# Assignment on Central Tendency and Dispersion

1. A manufacturer of hand shovels is deciding what length handles to use. Studies of user preference reveal that the average, the median, mean and mode of preferred length are all different. What are the implications of using each of these values? Which value would you decide?

2. A given machine is assumed to depreciate 40 percent in value in the first year, 25 percent in value in the 2nd year and 10 percent in value in the next three years; each percentage is being calculated on the diminishing value. What is the average percentage depreciation, reckoned on the diminishing value for the five years?

3. The mean age of a group of 100 persons was found to be 32.02.Later, it was discovered that age 57 was misread as 27. Find the corrected arithmetic mean.

4. Out of the total population of certain town in South Africa 60% belonged to the Black Race and the rest belonged to the white race. It was estimated that their mean incomes were 2000 and 5000 pounds respectively. Find the average income of the entire town?

5. The following data represents travel expenses (other than transport) for trips made during November by a salesman of a firm.

Trip Days Expense Expense per day

1 .5 13.50 27.00

2 2 12.00 6.00

3 3.5 17.50 5.00

4 1.0 9.00 9.00

5 9.0 27.00 3.00

6 .5 9.00 18.00

7 8.5 17.00 2.00

An auditor criticized these expenses as excessive asserting that the average expense per day is Rs10/- (Rs 70 divided by 7). The salesman replhed that the average is only Rs 4: 20 (Rs105 divided by 25) and that in any evejt the median is the appropriate measure and is only Rs3. The auditor rejoined...

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