The number of women in senior management positions at a number of companies was investigated. The number of women at each of the 25 service companies and at each of the 16 industrial companies are denoted by w_S and w_I, respectively. The findings are summarised by the totals:

Σ(w_s – 5)² = 28, Σ(w_s – 5) = 15, Σ(w_l – 3)² = 12 and Σ(w_l – 3) = -4

a. Show that there are, on average, more than twice as many women in senior management positions at the service companies than at the industrial companies.

b. Show that Σw²_s ≠ (Σw_s)² and that Σw²_l ≠ (Σw_l)².

c. Find the standard deviation of the number of women in senior management positions at all of these service and industrial companies together.