Worksheet: Interquartile Range

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:

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

  • Arange: 16, interquartile range: 24
  • Brange: 24, interquartile range: 16
  • Crange: 93, interquartile range: 92
  • Drange: 93, interquartile range: 16
  • Erange: 24, 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 MemberMichaelNatalieMadisonJenniferJacobJamesJackson
Number of Artifacts54556510
  • ARange: 10, interquartile range: 1
  • BRange: 6, interquartile range: 6
  • CRange: 6, interquartile range: 1
  • DRange: 10, interquartile range: 6

Q6:

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

  • A26, 14, 21, 26, 23, 23 and 30, 23, 19, 15, 24, 14
  • B21, 22, 14, 25, 28, 29 and 28, 24, 19, 17, 15, 17
  • C8, 12, 13, 6, 5, 5 and 5, 13, 5, 8, 10, 10
  • D8, 10, 9, 11, 9, 11 and 6, 9, 7, 11, 9, 11

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 2004 to December 2004. Given that the table shows the published data, calculate the interquartile range.

MonthAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember
Index0.31.21.50.92.00.11.20.10.4

Q9:

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

LanguageGreekArmenianBengaliUrdu SpanishHindi KoreanHebrew
Number of Speakers304,900246,900800,000373,80037,580,000648,9001,410,000216,300
  • Arange =37,363,700, interquartile range =829,100
  • Brange =37,580,000, interquartile range =829,100
  • Crange =37,363,700, interquartile range =829,099
  • Drange =37,580,000, interquartile range =1,105,000
  • Erange =829,100, interquartile range =37,363,700

Q10:

Find the interquartile range of the data.

Score16141936171839
Frequency2353135

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, interquartilerange=0.5
  • BRange=3.5, interquartilerange=3.3
  • CRange=1.5, interquartilerange=0.5
  • DRange=1.5, interquartilerange=3.3
  • ERange=0.5, interquartilerange=1.5

Q12:

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

Time Spent Studying1–1011–2021–3031–4041–50
Frequency156121215

Q13:

Data Set 125222851262829
Data Set 221271926242328

Calculate the interquartile range for each data set.

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

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

  • AThe mode of the two data sets should be the same.
  • BThe median of the two data sets should be the same.
  • CThe difference between the minimum and maximum values is similar for both data sets.
  • DThe mean of the two data sets should be the same.
  • EThe spread of the middle 50% of the values is similar for both data sets.

Q14:

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

ChildChild 1Child 2Child 3Child 4Child 5Child 6Child 7Child 8
Savings in Dollars34.0030.1027.0021.9031.0046.3038.2043.80
  • Arange=$24.40, interquartile range=$41.00
  • Brange=$24.40, interquartile range=$12.45
  • Crange=$12.45, interquartile range=$24.40
  • Drange=$46.30, interquartile range=$41.00
  • Erange=$46.30, interquartile range=$12.45

Q15:

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

18.3717.8320.1618.76
24.6420.5723.7418.33
15.9823.3920.1117.93
  • Arange =8.66, interquartile range =3.85
  • Brange =24.64, interquartile range =21.98
  • Crange =8.66, interquartile range =2.85
  • Drange =3.85, interquartile range =8.66
  • Erange =24.64, interquartile range =3.85

Q16:

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

  • Ameasure of center
  • Bmeasure of variability
  • Cneither

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.

Q20:

Which measure is less sensitive to outliers in comparing the spread of the two data sets shown?

Data Set 12522285126282932
Data Set 22127192624232825
  • Arange
  • Binterquartile range

Q21:

What is the simplest and easiest dispersion measure?

  • ARange
  • BVariance
  • CInterquartile Range
  • DMean Absolute Deviation
  • EStandard Deviation

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