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ISEE Upper Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Upper Level Math

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All ISEE Upper Level Math Resources

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Example Questions

Example Question #31 : Data Analysis

Find the median in the following set of data:

$\left \{ 2,3,4,1,2,4,3,7,3,4 \right \}$

Possible Answers:

Correct answer:

Explanation:

In order to find the median, the data must first be ordered. So we should write:

$\left \{ 1,2,2,3,3,3,4,4,4,7 \right \}$

When the number of values is even, the median is the mean of the two middle values. In this problem we have values, so the median would be the mean of the 5th and 6th values:

$Median=\frac{3+3}{2}=3$

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Example Question #1 : How To Find Median

If is a real number, find the median in the following set of data in terms of .

$\left \{ t,t+4,t+2,t+5,t+1,t+8 \right \}$

Possible Answers:

t+1

t+3

t-2

t+4

t+2

Correct answer:

t+3

Explanation:

The data should first be ordered:

$\left \{ t, t+1, t+2, t+4, t+5, t+8 \right \}$

When the number of values is even, the median is the mean of the two middle values. So in this problem we need to find the mean of the 3th and 4th values:

$Median=\frac{(t+2)+(t+4)}{2}=\frac{2t+6}{2}=t+3$

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Example Question #21 : Median

The heights of the members of a basketball team are 64,78,76,80,82,83,75,x inches. The mean of the heights is $78\ in$ . Give the median of the heights.

Possible Answers:

$80\ in$

$82\ in$

$81\ in$

$79\ in$

$83\ in$

Correct answer:

$79\ in$

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum$ indicates the sum of the data values $x_{i}$ and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{(64+78+76+80+82+83+75+x)}{8}$

$\Rightarrow \bar{x}=\frac{538+x}{8}=78\Rightarrow 538+x=78\times 8$

$\Rightarrow 538+x=624\Rightarrow x=624-538=86\ in$

In order to find the median, the data must first be ordered:

$\left \{ 64,75,76,78,80,82,83,86 \right \}$

Since the number of values is even, the median is the mean of the two middle values. So we get:

$Median=\frac{78+80}{2}=79\ in$

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Example Question #31 : Data Analysis And Probability

Give the median of the frequency distribution shown in the following table:

$\begin{matrix} Data \ Value & Frequency \\ 120 & 7\\ 142& 3\\ 160& 4\\ 174& 6 \end{matrix}$

Possible Answers:

150

142

144

151

138

Correct answer:

151

Explanation:

There are 7+3+4+6=20 data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the 10th and 11th largest values. So we can write:

$10th\ largest \ value=142$

$11th\ largest \ value=160$

So:

$Median=\frac{142+160}{2}=151$

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Example Question #33 : Data Analysis And Probability

Consider the data set

$\left \{ 24,61, 27, 57, 34, 37, 63, 50, N\right \}$ .

For what value(s) of would this set have median ?

Possible Answers:

Any number greater than or equal to

Any number except

Any number greater than

Any number less than

Any number less than or equal to

Correct answer:

Any number greater than or equal to

Explanation:

Arrange the eight known values from least to greatest.

$\left \{ 24, 27, 34, 37, 50, 57,61, 63\right \}$

For to be the median of the nine elements, it muct be the fifth-greatest, This happens if $N \geq 50$ .

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Example Question #32 : Data Analysis

Consider the data set: $\left \{ 12, 15, 18, 20, 20, 21, 23, 26, N\right \}$

where is not known.

What are the possible values of the median of this set?

Possible Answers:

$18 \textrm{ or }20$

$18, 20,\textrm{ or }21$

$20\textrm{ or }21$

Correct answer:

Explanation:

The median of this nine-element set is its fifth-highest element. Of the eight known elements, the fourth-highest and fifth-highest elements are both 20. Regardless of the value of , 20 is the fifth-highest element of the nine.

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Example Question #12 : Median

Examine this stem-and-leaf display for a set of data:

$\left.\begin{matrix} 4\\ 5\\ 6\\ 7\\ 8 \end{matrix}\right|\begin{matrix} \textrm{7 9}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \;\\ \textrm{4 4 7 7}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \\ \textrm{0 1 2 2 4 5 5 8 8 9}\\ \textrm{3 5 5 8}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \\ \textrm{4 7}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \end{matrix}$

What is the median of this data set?

Possible Answers:

64.5

Correct answer:

64.5

Explanation:

The "stem" of this data set represents the tens digits of the data values; the "leaves" represent the units digits.

There are 22 elements, so the median is the arithmetic mean of the eleventh- and twelfth-highest elements, which are 64 and 65, the middle two "leaves". Their mean is $\left (64 + 65 \right )\div 2 = 64.5$ .

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Example Question #33 : Data Analysis

Determine the median of the following seven test scores:

88, 93, 79, 95, 80, 81, 93

Possible Answers:

Correct answer:

Explanation:

To determine the median of a set of numbers, you first need to order them from least to greatest:

79, 80, 81, 88, 93, 93, 95

Since there is an odd number of scores, the median is the score that falls exactly in the middle of the new list. Thus, the median is 88.

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Example Question #14 : Median

Determine the median of the following set of numbers:

55, 34, 27, 36, 44, 51

Possible Answers:

Correct answer:

Explanation:

To determine the median of a set of numbers, you first need to order them from least to greatest:

27, 34, 36, 44, 51, 55

Since there is an even amount of numbers, the median is determined by finding the average of the two numbers in the middle - 36 and 44.

$36+44 = 80 \div 2 = 40$

Thus, the median is 40.

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Example Question #34 : Data Analysis

Find the median of the following numbers:

2,7,14,4,3

Possible Answers:

Correct answer:

Explanation:

The median is the center number when the data points are listed in ascending or descending order. To find the median, reorder the values in numerical order:

2,3,4,7,14

In this problem, the middle number, or median, is the third number, which is

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #31 : Data Analysis

Example Question #1 : How To Find Median

Example Question #21 : Median

Example Question #31 : Data Analysis And Probability

Example Question #33 : Data Analysis And Probability

Example Question #32 : Data Analysis

Example Question #12 : Median

Example Question #33 : Data Analysis

Example Question #14 : Median

Example Question #34 : Data Analysis

All ISEE Upper Level Math Resources

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