Replacing data values

Questions where one or more data values are removed and simultaneously replaced with different values, requiring calculation of the effect on mean and/or standard deviation.

2 questions · Standard +0.0

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OCR MEI AS Paper 2 2018 June Q7
8 marks Moderate -0.8
Rose and Emma each wear a device that records the number of steps they take in a day. All the results for a 7-day period are given in Fig. 7.
Day1234567
Rose10014112621014993619708992110369
Emma9204991387411001510261739110856
Fig. 7 The 7-day mean is the mean number of steps taken in the last 7 days. The 7-day mean for Rose is 10112.
  1. Calculate the 7-day mean for Emma. [1]
At the end of day 8 a new 7-day mean is calculated by including the number of steps taken on day 8 and omitting the number of steps taken on day 1. On day 8 Rose takes 10259 steps.
  1. Determine the number of steps Emma must take on day 8 so that her 7-day mean at the end of day 8 is the same as for Rose. [4]
In fact, over a long period of time, the mean of the number of steps per day that Emma takes is 10341 and the standard deviation is 948.
  1. Determine whether the number of steps Emma needs to take on day 8 so that her 7-day mean is the same as that for Rose in part (ii) is unusually high. [3]
OCR MEI Paper 2 Specimen Q8
3 marks Standard +0.8
Alison selects 10 of her male friends. For each one she measures the distance between his eyes. The distances, measured in mm, are as follows: 51 57 58 59 61 64 64 65 67 68 The mean of these data is 61.4. The sample standard deviation is 5.232, correct to 3 decimal places. One of the friends decides he does not want his measurement to be used. Alison replaces his measurement with the measurement from another male friend. This increases the mean to 62.0 and reduces the standard deviation. Give a possible value for the measurement which has been removed and find the measurement which has replaced it. [3]