(brainiest)A data set is made up of these values. 1, 4, 5, 6, 6, 9, 11
Find the interquartile range.
A. 4 – 1 = 3

B. 11 – 9 = 2

C. 11 – 1 = 10

D. 9 – 4 = 5

Step-by-step explanation:

What is an Interquartile Range?

The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie. That’s why it’s preferred over many other measures of spread when reporting things like school performance or SAT scores.

The interquartile range formula is the first quartile subtracted from the third quartile:

IQR = Q3 – Q1.

Steps:

Step 1: Put the numbers in order.

1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.

Step 2: Find the median.

1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.

Step 3: Place parentheses around the numbers above and below the median.

Not necessary statistically, but it makes Q1 and Q3 easier to spot.

(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).

Step 4: Find Q1 and Q3

Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.

(1, 2, 5, 6, 7),  9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.

Step 5: Subtract Q1 from Q3 to find the interquartile range.

18 – 5 = 13.

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step explanations, just like this one!

What if I Have an Even Set of Numbers?

Example question: Find the IQR for the following data set: 3, 5, 7, 8, 9, 11, 15, 16, 20, 21.

Step 1: Put the numbers in order.

3, 5, 7, 8, 9, 11, 15, 16, 20, 21.

Step 2: Make a mark in the center of the data:

3, 5, 7, 8, 9, | 11, 15, 16, 20, 21.

Step 3: Place parentheses around the numbers above and below the mark you made in Step 2–it makes Q1 and Q3 easier to spot.

(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21).

Step 4: Find Q1 and Q3

Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data.

(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.

Step 5: Subtract Q1 from Q3.

16 – 7 = 9.

This is your IQR.

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