean: Practice Questions

    Now that you know how to find the average—in other words, how to calculate the mean of a given set of data—it’s time to test what you’ve learned. In this section, we’ll give you four math questions that involve finding or using the mean.

    The first two questions are our own, whereas the second two are official SAT/ACT questions; as such, these two will require a little bit more thought.

    Scroll past the questions for the answers and answer explanations.

     

    Practice Question 1

    Find the mean of the following set of numbers: 5, 26, 9, 14, 49, 31, 109, 5.  

     

    Practice Question 2

    You are given the following list of numbers: 4, 4, 2, 11, 6, $X$, 1, 3, 2. The arithmetic mean is 4. What is the value of $X$?

     

    Practice Question 3

    The list of numbers 41, 35, 30, $X$,$Y$, 15 has a median of 25. The mode of the list of numbers is 15. To the nearest whole number, what is the mean of the list?

    1. 20
    2. 25
    3. 26
    4. 27
    5. 30

    Source: 2018-19 Official ACT Practice Test

     

    Practice Question 4

    At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age $m$ of the combined group of male and female primates at the primate reserve?

    1. $m = 17$
    2. $m > 17$
    3. $m < 17$
    4. $15 < m < 19$

    Source: The College Board

     

     

    How to Find the Average: Answers + Explanations

    Once you’ve tried out the four practice questions above, it’s time to compare your answers and see whether you understand not just how to find the mean of data but also how to use what you know about the mean to more effectively approach any math questions that deal with averages.

    Here are the answers to the four practice questions above:

    • Practice Question 1: 31
    • Practice Question 2: 3
    • Practice Question 3: C. 26
    • Practice Question 4: D. $15 < m < 19$

    Keep reading to see the answer explanation for each question.

     

    Practice Question 1 Answer Explanation

    Find the mean of the following set of numbers: 5, 26, 9, 14, 49, 31, 109, 5.

    This is a straightforward question that simply asks you to calculate the arithmetic mean of a given data set.

    First, add up all the numbers in the data set (remember that you don’t need to arrange them in order from lowest to highest—only do this if you’re trying to find the median):

    $$5 + 26 + 9 + 14 + 49 + 31 + 109 + 5 = \bo248$$

    Next, take this sum and divide it by the number of values in the data set. Here, there are eight total values, so we’ll divide 248 by 8:

    $$248 / 8 = 31$$

    The mean and correct answer is 31.

     

    Practice Question 2 Answer Explanation

    You are given the following list of numbers: 4, 4, 2, 11, 6, $X$, 1, 3, 2. The arithmetic mean is 4. What is the value of $X$?

    For this question, you’re essentially working backward: you already know the mean and now must use this knowledge to help you solve for the missing value, $X$, in the data set.

    Recall that to find the mean, you add up all the numbers in a set and then divide the sum by the total number of values.

    Since we know the mean is 4, we’ll start by multiplying 4 by the number of values (there are nine separate numbers here, including $X$):

    $$4 * 9 = 36$$

    This gives us the sum of the data set (36). Now, the question becomes an algebra problem, in which all we need to do is simplify and solve for $X$:

    $$4 + 4 + 2 + 11 + 6 + X + 1 + 3 + 2 = 36$$

    $$33 + X = 36$$

    $$X = 3$$

    The correct answer is 3.

     

    Practice makes perfect!

     

    Practice Question 3 Answer Explanation

    The list of numbers 41, 35, 30, $X$, $Y$, 15 has a median of 25. The mode of the list of numbers is 15. To the nearest whole number, what is the mean of the list?

    1. 20
    2. 25
    3. 26
    4. 27
    5. 30

    This tricky-looking math problem comes from an official ACT practice test, so you can expect it to be a little less direct than your typical arithmetic mean problem.

    Here, we’re given a data set with two unknown values:

     41, 35, 30, $X$, $Y$, 15

    We’re also given two critical pieces of information:

    • The mode is 15
    • The median is 25

    To solve for the mean of this data set, we will need to use all the information we’ve been given and will also need to know what the mode and median are.

    As a reminder, the mode is the value that appears most frequently in a data set, while the median is the middle value in a data set (when all values have been arranged from lowest to highest).

    Since the mode is 15, this must mean that the value 15 appears at least twice in the data set (in other words, more times than any other value appears). As a result, we can say replace either $X$ or $Y$ with 15:

    41, 35, 30, $X$,15,15

    We’re also told that the median is 25. To find the median, you must first rearrange the data set in order from lowest value to highest value.

    Since the median is more than 15 but less than 30, we should put $X$ between these two values. Here’s what we get when we rearrange our values from lowest to highest:

    15, 15, $X$, 30, 35, 41

    There are six values in total, (including $X$) meaning that the median will be the number exactly halfway between the third and fourth values in the data set. In short, 25 (the median) must come halfway between $X$ and 30.

    This means that $X$ must equal 20, since that would put it 5 away from 20 and 5 away from 30 (or halfway between the two values).

    We now have a complete data set with no unknown values:

    15,15, 20, 30, 35, 41

    All we have to do now is use these values to solve for the mean. Start by adding them all up:

    15+15+20+30+35+41=156

    Finally, divide the sum by the number of values in the data set (that’s six):

    156/6=26

    The correct answer is C. 26.

     

    Practice Question 4 Answer Explanation

    At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age $m$ of the combined group of male and female primates at the primate reserve?

    1. $m = 17$
    2. $m > 17$
    3. $m < 17$
    4. $15 < m < 19$

    This practice problem is an official SAT Math practice question from the College Board website.

    For this math question, you’re not expected to solve for the mean but must instead use what you know about two means to explain what the mean of the larger group could be. Specifically, we’re being asked how we can use these two means to express, in algebraic terms, the mean age ($\bi m$) for both male and female primates.

    Here’s what we know: first, the mean age of all male primates is 15 years. Secondly, the mean age of all female primates is 19 years. This means that, in general, the female primates are older than the male primates.

    Since the mean age for male primates (15) is lower than that for female primates (19), we know that the mean age for both groups cannot logically exceed 19 years.

    Similarly, because the mean age for female primates is greater than that for male primates, we know that the mean age for both cannot logically fall below 15 years.

    We are therefore left with the understanding that the mean age for the male and female primates together must be greater than 15 years (the mean age of the males) but also less than 19 years (the mean age of the females).

    This rationale can be written as the following inequality:

    $$15 < m < 19$$

    The correct answer is D. 15 < $\bi m$ < 19.

     

    What’s Next?

    To learn even more about data sets, look at our guide to the best strategies for mean, median, and mode on SAT Math.

    Taking the SAT or ACT soon? Then you’ll definitely want to know what kind of math you’re going to be tested on. Check out our in-depth guides to the SAT Math section and the ACT Math section to get started.

    What are the most important math formulas to know for the SAT and ACT? Get an overview of the 28 critical SAT formulas and the 31 critical ACT formulas you should know.

     

    Need more help with this topic? Check out Tutorbase!

    Our vetted tutor database includes a range of experienced educators who can help you polish an essay for English or explain how derivatives work for Calculus. You can use dozens of filters and search criteria to find the perfect person for your needs.

     

    Have friends who also need help with test prep? Share this article!

    Hannah Muniz

    About the Author

    Hannah received her MA in Japanese Studies from the University of Michigan and holds a bachelor’s degree from the University of Southern California. From 2013 to 2015, she taught English in Japan via the JET Program. She is passionate about education, writing, and travel.

    what it is, how to calculate it, which one is needed for admission to college after grade 9 in Russia

    The admission committee of a college or university looks not only at the results of the OGE or USE and entrance exams, but also at the grades in the certificate. The average score of the certificate reflects the progress of the student. This is the mark with which a former high school student participates in the competition, entering an educational institution. GPA is especially important for college applicants because a high GPA is often the only selection criterion.

    How to Calculate GPA

    Colleges look at GPA to find out which students are stronger. This is the arithmetic average of grades in all subjects. To calculate the average score, add up all the grades in the certificate and divide the resulting amount by the number of subjects. This algorithm is suitable for both 9th graders and 11th graders. No other grades (semi-annual, quarterly, examination) need to be taken into account.

    Examples:

    In the certificate for 9class 12 subjects with grades 3, 4, 3, 4, 5, 3, 4, 5, 4, 5, 4, 3. Add all the numbers and divide by 12: 47/12 = 3.91.

    Further, the result is rounded up to 4. This value will be the average grade of the certificate for the 9th grade.

    In the certificate for grade 11, there are already more subjects and marks for them — 18. Let’s say these will be the values: 3, 5, 4, 4, 5, 4, 3, 4, 3, 4, 4, 5, 3, 4 , 5, 4, 5, 4. We also add up the numbers and now divide by 18: 73/18 = 4.05.

    This result is also rounded down, but in a smaller direction, according to mathematical rules. It turns out that the certificate for grade 11 has an average score of 4. The value of the average score of the certificate cannot exceed 5.

    In the 11th grade, the scores obtained on the Unified State Examination do not affect the grades in any way. But the last two years of study are important — grades 10-11. The final mark in the certificate will be calculated as the arithmetic mean of semi-annual (or quarterly) and annual grades for the subject studied in the senior classes.

    Useful information about the average GPA in Russia

    Those with an average GPA above Even if the college has entrance exams (for example, physical education or drawing), the commission still takes into account the average score.
    The certificate has no expiration date — you can enroll at any time The legislation of the Russian Federation does not specify time limits, so you can immediately or a year or even several years after graduation.
    The final grades in the certificates for grades 9 and 11 are given differently. The certificate includes a final grade calculated on the basis of the annual and the marks obtained in the exam. For the rest of the subjects, they simply give annual grades.

    What is the average GPA required for college admission after grade 9

    GPA plays a different role when entering universities and colleges. In the latter, it is of paramount importance. To enter a college or technical school, you do not need to take entrance exams (except for creative and some other professions). Applicants are enrolled according to the competition of certificates. The higher the score, the more chances to study for free.

    The average score in Russia with which you can enter is 3.45. In prestigious colleges, such as MGIMO and RANEPA, for popular specialties (economics, law, humanities), the average passing grade of the certificate is 4.85. There are much more people who want to study than budget places, so sometimes points are taken into account up to hundredths.

    interesting

    10 best professions after 9th grade

    List of popular areas and tips to help you make a choice

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    In less well-known educational institutions with a large number of state-funded places, the passing score is lower — from 3 to 4. 3. There are educational institutions where graduates of the 9th grade are accepted with an average grade of 3. Basically, these are culinary and hairdressing colleges, as well as auto-mechanical technical schools.

    In disputable situations (for example, with the same value of the average score for several applicants), marks in profile school subjects for the future specialty can be taken into account.

    It should be noted that there is no exact value of the GPA for admission to the budget. This indicator depends on the rating of the college and the demand for the direction or specialty. It is better to decide in advance on the choice of an educational institution and find out what score is needed for admission. You can find this out at the admissions office or on the college website.

    Popular questions and answers

    Answered by Daria Deigen, mathematics teacher, USE expert in mathematics

    Can I get into college with a low GPA?

    Admission to most colleges is based on the competition of certificates. The advantage is for children with a high GPA or GPA in specialized subjects. At the same time, there are options to go to college without a competition of certificates, if you are a prize-winner or winner of olympiads, championships. The WorldSkills championship of professional skills may be of particular interest.

    Children participating in volunteer movements also have benefits upon admission.

    There is also the possibility of targeted income when providing an agreement with the company — the future employer.

    So GPA is important for college admissions, but there are other ways you can make up for a low GPA.

    We also note the possibility of entering paid education. Most likely, there will be no high competition for not the most popular areas, which means that a high average score for admission will not be needed.

    Which majors require a high GPA?

    A high average score, as well as in some cases passing an additional entrance test, is required for the most popular areas of secondary vocational education related to economics, management, IT technologies, medicine, and advertising. Recently, due to educational policy, interest in SVE has been growing, more and more children are choosing just such an educational trajectory for themselves. In this regard, the competition for prestigious areas is also growing, which makes it possible to form strong study groups, improve the level of education and bring education in colleges to a new level.

    What does the GPA after grade 11 affect?

    If after the 11th grade a child plans to enter a university in Russia, then the average score of the certificate does not affect practically anything. Admission to universities is based on the results of the Unified State Examination and additional entrance tests. Only an excellent certificate will be a bonus, which will add a few points to the total amount. If, after the 11th grade, the student goes to college, then the same rules apply as after the 9th grade — a competition based on the average score, taking into account achievements in olympiads, competitions, projects.

    Average score of the certificate in the ranking — HSE Lyceum — National Research University Higher School of Economics

    When will the final grades be posted?

    Until April 29, 2023. However, in May, studies will continue as scheduled. From May 22 to June 2, 2023, inclusive, each student in grade 11 will have to reconcile data for the certificate in the electronic diary (Elzhur). Errors found in the final marks after June 2, 2023 will not be taken into account in the calculation of the final personal rating of the graduate. At the same time, the possibility of making adjustments to the certificate form will remain.

    How is the GPA calculated?

    The average score of the certificate is calculated as the arithmetic mean of the final marks in the certificate (excluding the mark for the IVR), rounded up to the 3rd decimal place.

    How are the final grades for academic subjects in the certificate?

    The final grades are set as the arithmetic average of the student’s semi-annual and annual grades for each year of study (grades 10, 11) in accordance with the individual curriculum (hereinafter — IEP) and are set as whole numbers in accordance with the rules of mathematical rounding. The results of GIA-11 are not taken into account when calculating the final mark.

    In what subjects are final grades given in the certificate?

    For each academic subject included in the current IEP (mandatory part of the IEP and IEP, formed by participants in educational relations), if at least 64 hours were allotted for its study in two academic years.

    Academic subjects, which were given less than 64 hours for 2 academic years, will be listed in the Appendix to the certificate in additional information (without a mark).

    Items from the 9th grade certificate are not transferred to the 11th grade certificate and do not affect the final grades.

    Which IEP is considered relevant?

    IEP is called actual, according to which education ends in 11th grade. Academic subjects that the lyceum student studied earlier (for example, having studied in another direction before participating in St. George’s Day, including in the amount of more than 64 hours), will not be included in the certificate and will be taken into account when calculating the average score.

    How marks will be taken into account if the lyceum student came to the extra. class 11 set?

    Grade 10 marks are taken into account only for those subjects that are in the current Grade 11 IEP.

    What are the features of grading in Mathematics?

    • The final mark in the subject Mathematics (basic level) for grades 10-11 is set as the arithmetic average of the marks of the semi-annual and annual intermediate certification in the subject «Mathematics» as an integer in accordance with the rules of mathematical rounding.
    • The final mark in the subject Mathematics (advanced level) is set as the arithmetic average of the marks of the semi-annual and annual intermediate certification for grades 10-11 in the courses «Algebra and the beginning of mathematical analysis» and «Geometry» as an integer in accordance with the rules of mathematical rounding.
    • In the event of a change in the level of study of the subject «Mathematics» (transition from a basic level to an advanced level or from an advanced level to a basic level), all marks of the semi-annual and annual intermediate certification in the subject of Mathematics (basic level) and the courses «Algebra and the beginning of mathematical analysis ”, “Geometry” for grades 10-11 are taken into account when setting the final mark in the certificate as an integer in accordance with the rules of mathematical rounding.

    What are the peculiarities of social studies marks for students of the Humanities direction?

    The mark of the annual intermediate attestation in the subject of Social Science (advanced level) for students of the direction «Humanities» of grades 10-11 is set as the arithmetic average of the marks of the semi-annual intermediate attestation for the study of two (three) modules of the subject of social science (advanced level) as a whole number according to the rules of mathematical rounding.

    What are the peculiarities of grading in Biology for students in the field of «Natural Sciences»?

    The mark of the semi-annual intermediate certification in the subject Biology (advanced level) for students of the direction «Natural Sciences» of grade 10 is set as the arithmetic average of the marks of the semi-annual intermediate certification for the study of two modules of the subject Biology (advanced level).

    What are the peculiarities of grading in Informatics for students in the field of «Computer Science, Engineering and Mathematics»?

    The mark of the semi-annual interim assessment in the subject Informatics (advanced level) for students of the direction «Mathematics, Informatics, Engineering» grades 10-11 is set as the arithmetic average of the marks of the semi-annual interim assessment for the study of two (three) modules of the subject Informatics (advanced level).

    By alexxlab

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