MEASURE OF CENTRAL TENDENCY
1. If A.M. and G.M. of two numbers are 4 and 4 respectively, find their H.M. and those two numbers.
2. Prove that –
3. If prove that (a and b are constant.)
4. If a constant 2 is added to each observation of series, prove that AM is increased by 2.
5. Fill up the gaps:
(i) H.M. of 3 and 4 is ____.
(ii)
(iii)
(iv) is called. ____.
6. Find median of 8, 6, 11, 14, 10 and 16.
7. Prove that
8. If and , find
9. Write down one use of each of G.M. and H.M.
10. Prove that :
11. If median = 27.5, find mode.
12. ____ is called average of position. (Fill in the blank)
13. If any value of set of observations is zero, then ____ of the observation will be zero. (Fill in the blank)
14. Which measure of central tendencies may be of more than one value?
15. The point where the two ogives intersect is the ____ of the distribution. (Fill in the blanks)
16. What is geometric mean of 4, 10 and 25?
17. The algebraic sum of deviations of the observations from their arithmetic mean is ____.
18. The geometric mean of n observations is G. If each observations is multiplied by 3, then what will be the new geometric mean?
19. If AM of is , then AM of is ____. (Fill in the blank)
20. Arithmetic mean of samples of sizes 50 and 75 and 60 and x respectively. If the arithmetic mean of 125 observations of both the samples taken together be 54, find x.
21. Which of the following is affected by extreme values? (i) Arithmetic mean. (ii) Median. (iii) Mode.
22. Find the weighted AM of 1, 2, 3, 4 with corresponding weights 4, 3, 2,and 1 respectively.
23. What type of average should be used in the following cases? (i) Size of readymade shirts in a shop. (ii) Estimation of intelligence of students in a class. (iii) To find the average speed when time of journey is given.
24. If a constant 2 is added to each observation of series, prove that AM is increased by 2.
25. Calculate Mean, Median, Mode, Q1, Q3, D9 and P60 from the below mentioned data:
a) 4, 4, 3, 3, 4, 5, 7, 8, 7, 8, 15, 20, 10, 3.
b) 1, 2, 3, 4, 5, 6
26. Find the weighted AM of 1, 2, 3, and 4 with corresponding weights 4, 3, 2, and 1 respectively.
Measure of Dispersion
Q. Find Range, QD, MD and SD from the following data: 1, 3, 5, 7, 9
Q. If S.D of x is 5, find S.D. of: (i) 2x – 3 (ii) 2x + 5 (iii) x/5 + 1
Q. Given , and , find [H.S.’ 99]
Q. Fill up the gaps: (i) S.D. of 3 and 4 is ____. (ii) is called ____.
Q. If , and , find
Q. What purpose do dispersion serve? Give two examples.
Q. If S.D of x is 5, find S.D. of: (i) and (ii)
Q. If and are the standard deviations of series I and series II respectively, find the relations between and :
Series I :

5

7

12

17

20

Series II :

17

23

38

53

62

Q. Find the coefficient of variation of the following numbers: 1, 2, 3, 4, 5
Q. Find Standard Deviation: , ,
Q. is S, then SD of .
Q. Standard deviation of 7 and 3 is ____. (Fill in the blank)
Q. SD of 1, 2, 3, 4, 5 is
Q. If , , find the coefficient of variation.
Q. If SD of be , what will be SD of ?
Q. If , , , then find the value of r.
Q. If the mean deviation for a group of 50 items is 16.2, what will be their SD?
Q. AM and SD of a set of values are 30 and 8 respectively. If 2 is added to each value, then what will be the coefficient of variation of the series? Find it.
Q. If AM of , then find .
Q. SD of 7, 7, 7, 19, 19, 19 is ____.
Q. Coefficient of variation is expressed in ____.
Q. AM and SD of a set of values are 30 and 8 respectively. If 2 is added to each value, then what will be the coefficient of variation of the series? Find it.
Q. If S.d. of 2,5,6,8,9,is 2.449, then find the sd of (i) 15,18,19,21,22 (ii) 4,10,12,16,18 (iii) 5,11,16,17,19.
35. A car covers four sides of a square at speed 5, 10, 20 and 25 km/hr. respectively. What is the average speed of the car around the square?
36. A man travelled 20 km at 5km/h and again 24 km at 4 km/h. Find the average speed of the man.
37. The arithmetic mean of the marks secured by two groups of students are respectively 70 and 80. If the AM of the marks secured by all the students is 74, find the ratio of number of students of the3 two groups.
38. The average marks secured by boys and girls in a class are respectively 45 and 55, and the average marks secured by all of them is 48. Find the P.C. of boys and girls in the class.
39. Arithmetic mean of samples of sizes 50 and 75 and 60 and x respectively. If the arithmetic mean of 125 observations of both the samples taken together be 54, find x.
Q. The mean and S.D of 100 numbers are found to be 30 and 10 respectively. Two numbers were taken by misstate as 12 and 31 instead of 21 and 13 respectively. Find the correct mean and S.D.
Q. From a certain frequency distribution consisting of 20 observations the mean and SD were found to be 10 and 2 respectively. At the time of checking it was found that a figure 12 was miscopied at 8. Calculate the correct mean, SD and Coefficient of variation if wrong item is replaced.
Q. Mean and S.D. of 18 observations are found to be 7 and 4 respectively. But on comparing the original data it was found that on observation 12 was miscopied as 21 in the calculation. Calculate correct mean and S.D. if wrong item is omitted.
Q. From the following data, find coefficient of variation : A = 10, Sum of D2 = 10, N = 5, Mean = 8.
Q. Following are the heights (in cm) of 11 students: 124, 127, 126, 123, 127, 129, 125, 130, 132, 130, 121. Calculate the quartile deviation.
Q. The weekly wages of workers in two factories show the following results :
Factory –A

Factory –B
 
Mean Wages :
Standard Deviation of Wages :

500
28

425
35

a) In which factory is there greater variation in the distribution of wages?
b) Which factory is paying highest amount of wages?
Q. Fill in the blanks: If AM and SD of a series are respectively 80 and 16, then the coefficient of variation would be ____ which means that the SD is ____% of the mean. If coefficient of variation of the series A is greater than that of the series B, then series A is ____ uniform than the series B.
Q. The mean of five observations is 4.4 and variance is 8.24. If three of observations are 4, 6 and 9, then find the other two.
CORRELATION AND REGRESSION ANALYSIS
Q. Pearson’s coefficient of correlation of two variates X and Y is 0.28, their covariance is + 7.6. If the variance of X is 9, then find the s.d. of Y series.
Q. Find the correlation coefficient from the following data: Sum of X = 56, Sum of Y = 40, Sum of X2 = 524, Sum of Y2 = 256, Sum of Product of XY = 364, n = 8.
Also find two regression equations. If the value of X is 30 then find the value of Y and again if the value of Y is 50 then find the value of X.
Q. A computer while calculating the correlation coefficient between two variable X and Y obtained the following results: Sum of X = 56, Sum of Y = 40, Sum of X2 = 524, Sum of Y2 = 256, Sum of Product of XY = 364, n = 8. It was, however, later discovered that two pairs of observations (6,4) and (3,5) were taken wrongly instead of correct values (4,6) and (7,1) respectively. Calculate the correct value of correlation coefficient between X and Y.
Q. Find Pearson’s coefficient of correlation from the following data: N=10, Sum of X =140, Sum of Y = 150, Sum of (X – 10)2=180, Sum of (Y – 15)2= 215, Sum of (X – 10)(Y – 15)=60.
Q. Given the two regression equation as 8x – 10y + 66 = 0 and 40x – 18y =214? Do you agree with the given equations? If yes then state which equation is of X on Y and Y on X find:
a) The coefficient of correlation between x and y.
b) Mean for X and Y.
c) SD of X if variance of Y is 100.
TIME SERIES ANALYSIS
Q. The trend equation for publicity cost (Rs. In’ 000) of a company is YC=20.2 – 0.8t. Origin 2001 (1st July), t unit = 1 year, Y unit = yearly cost. Shift the origin to 2010.
Q. The equation for yearly sales for a commodity with 1st July 1971 as origin is Y = 81.6 + 28.8X. Determine the trend equation to give monthly trend values with 15th Jan 1972 as origin.
Q. The Parabolic trend equation for the sales (in ‘000 Rs.) of a company is given as: Y = 14.1 – 0.80x + 0.5x2. origin = 1984 (1st July); unit = 1 year; y = yearly sales. Shift the origin to 1988.
Q. On the basis of quarterly sales of a certain commodity for the period 1961 – 63, the following results were computed: Trend values: Y = 27.2 + 0.6 t, with origin 1st quarter 1961, t = time units and y = quarterly sales. The seasonal index are 1st qtr” 90, 2nd qtr = 95, 3rd qtr = 110 and 4th qtr = 105. Estimate the quarterly sales for the year 1963.
Q. Deseasonalised the following data using a multiplicative model:
Quarter:

1

2

3

4

Sales:

65.4

25.2

23.7

21.4

Seasonal Index:

148

124

78

59

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