Worksheet: Interquartile Range

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In this worksheet, we will practice finding the interquartile range.

Q1:

Using the given box-and-whisker plot, find the interquartile range of the data.

Q2:

Find the interquartile range of this set of data: 29.7, 36.2, 29.1, 11.7, 45.3, 19.6, 42.8, 57.9, 51.9, 42.9, 51.2, 5.4, 29.2, 15.4, and 11.6.

Q3:

Find the interquartile range of this set of data: 96, 52, 87, 114, 76, 101, 76, 114, 99, 96, 88, 111, 88, 94, 53.

Q4:

Nader’s maths test scores are 90, 92, 69, 76, 93, and 84. Find the range and interquartile range of his scores.

  • Arange: 93, interquartile range: 16
  • Brange: 16, interquartile range: 24
  • Crange: 24, interquartile range: 92
  • Drange: 24, interquartile range: 16
  • Erange: 93, interquartile range: 92

Q5:

The table shows the number of artifacts found by each member of an expedition during an excavation at a historical site. Find the range and the interquartile range of the data.

Expedition Member Sameh Yasmine Samar Sally Bassem Adam Nabil
Number of Artifacts 5 4 5 5 6 5 10
  • Arange: 6, interquartile range: 6
  • Brange: 10, interquartile range: 1
  • Crange: 10, interquartile range: 6
  • Drange: 6, interquartile range: 1

Q6:

Which two sets of data have the same range but different interquartile ranges?

  • A8, 10, 9, 11, 9, 11 and 6, 9, 7, 11, 9, 11
  • B21, 22, 14, 25, 28, 29 and 28, 24, 19, 17, 15, 17
  • C26, 14, 21, 26, 23, 23 and 30, 23, 19, 15, 24, 14
  • D8, 12, 13, 6, 5, 5 and 5, 13, 5, 8, 10, 10

Q7:

A set of data’s minimum is 1.71, its lower quartile is 2.05, its median is 6.86, its upper quartile is 7.99, and its maximum is 14.16. Determine its interquartile range.

Q8:

The Bureau of Labor Statistics published the over-the-month percent change in the price index for imports from April 2,004 to December 2,004. Given that the table shows the published data, calculate the interquartile range.

Month April May June July August September October November December
Index − 0 . 3 − 1 . 2 − 1 . 5 0.9 2.0 − 0 . 1 1.2 − 0 . 1 0.4

Q9:

The table shows some non-English languages spoken by some of the US population. Determine the range and interquartile range of the data.

Language Greek Armenian Bengali Urdu Spanish Hindi Korean Hebrew
Number of Speakers 304,900 246,900 800,000 373,800 37,580,000 648,900 1,410,000 216,300
  • Arange = 8 2 9 , 1 0 0 , interquartile range = 3 7 , 3 6 3 , 7 0 0
  • Brange = 3 7 , 5 8 0 , 0 0 0 , interquartile range = 8 2 9 , 1 0 0
  • Crange = 3 7 , 3 6 3 , 7 0 0 , interquartile range = 8 2 9 , 0 9 9
  • Drange = 3 7 , 3 6 3 , 7 0 0 , interquartile range = 8 2 9 , 1 0 0
  • Erange = 3 7 , 5 8 0 , 0 0 0 , interquartile range = 1 , 1 0 5 , 0 0 0

Q10:

Find the interquartile range of the data.

Score 16 14 19 36 17 18 39
Frequency 2 3 5 3 1 3 5

Q11:

The given line plot shows the magnitudes of earthquakes that recently took place around the world. Determine the range and interquartile range of the data.

  • Arange = 3.5, interquartile range = 0.5
  • Brange = 0.5, interquartile range = 1.5
  • Crange = 1.5, interquartile range = 3.3
  • Drange = 1.5, interquartile range = 0.5
  • Erange = 3.5, interquartile range = 3.3

Q12:

Find the interquartile range of the grouped data in the table.

Time Spent Studying 1–10 11–20 21–30 31–40 41–50
Frequency 15 6 12 12 15

Q13:

Data Set 1 25 22 28 51 26 28 29
Data Set 2 21 27 19 26 24 23 28

Calculate the interquartile range for each data set.

  • Adata set 1: 4, data set 2: 7
  • Bdata set 1: 5, data set 2: 6
  • Cdata set 1: 5, data set 2: 7
  • Ddata set 1: 4, data set 2: 6
  • Edata set 1: 6, data set 2: 4

What do the interquartile ranges reveal about the two data sets?

  • AThe spread of the middle 5 0 % of the values is similar for both data sets.
  • BThe mean of the two data sets should be the same.
  • CThe median of the two data sets should be the same.
  • DThe difference between the minimum and maximum values is similar for both data sets.
  • EThe mode of the two data sets should be the same.

Q14:

The table shows the savings of a group of 8 children. Determine the range and interquartile range of the data.

Child Child 1 Child 2 Child 3 Child 4 Child 5 Child 6 Child 7 Child 8
Savings in Dollars 34.00 30.10 27.00 21.90 31.00 46.30 38.20 43.80
  • Arange=$46.30, interquartile range=$12.45
  • Brange=$12.45, interquartile range=$24.40
  • Crange=$24.40, interquartile range=$41.00
  • Drange=$24.40, interquartile range=$12.45
  • Erange=$46.30, interquartile range=$41.00

Q15:

Shown are the monthly subscription fees (in dollars) for various science magazines. Determine the range and the interquartile range for this data.

18.37 17.83 20.16 18.76
24.64 20.57 23.74 18.33
15.98 23.39 20.11 17.93
  • Arange = 3 . 8 5 , interquartile range = 8 . 6 6
  • Brange = 2 4 . 6 4 , interquartile range = 3 . 8 5
  • Crange = 8 . 6 6 , interquartile range = 2 . 8 5
  • Drange = 8 . 6 6 , interquartile range = 3 . 8 5
  • Erange = 2 4 . 6 4 , interquartile range = 2 1 . 9 8

Q16:

Is the interquartile range an example of a measure of center or a measure of variability?

  • Aneither
  • Bmeasure of center
  • Cmeasure of variability

Q17:

Using the given box-and-whisker plot, find the interquartile range of the data.

Q18:

Using the given box-and-whisker plot, find the interquartile range of the data.

Q19:

Using the given box-and-whisker plot, find the interquartile range of the data.

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