Question

The total cost function for a factory is y = 10 + 3x where x = No. of units produced and y = total cost of producing x units. The range, the quartile deviation, the mean deviation and standard deviation of daily production of the factory are 50, 5, 8 and 10 units respectively. Find the range quartile deviation mean deviation and standard deviation for total cost y from it.

Answer 1

Here, x = No. of units of items produced y = Total production cost of x units y = 10 + 3x
For variable x: R = 50 units, Q_d = 5 units, MD = 8 units, s = 10 units

Measures of dispersion are independent of change of origin but they are changed by the change of scale.

y = 10 + 3x

Range of y = 3 (Range of x) = 3 × 50 = 150 units.

Quartile deviation of y = 3(Q_d of x) = 3 × 5 = 15 units.

Mean deviation of y = 3 (MD of x) = 3 × 8 = 24 units.

Standard deviation of y = 3(S of x) = 3 × 10 = 30 units.