8. State one notable property of arithmetic mean.

Ans. Anotable property of anithmetic mean is that the sum of deviations of differenttitems of as
deviations are taken from aithmetic mean, is always zero.

2. Short Answer Type Questions

seies,wte
1. What do you mean by statistical average or central tendency of a series? State its
[3-4 mark1
2. Explain the kinds of statistical averages.
funcions.
3. Define and explain anithmetic mean.
4. Define and explain weighted arithmetic mean.
5. Discuss the various properties of arithmetic mean.
6. The arithmetic mean is descrbed as the centre of gravity of the distribution of values of the ver
Explain.
7. Show that the sum of deviations of the values of the variable from their arithmetic mean is enls
zero.

8. Give the four objectives of statistical average.

9. State four merits of an ideal measure of central tendency.
10. State four merits of arithmetic mean.
11. State four demerits of arithmetic mean.

3. Long Answer Type Questions [6 marks

1. What is statistical average? What desirable properties should an average possess?
2. Discuss the various methods of measuring arithmetic mean and point out its merits and demerts
3. Why is the arithmetic mean the most commonly used measure of central tendency?
4. Explain the step-deviation method of calculating arithmetic mean, taking an imaginary set of data
4. Essential Practicals
1. Eight workers earm the following income:
30, 36,34, 40, 42, 46, 54,62
Find out arithmetic mean. (Ans. Arithmetic Mean =74
2. Pocket allowance of 5 students respectively are:
125,75, 150, 175, 200
Findout arithmetic mean. (Ans. Arithmetic Mean 14)
3. Following is the height of 10 students:
Students A B C D E F G H
168
157
Height (cm) 155 153 168 160 162 166 164 180

Calculate aithmetic mean using Direct and Short-cut Methods. (Ans. Arithmetic Mean =10
4. Weight of 15persons is as follows: 79
78
Weight (kg) 20 28 34 39 42 50 53 54 59 64 72 74 74

Find out mean weight, using Direct Method as well as Short-cut Method. =54.67kø
(Ans. Weighted MMean
 average ofthe following
s
Calculate discrete series. Use Short-cut Method by laking 25 as assumed
average.
30 29
Size
27 26 25 24 23 22 21
Frequency() 5 2 7 4 5 7

(Ans. Average =24.925)

Markssecured
by42 students in Economics are:
6.
20 22 92
Marks 27 35
NumberofStudents 8 4 7 7 5
Findaveragemarks.
(Ans.Average Marks =23.2)
7. Averageage of the people of a country is shown in the following table:
Age(lears) 10-20 20-30 30-40 40-50 50-60
People(000) 30 32 15 12 9
Method
Findout mean age by Direct (Ans. Mean Age =28.7 years)
8. Calculate arithmetic mean of the following| frequency distribution by Direct Method:
the
Class Interval 10-20 2040 40-70 70-120 120-200

Frequency 10 26
(Ans.Arithmetic Mean =574)
a Calculate arithmetic mean from the followingdata by Short-cut Method:
Class Interval 20-25 25-30 30-35 3540 40-45 45-50 50-55

10 12 8 20 11 5
Frequency
(Ans.Arithmetic Mean=35.5)
10. Findout arithmetic mean from the following distribution by Short-cut Method:
64 4-2. 2-0
Items 10-8 8-6
6 4 2
10
Frequency
(Ans.Arithmetic Mean =6.33)

11. Sachin made the following runs in different matches:

25-35 35-45 45-55
Runs 5-15 15-25
19 99
12 17
10
Frequency
Step-deviation Method.
Calculate the average mean of the runs by (Ans.Average Mean =33.875 runs)
12. Calculate arithmetic mean of the following frequency
distribution:
more than 60 50-60
20-30 30 40 40-50
Class less than 10 10-20
6 4
12 18 22
Frequency (Ans.Arithmetic Mean=30.14)
subjects are 15. In English he secures 8 marks, in
o Mean marks obtained by astudent in his five the marks he secured in Statistics.
EConomics 12, in Mathematics 18.,and in Commerce 9. Find out
(Ans. Marks secured in Statistics =28 marks)
the calcuBation, income of one family
Mean value of the weekly income of 40 families is 265. But in
instead of 115. Find the "Corrected" mean. (Ans. Corrected Mean =264.125)
WaS read as 150

Mean 195
Measures of Central Tendency-Arithmetic
 15. Average pocket allowance of 6 studentsis 45. Of these, pocket allowance of 5students
22, 24 and 32 respectively. What is the pocket allowance of the sixthstudent? sis 20,30
(Ans. Pocket Allowance of the Sixth
16. The following table shows wages of the workers. Calculate the average wage of the workere
Wages () 10-19 20-29 30-39 4049
Sudent:=142
Number of Workers 8 12 50-59
6
(Ans. Average Wage of the Workers =3AN
17. Ten players of the Australian team made an average of 63 runs and ten players of the
Indian to
made an average of 77 runs.Calculate the average run made by both the teams.
(Ans.
18. Average income of 50 families is3,000. Of these average income of Collective Average Run =70
12 families is 1,800. Findod
the average income of the remaining families.
(Ans. Average income of the remaining families =73,378.95
19. In the following frequency distribution, if the arithmetic mean is
45.6, find out missing frequency.
Wages () 10-20 20-30 30 40 40-50 50-60 60-70
Number of Workers 7 X 4
70-80
9

20. Calculate the weighted mean of the (Ans. Missing Frequency =16)
following data:oono
Items 96 102 104 124 148 164
Weight 6 9 7 12 9

21. Astudent obtained 60 marks in English, 75 in Hindi, 63 in (Ans. Weighted Mean =131.52)
Statistics. Calculate weighted mean of the marks if weightsMathematics, 59 in Economics and 55 in
are respectively 2, 1, 5, 5and 3.
(Ans. Weighted Mean =60.625 mars)
22. Ahousewife uses 10kg of Wheat, 20 kg of Fuel, 5 kg
of Sugar, and 2 kg of oil. Prices (per kg) df
these items are 1.50,50paise, ? 2.80and 10
find out the weighted arithmetic average of the respectively. Takingquantities used as weights
prices.
23. Calculate weighted mean of the following data by(Ans. Weighted Arithmetic Average = 1.59 per kg
Items
using Direct and Short-cut Methods:
81 76 74 58 70 73
Weight 2 3 6 7

5. NCERT Textbook (Ans. Weighted Mean =70.04)

Questions [With Hints to Answers]
1. Which average would be suitable in the
(i) Average size of following cases?
readymade garments.
(ii) Average intelligence of students in a class.
(ii) Average production in a factory per shift.
(iv) Average wages in an industrial concern.
(v) When the sum of absolute deviations from
average is least.

196 Statistics for Economics

 (vi) When
quantities of the variable are in ratios.
(vii)In case of
open-ended frequency distribution.
[)Mode(indicating atypical value of the series).
(ü) Mode (identifying modal value by ranking intelligence on the scale of 1-10).
(ii) Arithmetic mean.
(iv)
Median (indicating less than or equal to wage' for 50% of the workers, and'more
than or equal to wage for the other 50%).
(v) Arithmetic mean.

(vi) Weighted arithmetic

mean,
the a
(vi) Median (as it is not sensitive to all values in series).)choices provided against
multiple
o Indicate the most appropriate alternative from the
each question.
measurement is:
(i) The most suitable average for qualitative
(a) arithmetic mean (b) median
(c) mode
the presence of extreme items?
(ii) Which average is affected most by
(a) median (b)mode
(c) arithmetic mean (d) geometric mean
(e) harmonic mean A.M. is
The algebraic sum of deviation of a set of n values from
(iüi)
(b) 0
(a) n
(d) none of these
(c) 1
[0 (c), (ü) (c), (iü) (b)] arithmetic
daily income of ten workers in a factory. Find the
the
3. The following table gives
mean. F G H
D
A B 370 260
Workers 300 220 350
180 200 250
120 150
|Daily Income (in )
Daily Income (in )
Workers (X)
120
A 150
B 180
C 200
D 250
300
F 220
G 350
370
260
EX = 2,400

Tendency-Arithmetic Mean 1997

Measures of Central
 2.400
= 240
10

.. Arithmetic mean = 240.]

4. Following infornmation pertains to the daily income of 150 families.
arithmetic mean.
Income Number of
Calculate
(in ) Families
More than 75 150
More than 85 140
More than 95 115
More than 105 95
More than l15 70
More than 125 60
More than 135 40
More than 145 25

[Conversion ofa Cumulative Frequency Distribution into aSimple Frequency Distribution

(Assumed Average, A= 110)
Income Mid-value Number of Deviation
Step-deviation Multiple of
(in ) Families or (d= m- A) '=n-A
m= Step-deviation
Frequency
()
A = 110
and Frequency
C= 10
75-85 80 150- 140 = 10 -30 -3 -30
85-95 90 140- 115 = 25 -20 -2 -50
95-105 100 115 - 95 = 20 - 10 -20
105-115 110 95 -70= 25 0 0
I15-125 120 70 - 60 = 10 10 10
125-135 130 60-40 = 20 20 40
135-145 140 40 - 25 = 15 30 3 45
145-155 150 25 40 100
4
£f = 150 Efd' = 95

Efd'
X= A+
Ef
95
=|10+. -X10
150
=110+ 6.3
=l16.3
.. Arithmetic mean =116.3.]

498 statistics for Economics