# Statistics Long Questions (Question 3 & 4)

Question 3:
The mean of the data 1, a, 2a, 8, 9 and 15 which has been arranged in ascending order is b. If each number of the data is subtracted by 3, the new median is $\frac{4}{7}b$ . Find
(a) The values of a and b,
(b) The variance of the new data.

Solution:
(a)

(b)
New data is (1 – 3), (3 – 3), (6 – 3), (8 – 3), (9 – 3), (15 – 3)
New data is  – 2, 0, 3, 5, 6, 12

Question 4:
A set of data consists of 20 numbers. The mean of the numbers is 8 and the standard deviation is 3.
(a) Calculate  $\sum x$ and $\sum {x}^{2}$ .
(b) A sum of certain numbers is 72 with mean of 9 and the sum of the squares of these
numbers of 800, is taken out from the set of 20 numbers. Calculate the mean and
variance of the remaining numbers.

Solution:
(a)

(b)