# Lesson Worksheet: Measuring Dispersion Mathematics

In this worksheet, we will practice finding the measures of dispersion of a data set such as upper quartile, lower quartile, and interquartile range.

Q1:

Find all the outliers, if there are any, in the following set of data: 31.9, 44.2, 31.3, 48.7, 23.4, 35.5, 34.5, 26.5, 41.6, 9.5, 60.2, 52.9, 46.1, 41.8, 51.3.

• A9.5, 60.2
• B60.2
• C9.5
• D31.3
• Eno outliers

Q2:

The number of Bonus Bugs won by each of 15 students in the first level of a computer game tournament was recorded. The results are in the table below.

Find the median (Q2) and the lower and upper quartiles (Q1 and Q3) for the number of Bonus Bugs won.

• AMedian = 22, Q1 = 29, Q3 = 17
• BMedian = 15, Q1 = 17, Q3 = 31
• CMedian = 15, Q1 = 22, Q3 = 29
• DMedian = 21, Q1 = 18, Q3 = 31
• EMedian = 22, Q1 = 17, Q3 = 29

If the organizers of the tournament decide that the top ‎ of students can compete in Level 2, above what number of Bonus Bugs must a student win to go to the next level?

• A15 or above
• B29 or above
• C31 or above
• D17 or above
• E22 or above

Q3:

Khalid’s history test scores are 74, 96, 85, 90, 71, and 98. Determine the upper and lower quartiles of his scores.

• Alower quartile = 74, upper quartile = 96
• Blower quartile = 87.5, upper quartile = 96
• Clower quartile = 74, upper quartile = 87.5
• Dlower quartile = 71, upper quartile = 98
• Elower quartile = 96, upper quartile = 74

Q4:

Determine the outlier of the following data: 16, 16, 15, 18, 15, 15, 56.

Q5:

Determine the upper and the lower quartiles of the following set of data: 19.4, 42.1, 56.1, 27.5, 5.3, 49.9, 48.8, 44.3, 13.1, 15.4, 20.1, 4.1, 38.1, 33.8, and 41.5.

• Alower quartile = 4.1, upper quartile = 44.3
• Blower quartile = 33.8, upper quartile = 44.3
• Clower quartile = 4.1, upper quartile = 33.8
• Dlower quartile = 15.4, upper quartile = 33.8
• Elower quartile = 15.4, upper quartile = 44.3

Q6:

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 , interquartile range
• Brange , interquartile range
• Crange , interquartile range
• Drange , interquartile range
• Erange , interquartile range

Q7:

Determine the median and quartiles of the following set of data: 56, 55, 90, 50, 41, 84, 68, 75, 92, 50, and 71.

• AThe median is 68, and the quartiles are 52.5 and 79.5.
• BThe median is 69.5, and the quartiles are 50 and 84.
• CThe median is 68, and the quartiles are 50 and 84.
• DThe median is 71, and the quartiles are 55 and 90.

Q8:

Determine the median and quartiles of the following set of data: 1.8, 1.6, 1.1, 2.4, 0.6, 1.3, 2.9, 1.5, 0.4, 1.9, 2.9.

• AThe median is 1.6, and the quartiles are 1.3 and 2.9.
• BThe median is 1.6, and the quartiles are 1.1 and 2.4.
• CThe median is 1.8, and the quartiles are 1.1 and 2.4.
• DThe median is 1.6, and the quartiles are 0.6 and 1.9.

Q9:

A group of fourteen students were asked to log the number of friends they each had on the new social media site “Nosebook,” one month after joining the site, with the following results.

Find the median number of friends.

Find the quartiles Q1 and Q3 of the data.

• AQ1 = 68, Q3 = 70
• BQ1 = 53, Q3 = 82
• CQ1 = 71, Q3 = 68
• DQ1 = 50, Q3 = 89
• EQ1 = 32, Q3 = 95

Q10:

Hassan’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