# Lesson Worksheet: Box-and-Whisker Plots Mathematics • 6th Grade

In this worksheet, we will practice constructing and analyzing data from box-and-whisker plots.

Q1:

Noah has calculated the following information from a data set about the ages of swimmers on a Saturday morning in a swimming pool:

• Lowest value: 7
• Lower quartile: 10
• Median: 15
• Upper quartile: 22
• Highest value: 31

Draw a box-and-whisker plot using the information Noah has calculated from the data set.

• A • B • C • D • E

What is the overall age range of the Saturday morning swimmers?

What percentage of Saturday morning swimmers were between 7 and 22 years old?

• A
• B
• C
• D
• E

Calculate and interpret the percentage of Saturday morning swimmers covered by the box.

• A‎ of the Saturday morning swimmers were between 10 and 22 years old.
• B‎ of the Saturday morning swimmers were between 10 and 22 years old.
• C‎ of the Saturday morning swimmers were between 10 and 22 years old.
• D‎ of the Saturday morning swimmers were between 10 and 22 years old.

Q2:

A middle school surveyed the heights (in centimeters) of 100 students and summarized the results in the following table.

Lowest ValueLower QuartileMedianUpper QuartileHighest Value
120145157165200

Which of the following box-and-whisker plots could represent this data set?

• A • B • C • D • E Q3:

Liam has calculated the following information from a data set about the ages of people present on a Saturday morning in a swimming pool:

lowest value: 7

lower quartile: 10

median: 15

upper quartile: 22

highest value: 31

Liam draws a box plot from the data. Which of the following box plots did Liam draw?

• A • B • C • D • E Q4:

The box plot shows the daily temperatures at a seaside resort during the month of August. On roughly what percentage of days was the temperature between and ?

On roughly what percentage of days was the temperature greater than ?

What was the median temperature?

What was the maximum temperature recorded?

What was the minimum temperature recorded?

What was the lower quartile of the temperatures?

What was the upper quartile of the temperatures?

What was the interquartile range of the temperatures?

What was the range of the temperatures?

Q5:

An international meteorological society has collected data on the highest temperatures, in degrees Celsius, in the year 2020 from 20 different cities around the world. This data is given below.

 11 20 22 24 25 26 26 28 29 30 31 33 33 34 37 38 38 38 40 56

Calculate , , and .

• A11, 30.5, 40
• B25, 30, 37
• C11, 30.5, 56
• D26, 31, 38
• E25.5, 30.5, 37.5

Use the 1.5 IQR rule to identify outliers.

• AThere are more than two outliers.
• BThere are no outliers.
• C56 only
• D11 and 56
• E11 only

Which of the following box-and-whisker plots represents this data?

• A • B • C • D • E Q6:

Which of the following sets of data can be represented by this box-and-whisker plot? • A17, 20, 18, 19, 20, 16, 16
• B16, 14, 27, 20, 22, 17, 16
• C19, 19, 17, 14, 22, 20, 21
• D17, 16, 18, 14, 20, 19, 22
• E18, 19, 14, 19, 16, 22, 17

Q7:

Chloe counted the number of cars that were parked on her road at 8:00 pm on 11 successive days. She presented her data as a list: 3, 8, 12, 6, 5, 6, 7, 9, 4, 10, 8.

She was surprised to find that the minimum number of cars that she counted was 3 and that the maximum number of cars was 12.

Calculate the median number of cars.

Calculate the lower quartile for the number of cars.

Calculate the upper quartile for the number of cars.

Chloe draws a box plot of the data. Which of the following is correct?

• A • B • C • D • E Q8:

Matthew and Benjamin are two of the best basketball players in the same amateur league. Their points from every game of this season are summarized into the following box-and-whisker plots. Based on these box plots, which player would a recruiter from the professional league favor? Explain your answer.

• AThey would favor Matthew because Matthew has scored more points than Benjamin on average.
• BThey would favor Matthew because the median points for both players are the same but Matthew’s performance is more consistent.
• CThey would favor Benjamin because Benjamin has scored more points than Matthew on average.
• DThey would favor Benjamin because the median points for both players are the same but Benjamin’s performance is more consistent.

Q9:

A middle school surveyed the heights (in centimeters) of its female and male students and summarized the data in the box-and-whisker plots below. Which of the following is a correct statement regarding the center and spread of the data sets based on these plots?

• AThe median height of female students is smaller than that of male students, and the IQR for both male and female students is the same.
• BThe median height of female students is smaller than that of male students, and the IQR for female students is larger than that for male students.
• CThe median height of female students is smaller than that of male students, and the IQR for male students is larger than that for female students.
• DThe median heights for both male and female students are the same, and the IQR for both male and female students is the same.

Which of the following is a correct statement regarding the maximum and minimum heights?

• AThe maximum and the minimum heights are the same for both male and female students.
• BThe height of the tallest male student is greater than that of the tallest female student.
• CThe height of the shortest female student is smaller than that of the shortest male student.
• DAll male students are always taller than all female students.

Q10:

The box plots represent household income data collected from neighborhoods A and B. The unit is one thousand British pounds. Which of the following is a correct statement regarding the comparison of these box plots?

• AThe minimum household income of neighborhood B is less than that of neighborhood A.
• BThe highest household income in neighborhood B is greater than that in neighborhood A.
• CAll households in neighborhood A have greater incomes than those in neighborhood B.
• DThe center of household income in neighborhood A is greater than that in neighborhood B.
• EThe spread of household income of neighborhood A is less than that of neighborhood B.

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