This data represents the number of jumps in a row 10 students made during a jump-rope competition.

Question

30, 36, 38, 45, 57, 60, 77, 86, 88, 88

Question
What is the interquartile range? Enter the answer in the box.

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jumps

Answer 1

To calculate the interquartile range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3) of the given data set.

Here are the sorted jumps:

30, 36, 38, 45, 57, 60, 77, 86, 88, 88

Step 1: Find Q1 and Q3.

Since there are 10 data points, Q1 is the median of the first half of the data (the first 5 points), and Q3 is the median of the second half of the data (the last 5 points).

• First half (for Q1): 30, 36, 38, 45, 57
• Second half (for Q3): 60, 77, 86, 88, 88

Q1 Calculation: For the first half:

• The median (Q1) is the average of the middle two values (38 and 45).
• Q1 = (38 + 45) / 2 = 83 / 2 = 41.5

Q3 Calculation: For the second half:

• The median (Q3) is the average of the middle two values (77 and 86).
• Q3 = (77 + 86) / 2 = 163 / 2 = 81.5

Step 2: Calculate the IQR.

IQR = Q3 - Q1 IQR = 81.5 - 41.5 = 40

So, the interquartile range is 40 jumps.