Assignment on Central Tendency and Dispersion

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 that the arithmetic mean is the a0propriate measure, but the median is Rs6.

1. Explain the proper interpretation of each of the four averages mentioned 2. Which average seems to you appropriate?

6. Twenty percent of workers in a firm employing a total of 2000 earn less than Rs 2 per min. 440 earn Rs. 2 to 2.24 per min.24% earn from Rs. 2.25 to 2.49 per hour. 370 earn from rs2.50 to 2.74 per min.12% earn rs2.75 to 2.99 per min. and the rest earn Rs. 3 or more per min. Set up a frequency distribution and set up a modal wage.

7. For a group of 100 weavers in a factory the median and quartile earnincs per day are Rs 88.6 and Rs.86 and Rs.91.8 respectively. The earnings for the group range between Rs 80 and Rs100. Ten % of the grkup earn under Rs.84 per day.13% earn Rs 9$ and 6% Rs 96 and over.
Put these data into a frequency distribution and obtain an estimate of the mean wage.

8. From the following data calculate the missing frequency.

Class interval 4- 8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40
Frequency 11 13 16 14 ?? 9 17 6 4

A.M is given to be 19.9

9. The following are the scores of two batsmen A and B in a series of innings:

A: 12 115 6 73 7 19 119 36 84 29

B: 47 12 76 42 4 51 37 48 13 0

Who is more consistent? Who is a better run getter?

10. An insurance agency as a marketing strategy decided to give old age fee discounts to people over 60 years of age
The scales of discounts are fixed as follows:
Age group 60 to 65……….Rs 2,500
Age group 65 to 70……….Rs 3000
Age group 70 to 75……….Rs 3500
Age group 75 to 80……….Rs 4000
Age group 80 to 85……….Rs 4500
The age of 25 people who secured the discount are given below.

74 62 84 72 61 83 72 81 65 71 63 61 60

67 74 66 64 79 73 75 76 69 68 78 61

Calculate the yearly average discount payable and the standard deviation.

11.A calculating machine while calculating mean and standard deviation of 25 readings misread one observation as 36 instead of 26. The following results were given by the machine. S.D = 5.0 Mean = 30. What are correct mean and S.D.

12. A collar manufacturer is considering the production of a new style of collar to attract young men. The following data of neck circumference are available based upon measurements of a typical group of college students:

Mid-value in inches No of students

12.5 04
13.0 19
13.5 30
14.0 63
14.5 66
15.0 29
15.5 18
16.0 01
16.5 01

What should be length of the largest and the smallest sizes of collars he should manufacture in order to meet the needs of practically all his customers, bearing in mind the collars are worn on average ¾ inches larger than the neck size.

Hint: Use M+ 3
13.For a certain group of wage- earners, the median and quartile wages per hour were Rs 44.3 , Rs 43, Rs 45.9 respectively. Wages for group ranged between Rs 40 and Rs 50. 10% of the group had under Rs 42 per hour, 13% had Rs 47 and over and 6% Rs 48 and over . Put the data into the from of a frequency distribution, and hence obtain an estimate of the mean wage and the standard deviation. Assume the group has 100 workers.