Single-variable data: diagrams and histogramsEdexcel A-Level Maths: Subtopic test

1. 1
   The durations of phone calls made from an office are shown in a histogram. The bar for calls from 2 to 6 minutes has frequency density 7.5, the bar for calls from 6 to 10 minutes represents 18 calls, and the bar for calls from 10 to 20 minutes has frequency density 1.2.

   (a)

   How many calls lasted between 2 and 6 minutes?

   [1 mark]

   • A7.5
   • B15
   • C30
   • D1.875

   (b)

   What is the frequency density for the bar from 6 to 10 minutes?

   [1 mark]

   • A4.5
   • B18
   • C72
   • D2.25

   (c)

   Estimate the number of calls that lasted between 8 and 12 minutes.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The marks, out of 50, scored by 11 students in a test were 12, 15, 17, 18, 20, 21, 23, 25, 26, 28 and 45. For this data take the lower quartile to be the median of the lowest five marks and the upper quartile to be the median of the highest five marks. A value is an outlier if it is more than $1.5\times$IQR above the upper quartile or below the lower quartile.

   (a)

   What is the median mark?

   [1 mark]

   • A21
   • B20
   • C22.7
   • D23

   (b)

   What is the interquartile range?

   [1 mark]

   • A33
   • B26
   • C17
   • D9

   (c)

   Show that the mark of 45 is an outlier.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The heights of 100 plants are summarised as follows: 8 plants are under 10 cm, 30 are under 20 cm, 65 are under 30 cm, 90 are under 40 cm and all 100 are under 60 cm. Assume the heights are spread evenly within each class.

   (a)

   Use linear interpolation to estimate the median height of the plants.

   [3 marks]

   (b)

   Estimate (i) the number of plants taller than 36 cm and (ii) the interquartile range of the heights.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A farmer records the masses of 200 eggs, in grams: 10 eggs have mass from 40 up to 50, 30 from 50 up to 55, 60 from 55 up to 60, 70 from 60 up to 65 and 30 from 65 up to 75.

   (a)

   (i) Find the frequency density of each class.
   (ii) Estimate the number of eggs with mass between 52 g and 62 g.
   (iii) State an assumption made in (ii).

   [6 marks]

   (b)

   The farmer redraws the histogram so that the total area of the bars is 1.
   (i) Find the height of the bar for the class 60 up to 65.
   (ii) Explain what the area of the bar for the class 55 up to 60 represents, and find its value.
   (iii) Use the histogram to estimate the probability that a randomly chosen egg has mass of 65 g or more.

   [6 marks]

   Total for question 4: 12 marks

End of questions