Question 1.EX.6: (a) Using the data in Exercise 1.5, calculate the average le...
(a) Using the data in Exercise 1.5, calculate the average level of profit over the time period and the average growth rate of profit over the period. Which appears more useful?
(b) Calculate the variance of profit and compare it to the variance of sales.
(a) The average profit is 35. The average rate of growth is calculated by comparing the end values 50 and 40, over the 10-year period. The ratio is 0.8. Taking the ninth root of this (nine years of growth) gives \sqrt[9]{0.8}= 0.926 so the annual rate of growth is 0.976 − 1 = −2.4%.
(b) The variances are (using the sample variance formula): for profits, Σ(x − μ)² = 4800 and dividing by 9 gives 533.3. For sales, the mean is 291 and Σ(x − μ)² = 4540.
The variance is therefore 4540/9 = 504.4. This is similar in absolute size to the variance of profits, but relative to the mean it is much smaller.