Histograms, stem and leaf diagrams and box plotsEdexcel International A Level Maths: Subtopic test

1. 1
   The lengths of 60 phone calls are grouped as follows: 12 calls lasted from 0 to 2 minutes, 21 calls from 2 to 5 minutes, 15 calls from 5 to 10 minutes, and 12 calls from 10 to 20 minutes. A histogram is drawn with frequency density on the vertical axis.

   (a)

   Find the frequency density of the class 5 to 10 minutes.

   [1 mark]

   • A$15$
   • B$75$
   • C$0.33$
   • D$3$

   (b)

   Estimate the number of calls that lasted between 5 and 8 minutes.

   [1 mark]

   • A$15$
   • B$9$
   • C$7.5$
   • D$3$

   (c)

   In the histogram, the bar for the class 2 to 5 minutes is 3.5 cm tall. Find the height of the bar for the class 10 to 20 minutes.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The scores of 15 players in a game are 23, 27, 31, 34, 34, 38, 41, 42, 45, 47, 52, 53, 58, 61 and 66. They are shown in an ordered stem and leaf diagram.

   (a)

   Find the median score.

   [1 mark]

   • A$42$
   • B$41$
   • C$45$
   • D$8$

   (b)

   Find the interquartile range of the scores.

   [1 mark]

   • A$22$
   • B$21$
   • C$19$
   • D$43$

   (c)

   Describe the skewness of the distribution, justifying your answer using the quartiles.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The times, in seconds, taken by 12 boys and 12 girls to complete an obstacle course are shown in a back-to-back stem and leaf diagram. The boys' times are 41, 43, 45, 47, 48, 52, 54, 55, 58, 61, 63 and 69. The girls' times are 38, 40, 42, 44, 45, 46, 49, 51, 53, 55, 57 and 62.

   (a)

   Find the median and the interquartile range of the girls' times.

   [3 marks]

   (b)

   Compare the times of the boys and the girls.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two classes, $X$ and $Y$, sat the same test, and their marks are compared using box plots drawn on the same scale. Class $X$ has 40 students and the five-number summary of its marks is: minimum 12, lower quartile 31, median 45, upper quartile 56, maximum 70. For class $Y$ the summary is: minimum 22, lower quartile 40, median 47, upper quartile 54, maximum 63.

   (a)

   (i) Find the range and the interquartile range of the marks for class $X$.
   (ii) Describe the skewness of the marks for class $X$, giving evidence.
   (iii) Estimate the number of students in class $X$ who scored at least 56 marks.

   [6 marks]

   (b)

   Compare the marks of the two classes and decide which class performed better, justifying your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions