Box Plots - Question + Revision (1), Exercises of Mathematics

Box Plots - Question + Revision

Typology: Exercises

2023/2024

Uploaded on 01/06/2026

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Box Plots - 1
Question 1
A group of students recorded the number of hours they studied in a week. The
data is as follows:
2, 3, 5, 5, 7, 8, 10, 10, 12, 15
a) Construct a box plot for this data.
b) Identify the median, lower quartile, upper quartile, minimum, and maximum
values from the box plot.
Question 2
The following data represents the scores of 15 students in a maths test:
15, 18, 20, 22, 22, 25, 27, 28, 30, 30, 32, 35, 37, 38, 40
a) Draw a box plot to represent the data.
b) Determine the range and interquartile range of the data.
Question 3
The ages of people attending a concert are recorded below:
16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30
a) Create a box plot for this data.
b) Calculate the median, lower quartile, and upper quartile.
Question 4
The heights (in cm) of 12 basketball players are listed below:
180, 182, 185, 188, 190, 192, 195, 198, 200, 202, 205, 208
a) Construct a box plot for this data.
b) Find the range and interquartile range of the heights.
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Box Plots - 1 Question 1 A group of students recorded the number of hours they studied in a week. The data is as follows: 2, 3, 5, 5, 7, 8, 10, 10, 12, 15 a) Construct a box plot for this data. b) Identify the median, lower quartile, upper quartile, minimum, and maximum values from the box plot. Question 2 The following data represents the scores of 15 students in a maths test: 15, 18, 20, 22, 22, 25, 27, 28, 30, 30, 32, 35, 37, 38, 40 a) Draw a box plot to represent the data. b) Determine the range and interquartile range of the data. Question 3 The ages of people attending a concert are recorded below: 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30 a) Create a box plot for this data. b) Calculate the median, lower quartile, and upper quartile. Question 4 The heights (in cm) of 12 basketball players are listed below: 180, 182, 185, 188, 190, 192, 195, 198, 200, 202, 205, 208 a) Construct a box plot for this data. b) Find the range and interquartile range of the heights.

Answers Question 1 To construct a box plot and identify the median, lower quartile, upper quartile, minimum, and maximum values, we'll follow these steps:

  1. Arrange the data in ascending order: Already done: 2, 3, 5, 5, 7, 8, 10, 10, 12, 15
  2. Identify the minimum and maximum values: o Minimum: 2 o Maximum: 15
  3. Calculate the median (Q2): o The median is the middle value of the data set. For an even number of data points, it's the average of the two middle values. o Median (Q2) = (7 + 8) / 2 = 7.
  4. Calculate the lower quartile (Q1): o The lower quartile is the median of the first half of the data. o Lower half: 2, 3, 5, 5, 7 o Lower quartile (Q1) = 5
  5. Calculate the upper quartile (Q3): o The upper quartile is the median of the second half of the data. o Upper half: 8, 10, 10, 12, 15 o Upper quartile (Q3) = 10 Here's a compact summary of the values:  Minimum: 2  Lower Quartile (Q1): 5  Median (Q2): 7.  Upper Quartile (Q3): 10  Maximum: 15

Upper Quartile (Q3): 35  Maximum: 40 Here's a visual representation of the box plot: Part (b): Determining the Range and Interquartile Range

  1. Range: o Range = Maximum - Minimum o Range = 40 - 15 = 25
  2. Interquartile Range (IQR): o IQR = Q3 - Q o IQR = 35 - 22 = 13 Summary:Range: 25  Interquartile Range (IQR): 13 Question 3 Part (a): Constructing the Box Plot
  3. Arrange the data in ascending order: o Already done: 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30
  4. Identify the minimum and maximum values: o Minimum: 16 o Maximum: 30
  5. Calculate the median (Q2): o Median (Q2) = Middle value (average of the 9th and 10th values, since there are 18 values)

o Median (Q2) = (22 + 23) / 2 = 22.

  1. Calculate the lower quartile (Q1): o Lower half: 16, 17, 17, 18, 19, 20, 21, 22, 22 o Lower quartile (Q1) = Median of the lower half = 19 (average of the 4th and 5th values) o Lower quartile (Q1) = (18 + 19) / 2 = 18.
  2. Calculate the upper quartile (Q3): o Upper half: 23, 24, 25, 25, 26, 27, 28, 29, 30 o Upper quartile (Q3) = Median of the upper half = 26 (average of the 13th and 14th values) o Upper quartile (Q3) = (25 + 26) / 2 = 25. Summary of ValuesMinimum: 16  Lower Quartile (Q1): 18.  Median (Q2): 22.  Upper Quartile (Q3): 25.  Maximum: 30 Here's a visual representation of the box plot: Part (b): Calculating the Median, Lower Quartile, and Upper Quartile
  3. Median (Q2): 22.
  4. Lower Quartile (Q1): 18.
  5. Upper Quartile (Q3): 25. Question 4 Part (a): Constructing the Box Plot

o Range = 208 - 180 = 28

  1. Interquartile Range (IQR): o IQR = Q3 - Q o IQR = 200 - 185 = 15 Summary:Range: 28  Interquartile Range (IQR): 15