A test, in which the marks obtainable range from 0 to 100 inclusive, was taken by 30 students who had been trained in such tests, and by 20 other students who had not. A summary of the results is given in Table Q1 below.

30 trained students

mean: 62

stand dev: 10

20 untrained students

mean: 52

stand dev: 12

Table Q1

(a)Calculate the mean and standard deviation of the combined set of 50 scores. Give your answers to two decimal places.

[Hint: you may use the result:variance,

(10 marks)

(b)One of the students was ill but took the test and scored only 1 mark. It was decided to exclude this result from the analysis.

(i)Calculate the mean and standard deviation of the remaining 49 scores. Give your answers to two decimal places.

(6 marks)

(ii)Briefly explain what would be the changes in the mode and median when compared to those of the full set of 50 scores.