Page 132 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

8. The mean age of a combined group of men and women is 30 years. If the mean age of the Notes
men’s group is 32 years and that for the women’s group is 27 years, find the percentage of
men and women in the combined group.
9. Locate median of the following data:
65, 85, 55, 75, 96, 76, 65, 60, 40, 85, 80, 125, 115, 40

10. In a class of 16 students, the following are the marks obtained by them in statistics. Find
out the lower quartile, upper quartile, seventh decile and thirty fifth percentile.

S. No. : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Marks : 5 12 17 23 28 31 37 41 42 49 54 58 65 68 17 77
11. Find out median from the following:
No. of Workers : 1- 5 6 -10 11-15 16 - 20 21- 25
No. of factories : 3 8 13 11 5

12. Find median from the following distribution:
X : 1 2 3 4 5 - 9 10 -14 15 -19 20 - 25
f : 5 10 16 20 30 15 8 6
13. Determine the mode of the following data:

58, 60, 31, 62, 48, 37, 78, 43, 65, 48
14. Find geometric mean from the following daily income (in ) of 10 families:

85, 70, 15, 75, 500, 8, 45, 250, 40 and 36.
15. Calculate geometric mean of the following distribution:
Marks (less than) : 10 20 30 40 50
No. of Students : 12 27 72 93 100
16. The value of a machine depreciates at a constant rate from the cost price of 1,000 to the
scrap value of 100 in ten years. Find the annual rate of depreciation and the value of the
machine at the end of one, two, three years.
17. The price of a commodity increased by 12% in 1986, by 30% in 1987 and by 15% in 1988.
Calculate the average increase of price per year.
18. The population of a city was 30 lakh in 1981 which increased to 45 lakh in 1991. Determine
the rate of growth of population per annum. If the same growth continues, what will be
the population of the city in 1995.
19. The value of a machine depreciated by 30% in 1st year, 13% in 2nd year and by 5% in each
of the following three years. Determine the average rate of depreciation for the entire
period.
20. The geometric means of three groups consisting of 15, 20 and 23 observations are 14.5, 30.2
and 28.8 respectively. Find geometric mean of the combined group.

21. A sum of money was invested for 3 years. The rates of interest in the first, second and third
year were 10%, 12% and 14% respectively. Determine the average rate of interest per
annum.
22. The weighted geometric mean of four numbers 8, 25, 17 and 30 is 15.3. If the weights of first
three numbers are 5, 3 and 4 respectively, find the weight of the fourth number.

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