Question

Compare each pair of distributions to decide which one has the greater mean and the greater standard deviation. You do not need to calculate the actual values of µ and σ, just how they compare with each other.

(a) i. 3, 5, 5, 5, 8, 11, 11, 11, 13.

ii. 3, 5, 5, 5, 8, 11, 11, 11, 20

(b) i. 0, 2, 4, 6, 8, 10.

ii. 20, 22, 24, 26, 28, 30.

Answer 1

(A) Here data set (ii) has almost same data values except the last data value, i.e. 20 instead of 13 in data set (i). So, all values remains same, but the last value is larger for data set (ii), which will provide us with greater mean and greater standard deviation for data set (ii)

(B) data set (i) has smaller values as compared to data set (ii), this shows that the mean will be smaller in data set (i) as compared to data set (ii). Difference between data values is exactly 2 in both data sets, this means that the standard deviation will be exactly same in both data sets.

So, data set (ii) has greater mean and standard deviation is same for both data sets.