1. Descriptive statistics
"Study little but study very thoroughly,
because it is thoroughness in work which pays in the long run."
PROBLEMS

2. Q1
If there are 7
observations
4,6,8,12,10,20,24,
then the sum of å ( x - x) =?
deviation of the
observations
from their AM is ?

3. Q2
If a variable assumes the values
1,2, 3 ... 5
with frequencies as
1, 2, 3 ... 5,
then what is the AM?

4. Q3
The average salary of a group of
unskilled workers is Rs.10000
and that of a group of
skilled workers is Rs.15,000.
If the combined salary is Rs.12000, then
what is the percentage of skilled workers?

5. Q4
The weighted arithmetic mean of the four
numbers
26, 128, 12 and 4 is 10.4.
If the weights of the first three numbers are
1, 3 and 4
respectively, find the weight of the
fourth number?

6. Q5
The weighted AM of
3, 5 and 10
with weights
x, y and z
respectively is known to be 8.
What is the weighted AM if the weights are
changed to 2x, 2y and 2z respectively?

7. Q6
The algebraic
sum of the deviations
of 25 observations measured from 45
is – 55
find the A.M. of the observations?

8. Q7
The weighted arithmetic mean of
first n natural numbers
whose weights are equal to the
corresponding numbers is equal to?

9. Q9
The average weight of the following frequency
distribution is 17.
Find the value of p
X 8 20 26 29
F 3 2 p 1

10. Q10
The mean age of a group of 50 persons was
found to be 48 Later, it was discovered
that age 40,34,56 was misread as 30,43,52
Then the correct mean is?

11. Q11
The numbers
3.2, 5.8, 7.9 and 4.5
have frequencies
x, x+2, x–3 and x+6
respectively, If the arithmetic mean is 4.876,
find the value of x?

12. Q13
 What is the GM for the numbers
8, 24 and 40?
 If A.M. = 25; H. M. = 9, then GM =?
 Calculate geometric mean of the four
numbers
5,8,6,1
with frequency
3,2,4,1

13. Q14
If the AM of two unequal positive real nos
a and b (a>b)
be twice as that of its GM for two numbers
then the
ratio a : b ?

14. Q15
If there are two groups with
75 and 65
as harmonic means and containing
15 and 13
observation then find the
combined HM ?

15. Q16
An, aero plane flies from
A to B
at the rate of 500 km/hour and comes back
from B to A
at the rate of 700 km/hour.
The average speed of the aero plane is?

16. Q17
A motor car covered a distance of
50 miles
four times
The first time at 50 mph, the second at 20
mph, the third at 40 mph and the fourth
at 25 mph.
Calculate the average speed.

17. Q18
“MOI” travelled some distance by cycle at a
speed of 15 km per hour.
On return journey he travelled the same
distance at a speed of 10 km per hour.
What was his
average speed per hour during the entire
journey?

18. Q19
Find the Harmonic mean of the following
numbers: 1, 1 , 1 ,........, 1 .
2 3 n
Find the Harmonic mean of the following
numbers: 1 1 1
1, , ,......,
3 5 2n − 1

19. Q20
What is the H.M of the following data
relating to the age distribution of 72
persons?
Age (Year): 20 30 40
No. of people: 13 28 31

20. Q21
Find the H.M of the following data
Class Frequency
10 – 15 4
15 – 20 8
20 – 25 12
25 – 30 20
30 – 35 11
35 – 40 6
40 – 45 5

21. Q22
The median of the following observation
22,24,33,37,x+1,x+3,44,47,51,58
arranged in ascending order is 42
find x?

22. Q23
You are given below a certain statistical
distribution. Calculate the most suitable
average.
Value Frequency
Less than 100 40
100 – 200 89
200 – 300 148
300 – 400 64
400 and above 39

23. Q24
If x and y are related by
2x – ½y =10
and mode of x is known to be 7.5,
then the mode of y is?

24. Q25
For the given data find the three quartiles
23, 14, 24,
45, 23, 34,
43, 12, 34,
45, 23, 23,
45, 56, 43,
42

25. Q25
The average American spends $65.88 per
month dinning out (the Des Moines register).
a sample 25 of young adults provided the
following dining out expenditures( in dollars)
over the past month.
253 101 245 467 131 0 225 80
113 69 198 95 129 124 11 178
104 161 0 118 151 55 152 134 169

26. ANSWER THE FOLLOWING?
1. COMPUTE THE MEAN MEDIAN AND MODE.
2. CONSIDERING THE RESULTS ABOVE DO THESE
YOUNG SEEM TO SPEND ABOUT SAME AS AN
AVERAGE AMERICAN EATING OUT.
3. COMPUTE THE FIRST AND THIRD QUARTILE.
4. COMPUTE THE RANGE AND THE I.Q.R.
5. COMPUTE THE VARIANCE AND THE SATANDRAD
DEVIATION.
6. THE SKEWNESS MEASURE FOR THE DATA IS
-1.54?
7. CHECK THE ACCURACY OF THE ABOVE
STATEMENT.

27. Q26
Find the standard deviation of first n natural
numbers?
If the quartile DEVIATION is 30 and median
22, find the coefficient of quartile
deviation, assuming the distribution to be
symmetrical.

28. Q27
The quartile deviation of the following
distribution is:
Weights (Kg) No. of men
40 – 45 10
45 – 50 22
50 – 55 28
55 – 60 20
60 – 65 12
65 – 70 8

29. Q28
If the relation between x and y is 5y – 3x =10
and the mean deviation about mean for x
is 12, then the mean deviation of y about
mean is?
Karl Pearson coefficient of skewness is
0.32.
Its standard deviation is 6.5 & mean is 29.6,
find the mode and median?

30. Q29
What is the value of
mean deviation about mean
for the following observations?
50, 60, 50, 50, 60,
60, 60, 50, 50, 50,
60, 60, 60, 50.

31. Q30
The mean deviation
about mode
for the numbers
4/11, 6/11, 8/11,
9/11, 12/11, 8/11
If the SD of the 1st n natural numbers is 2,
then the value of n must be?

32. Q31
Prices of a particular commodity in five years
in two cities are given below. Find from the
data the city which had more stable prices
Prices in city A Prices in city B
20 10
22 20
19 18
23 12
26 15

33. Q32
What is the standard deviation from the following
data relating to the age distribution of 200
persons?
Age (Year): 20 30 40 50 60 70 80
No. of people:13 28 31 46 39 23 20

34. Q33
The mean and SD
of a sample of 100 observations
were calculated as 40 and 5.1 respectively
by a CA student who took one
observations as 50 instead of 40 by
mistake.
The correct value of SD would be?

35. Q34
The standard deviation calculated from a
set of 32 observations is 5.
If the sum of the observations is 80,
what is the
sum of the squares
of these observations?

36. Q35
For a group containing
100
observations,
the A.M. and S.D. were 8 and 10.
For 50 observations selected from these 100
observations the
A.M and S.D are 10 and 2 respectively.
Find the A.M. and S. D. of the other half.

37. Q36
Find the coefficient of variation of the
following data:
Marks No of Students
0 – 10 4
10 – 20 10
20 – 30 16
30 – 40 12
40 – 50 8

38. Q37
The following data relates to the salary of
workers of two factories
Factory A Factory B
No. of workers 80 110
Mean Rs 2320 Rs 2160
SD Rs 120 Rs 122
In which factory is variation in salary
more?

39. Q38
For 2 values of a variable x,
the mean and the standard deviation
are 10 and 2
respectively.
What are the values of x?

40. Q39
For a set of ungrouped values the following sums
are found:
N = 15,
å X = 480,
å X = 15735.
2
Find the mean and standard deviation
of the values.

41. Q40
The INTER QUARTILE RANGE of the following
distribution is:
Weights (Kg) No. of men
400–450 10
450–500 22
500–550 28
550–600 20
600–650 12
650–700 8

42. Q42
Wageweb conducts surveys of salary data and present
the summaries on its website. Assume the following
data come from a sample of annual salaries for 20
marketing executives (data are in thousands)
145,140,145,
173,116,127,
155,134,138,
114,951,621,271,
131,781,439,316,516,157
184
CALCULATE PEARSON COEFFICENT?

43. Q43
Find mean deviation and its coefficient for the
data
wages No of workers
0 – 1000 4
1000 – 2000 10
2000 – 3000 16
3000 – 4000 12
4000– 5000 8

44. Q45
Prove that the
standard deviation
calculated from two values
a and b
is equal to half of their difference

45. Q46
The following table gives the earned run averages (eras) for the
2002 season for the pitching staffs of the 16 baseball teams in
the national league.
Arizona 3.92 Milwaukee 4.73
Atlanta 3.13 Montreal 3.97
Chicago 4.29 New York 3.89
Colorado 5.20 Philadelphia 4.17
Cincinnati 4.27 Pittsburgh 4.23
Florida 4.36 St. Louis 3.70
Houston 4.00 San Diego 4.62
Los Angeles 3.69 San Francisco 3.54

46. CALCULATE
 mean (eras)
 median and mode
 variance of the data
 standard deviation and its coefficient
 comment on skewness of the data
 calculate I.Q.R

47. ANALYSE
You are given the data of a factory before and after the
settlement of industrial dispute.
comment on the gain or losses from the point of the
workers and the management
BEFORE AFTER
NO OF 2440 2359
WORKERS
MEAN WAGES 45.5 47.5
MEDIAN WAGES 49.0 45.0
STANDARD 12.0 10.0
DEVIATION

48. ANALYSE
From the data given below state Which series is more
consistent?
Variable Series A Series B
10-20 20 13
20-30 18 22
30-40 32 40
40-50 40 32
50-60 22 18
60-70 18 10