Measures of location and spreadEdexcel A-Level Maths: Subtopic test

1. 1
   The delivery times, $x$ minutes, of 10 parcels have $\sum x=240$ and $\sum x^2=6100$.

   (a)

   What is the mean delivery time?

   [1 mark]

   • A240 minutes
   • B610 minutes
   • C34 minutes
   • D24 minutes

   (b)

   What is the value of $S_{xx}$?

   [1 mark]

   • A5760
   • B340
   • C34
   • D6100

   (c)

   Calculate the standard deviation of the delivery times.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A sample of 8 masses, $x$ grams, is coded using $y=\frac{x-400}{10}$. The coded data have $\sum y=24$ and $\sum y^2=130$.

   (a)

   What is the mean of the masses $x$?

   [1 mark]

   • A430 g
   • B3 g
   • C403 g
   • D424 g

   (b)

   What is the variance of the masses $x$?

   [1 mark]

   • A7.25 g$^2$
   • B72.5 g$^2$
   • C725 g$^2$
   • D26.9 g$^2$

   (c)

   A second sample is formed by adding 5 g to every mass in this sample. State the effect on (i) the mean and (ii) the standard deviation.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A clinic records the waiting times of 50 patients, in minutes: 4 patients waited from 0 up to 10, 12 from 10 up to 20, 20 from 20 up to 30 and 14 from 30 up to 50.

   (a)

   Estimate the mean waiting time.

   [3 marks]

   (b)

   Estimate the standard deviation of the waiting times.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student studies the daily mean air temperature, in $^\circ$C, for 31 days in July at one weather station: 3 days were from 12 up to 14, 7 from 14 up to 16, 9 from 16 up to 18, 8 from 18 up to 20 and 4 from 20 up to 24.

   (a)

   (i) Estimate the median temperature.
   (ii) Estimate the 10th to 90th interpercentile range.
   (iii) Give one reason for using the interpercentile range rather than the range to describe the spread.

   [6 marks]

   (b)

   (i) Estimate the mean and the standard deviation of the temperatures.
   (ii) The mean temperature for another July is $18.9^\circ$C with standard deviation $1.6^\circ$C. Compare the two Julys.

   [6 marks]

   Total for question 4: 12 marks

End of questions