9709. S1. Measures of Spread

9709/51/M/J/25q3 – Mark Scheme

Last Sunday, teams of runners took part in a charity event. The time taken, in seconds, to run 50m was recorded, correct to 1 decimal place, for each runner. The times recorded for 11 runners from each of the Gulls and the Herons are shown in the table.

Gulls	7.9	8.2	8.3	8.6	8.6	8.8	9.2	9.7	9.8	10.0	10.4
Herons	9.5	9.9	8.5	8.1	9.2	10.8	8.3	9.7	9.3	9.9	8.7

(a) Draw a back-to-back stem-and-leaf diagram to represent this information, with Gulls on the left-hand side. [4 marks]

(b) Find the median and the interquartile range of the times of the runners from the Gulls. [3 marks]

Two other teams of runners, the Eagles and the Swifts, also took part in the event. The recorded times in seconds for 20 runners from the Eagles and 30 runners from the Swifts are denoted by x and y respectively.

It is given that $\Sigma x = 175.0$ and that the mean of y is 8.4.

It is given that $\Sigma x^2 = 1823.0$

It is also known that the standard deviation of the times taken by all 50 runners is 1.38 seconds.

(d) Find the value of $\Sigma y^2$ , correct to 1 decimal place. [3 marks]

9709/52/M/J/25q5 – Mark Scheme

The times taken, t minutes, by 300 students to travel to Hollowton College are recorded. The results are summarised in the table below.

(a) Draw a cumulative frequency graph to illustrate this information. [2 marks]

(b) 120 students take more than k minutes to travel to college. Use your graph to estimate the value of k. [2 marks]

(c) Calculate estimates of the mean and standard deviation of the times taken to travel to college by the 300 students. [6 marks]

9709/53/M/J/25q1 – Mark Scheme

For a set of 40 values of x, it is found that $\sum (x-k) = 836.0$ , $\sum (x-k)^2 = 25410.8$ , where k is a constant.

(a) Given that the mean of these 40 values is 124.0, find the value of k. [2 marks]

(b) Find the standard deviation of these 40 values of x. [2 marks]

9709/53/M/J/25q4 – Mark Scheme

84 people attempt a particular puzzle. The times taken, in minutes, to complete the puzzle are recorded. These times are represented in the cumulative frequency graph below.

(a) Use the graph to estimate how many people took between 4 and 7.5 minutes to complete the puzzle. [1 mark]

(b) Draw a box-and-whisker plot to summarise the information in the cumulative frequency graph. [4 marks]

Time (t minutes)	$t \leq 10$	$t \leq 20$	$t \leq 30$	$t \leq 40$	$t \leq 60$	$t \leq 90$
Cumulative frequency	34	86	142	208	265	300

9709. S1. Measures of Spread

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