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SAT II Math II : Data Analysis and Statistics

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Example Questions

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Example Question #1 : Mean

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:

Median, mode, mean

Mean, mode, median

Mode, median, mean

Mean, median, mode

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

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

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

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

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

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

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Example Question #1 : Data Analysis And Statistics

Find the mean of the following data set:

33,67,87,23,45,55,136,67,93

Possible Answers:

67.33

113

Correct answer:

67.33

Explanation:

Find the mean of the following data set:

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.

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

So our mean is 67.33

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Example Question #2 : Data Analysis And Statistics

Find the mode of the data set.

({2,9,4,5,8,3,5,4})

Possible Answers:

4,5

Correct answer:

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.

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

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

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Example Question #3 : Data Analysis And Statistics

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

Possible Answers:

18.5

Correct answer:

Explanation:

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

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

The answer is:

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Example Question #4 : Data Analysis And Statistics

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

Possible Answers:

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

Correct answer:

Explanation:

The mean is the average of all the numbers given.

Add all the numbers and divide the total by five.

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

The answer is:

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Example Question #1 : Data Analysis And Statistics

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

Possible Answers:

Correct answer:

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.

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

The answer is:

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Example Question #2 : Data Analysis And Statistics

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

Possible Answers:

Correct answer:

Explanation:

The mean is the average of the numbers provided.

Sum the numbers and divide the sum by three.

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

The answer is:

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Example Question #3 : Data Analysis And Statistics

Find the median of the following data set:

33,67,87,23,45,55,136,67,93

Possible Answers:

67.33

Correct answer:

Explanation:

Find the median of the following data set:

33,67,87,23,45,55,136,67,93

First, put the numbers in ascending order:

23,33,45,55,67,67,87,93,136

Next, identify the median by identifying the middle term.

$23,33,45,55,{\color{DarkRed} 67},67,87,93,136$

So, our median is 67.

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Example Question #2 : Median

Determine the median of the following numbers: [5,-6,17,2]

Possible Answers:

$\frac{9}{7}$

$\frac{3}{2}$

$\frac{9}{2}$

$\frac{7}{2}$

Correct answer:

$\frac{7}{2}$

Explanation:

Order the numbers from least to greatest.

$[5,-6,17,2] \to [-6,2,5,17]$

The median of a even set of numbers is the average of the central two numbers.

$\frac{2+5}{2} = \frac{7}{2}$

The answer is: $\frac{7}{2}$

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Example Question #1 : Data Analysis And Statistics

Determine the median of the numbers: [1,9,10,11,15,23]

Possible Answers:

$\frac{7}{3}$

$\frac{21}{2}$

$\frac{23}{2}$

$\frac{23}{6}$

$\frac{7}{2}$

Correct answer:

$\frac{21}{2}$

Explanation:

The numbers provided are already in chronological order.

Since we have an even set of numbers, the median of the numbers is the average of the two central numbers.

$\frac{10+11}{2} = \frac{21}{2}$

Do not confuse the meaning of mean and median!

The answer is: $\frac{21}{2}$

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SAT II Math II : Data Analysis and Statistics

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

All SAT II Math II Resources

Example Questions

Example Question #1 : Mean

Example Question #1 : Data Analysis And Statistics

Example Question #2 : Data Analysis And Statistics

Example Question #3 : Data Analysis And Statistics

Example Question #4 : Data Analysis And Statistics

Example Question #1 : Data Analysis And Statistics

Example Question #2 : Data Analysis And Statistics

Example Question #3 : Data Analysis And Statistics

Example Question #2 : Median

Example Question #1 : Data Analysis And Statistics

All SAT II Math II Resources

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