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SAT II Math II : Mean

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Example Questions

Example Question #1 : Data Analysis And Statistics

Stem_and_leaf

Above is the stem-and-leaf display for a group of test scores. Order the mean, the median, and the mode of the scores from least to greatest.

Possible Answers:

Mode, median, mean

Mean, median, mode

Median, mode, mean

Mean, mode, median

Median, mean, mode

Correct answer:

Mean, median, mode

Explanation:

The scores represented can be found from matching the tens digits in the "stem" to the units digits that form the "leaves" in their row. For example, the "leaves" in the "5" row are "2 2 4 4 7 7 8", so the scores will be 52, 52, 54, 54, 57, 57, and 58.

There are 53 scores represented, so to find the median, look for the middle score, in position

$\frac{53+1}{2} = 27$ $\displaystyle \frac{53+1}{2} = 27$.

As can be seen in this diagram, the score - the median - is 74.

Stem_and_leaf_1

The most frequently occurring "leaf" is the "6" in the "7" row, so the mode is 76.

The mean is the sum of the scores divided by 53. If we add the scores, we get

$\sum x = 3,763$ $\displaystyle \sum x = 3,763$, the mean is

$\frac{\sum x }{n}=\frac{ 3,763}{53} = 71$ $\displaystyle \frac{\sum x }{n}=\frac{ 3,763}{53} = 71$

In ascending order, the values are mean, median, mode.

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Example Question #1 : Mean

Find the mean of the following data set:

$\displaystyle 33,67,87,23,45,55,136,67,93$

Possible Answers:

67.33 $\displaystyle 67.33$

$\displaystyle 55$

$\displaystyle 67$

113 $\displaystyle 113$

Correct answer:

67.33 $\displaystyle 67.33$

Explanation:

Find the mean of the following data set:

$\displaystyle 33,67,87,23,45,55,136,67,93$

To find the mean, add up all the terms and divide by the total number of terms.

We have 9 terms, so our denominator will be 9.

$\frac{33+67+87+23+45+55+136+67+93}{9}=\frac{606}{9}=67.3\bar{3}\approx67.33$ $\displaystyle \frac{33+67+87+23+45+55+136+67+93}{9}=\frac{606}{9}=67.3\bar{3}\approx67.33$

So our mean is 67.33

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Example Question #3 : Mean

Find the mode of the data set.

$\displaystyle ({2,9,4,5,8,3,5,4})$

Possible Answers:

4,5 $\displaystyle 4,5$

$\displaystyle 5$

$\displaystyle 7$

$\displaystyle 4$

$\displaystyle 3$

Correct answer:

4,5 $\displaystyle 4,5$

Explanation:

The mode of a data set is the data point(s) that appear the most often.

In the data set for this problem, both 4 and 5 appear twice, and no other number appears more than twice.

$({2,9,{\color{Blue} 4},{\color{Green} 5},8,3,{\color{Green} 5},{\color{Blue} 4}})$ $\displaystyle ({2,9,{\color{Blue} 4},{\color{Green} 5},8,3,{\color{Green} 5},{\color{Blue} 4}})$

So for this data set there are two modes, 4 and 5.

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Example Question #1 : Data Analysis And Statistics

Find the mean of the following numbers: $\displaystyle [14,8,23,51]$

Possible Answers:

$\displaystyle 22$

$\displaystyle 26$

18.5 $\displaystyle 18.5$

$\displaystyle 18$

$\displaystyle 24$

Correct answer:

$\displaystyle 24$

Explanation:

The mean is the average of all the number in the data set.

$\frac{14+8+23+51}{4} = \frac{96}{4}$ $\displaystyle \frac{14+8+23+51}{4} = \frac{96}{4}$

The answer is: $\displaystyle 24$

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Example Question #5 : Mean

Find the mean of the numbers: $\displaystyle [9,5,10,15,21]$

Possible Answers:

$\displaystyle 21$

$\displaystyle 12$

$\textup{The mean is not given.}$ $\displaystyle \textup{The mean is not given.}$

$\displaystyle 10$

$\displaystyle 14$

Correct answer:

$\displaystyle 12$

Explanation:

The mean is the average of all the numbers given.

Add all the numbers and divide the total by five.

$\frac{9+5+10+15+21}{5} = \frac{60}{5} = 12$ $\displaystyle \frac{9+5+10+15+21}{5} = \frac{60}{5} = 12$

The answer is: $\displaystyle 12$

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Example Question #2 : Data Analysis And Statistics

Determine the mean: $\displaystyle [13,5,8,-6]$

Possible Answers:

$\displaystyle 13$

$\displaystyle 5$

$\displaystyle 8$

$\displaystyle 6$

$\displaystyle 19$

Correct answer:

$\displaystyle 5$

Explanation:

The mean is the average of all numbers in the data set.

Add the numbers, and divide the total sum by four, since there are four numbers.

$\frac{13+5+8+(-6)}{4} = \frac{20}{4} =5$ $\displaystyle \frac{13+5+8+(-6)}{4} = \frac{20}{4} =5$

The answer is: $\displaystyle 5$

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Example Question #1 : Mean

Determine the mean of the three numbers: $\displaystyle [6,9,15]$

Possible Answers:

$\displaystyle 15$

$\displaystyle 6$

$\displaystyle 30$

$\displaystyle 20$

$\displaystyle 10$

Correct answer:

$\displaystyle 10$

Explanation:

The mean is the average of the numbers provided.

Sum the numbers and divide the sum by three.

$\frac{6+9+15}{3} = \frac{30}{3} = 10$ $\displaystyle \frac{6+9+15}{3} = \frac{30}{3} = 10$

The answer is: $\displaystyle 10$

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SAT II Math II : Mean

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #1 : Data Analysis And Statistics

Example Question #1 : Mean

Example Question #3 : Mean

Example Question #1 : Data Analysis And Statistics

Example Question #5 : Mean

Example Question #2 : Data Analysis And Statistics

Example Question #1 : Mean

All SAT II Math II Resources

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