Question

Find the quartiles for these data values:

5,7,7,8,10,11,12,15,17
A. Q1=7, Q2=11, Q3=15
B. Q1=7, Q2=10, Q3=13.5
C. Q1=6, Q2=9, Q3=12
D. Q1=7.5, Q2=10.5, Q3=13.5

Answer 1

B. Q1=7, Q2=10, Q3=13.5

Step-by-step explanation:

First Solution:

The first quartile of the data set is 7.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

5 7 7 8 10 11 12 15 17

So, the bottom half is

5 7 7 8

The median of these numbers is 7.

Second Solution:

The median of the data set is 10.

Quartile 2, also known as the median, is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

5 7 7 8 10 11 12 15 17

So, the median is 10 .

Third Solution:

The third quartile of the data set is 13.5.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

5 7 7 8 10 11 12 15 17

So, the upper half is

11 12 15 17

The median of these numbers is 13.5.

Answer 2

Answer: Choice B

Q1 = 7, Q2 = 10, Q3 = 13.5

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Step-by-step explanation:

Start with {5,7,7,8,10,11,12,15,17}

Notice how this data set is already sorted for us from smallest to largest.

Cross off the first and last items to get {7,7,8,10,11,12,15}

Repeat the last step to get this smaller set {7,8,10,11,12}

Repeat again: {8,10,11}

Repeat one more time: {10}

The 10 is at the very center, so it is the median aka the value of Q2.

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An alternative way to get the median is to follow these steps:

There are n = 9 numbers in the original set before we crossed off any items. The middle number is in slot 5 because n/2 = 9/2 = 4.5 rounds up to 5. The value in the fifth slot is 10, so 10 is the median.

There are 4 items below the median and 4 items above it, giving n = 4+1+4 = 9 items total.

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Next, break the data set into two smaller groups

L = lower set = every value below the median

L = {5, 7, 7, 8}

U = upper set = every value above the median

U = {11, 12, 15, 17}

The median itself is in neither set L nor set U.

The median of set L is (7+7)/2 = 7, so this is the value of Q1

The median of set U is (12+15)/2 = 13.5 which is the value of Q3

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Summary:

Q1 = 7

Q2 = 10 (aka the median of the original set)

Q3 = 13.5