NCERT Solutions for Class 11 Economics (Statistics for Economics) Chapter 5 Measures of Central Tendency
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Page 1
NCERT
SOLUTIONS
CLASS - 11th
aglase .co
SOLUTIONS
CLASS - 11th
aglase .co
Page 2
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Class : 11th
Subject : Statistics
Chapter : 5
Chapter Name : Measures of Central Tendency
Q1 Which average would be suitable in the following cases
(i) Average size of readymade garments.
(ii) Average intelligence of students in a class.
(iii) Average production in a factory per shift.
(iv) Average wage in an industrial concern
(v) When the sum of absolute deviations from average is least.
(vi) When quantities of the variable are in ratios.
(vii) In case of open-ended frequency distribution.
Answer.
(i) Mode, because it signifies the quantity with the highest frequency. Hence, the
average size would be the highest in production.
(ii) Median, because the average intelligence can be determined by sorting the students
based on their intelligence and then taking the middle value, which is the median.
(iii) Arithmetic Mean is the most suitable average value to represent the average value
of production in a factory per shift.
(iv) Mean will be the most suitable average in this case because it will take into account
the fluctuations in the parameters.
(v) Arithmetic mean, since the algebraic sum of deviations from the arithmetic mean is
zero.
(vi) Median is not affected by the end values, hence it will be the best suitable average
in this case.
Page 1 of 13
Class : 11th
Subject : Statistics
Chapter : 5
Chapter Name : Measures of Central Tendency
Q1 Which average would be suitable in the following cases
(i) Average size of readymade garments.
(ii) Average intelligence of students in a class.
(iii) Average production in a factory per shift.
(iv) Average wage in an industrial concern
(v) When the sum of absolute deviations from average is least.
(vi) When quantities of the variable are in ratios.
(vii) In case of open-ended frequency distribution.
Answer.
(i) Mode, because it signifies the quantity with the highest frequency. Hence, the
average size would be the highest in production.
(ii) Median, because the average intelligence can be determined by sorting the students
based on their intelligence and then taking the middle value, which is the median.
(iii) Arithmetic Mean is the most suitable average value to represent the average value
of production in a factory per shift.
(iv) Mean will be the most suitable average in this case because it will take into account
the fluctuations in the parameters.
(v) Arithmetic mean, since the algebraic sum of deviations from the arithmetic mean is
zero.
(vi) Median is not affected by the end values, hence it will be the best suitable average
in this case.
Page 1 of 13
Page 3
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
(vii) Median is not affected by the end values, hence it will be the best suitable average
in this case.
Page : 71 , Block Name : Exercises
Q2 Indicate the most appropriate alternative from the multiple choices provided against
each question.
(i) The most suitable average for qualitative measurement is
(a) arithmetic mean
(b) median
(c) mode
(d) geometric mean
(e) none of the above
(ii) Which average is affected most by the presence of extreme items?
(a) median
(b) mode
(c) arithmetic mean
(d) none of the above
(iii) The algebraic sum of deviation of a set of n values from A.M. is
(a) n
(b) 0
(c) 1
(d) none of the above
Answer.
(i) Median, as it is not affected by the end values and still divides the observations into
roughly equal parts.
(ii) Arithmetic mean, because it takes into account all the values of the observations.
(iii) Zero, by the properties of arithmetic mean.
Page : 71 , Block Name : Exercises
Q3 Comment whether the following statements are true or false.
Page 2 of 13
(vii) Median is not affected by the end values, hence it will be the best suitable average
in this case.
Page : 71 , Block Name : Exercises
Q2 Indicate the most appropriate alternative from the multiple choices provided against
each question.
(i) The most suitable average for qualitative measurement is
(a) arithmetic mean
(b) median
(c) mode
(d) geometric mean
(e) none of the above
(ii) Which average is affected most by the presence of extreme items?
(a) median
(b) mode
(c) arithmetic mean
(d) none of the above
(iii) The algebraic sum of deviation of a set of n values from A.M. is
(a) n
(b) 0
(c) 1
(d) none of the above
Answer.
(i) Median, as it is not affected by the end values and still divides the observations into
roughly equal parts.
(ii) Arithmetic mean, because it takes into account all the values of the observations.
(iii) Zero, by the properties of arithmetic mean.
Page : 71 , Block Name : Exercises
Q3 Comment whether the following statements are true or false.
Page 2 of 13
Page 4
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
(i) The sum of deviation of items from median is zero.
(ii) An average alone is not enough to compare series.
(iii) Arithmetic mean is a positional value.
(iv) Upper quartile is the lowest value of top 25% of items.
(v) Median is unduly affected by extreme observations.
Answer.
(i) False. The sum of deviation of items from arithmetic mean is zero.
(ii) True.
(iii) False, arithmetic mean is not a positional value.
(iv) True.
(v) False, it is not much affected by extreme observations.
Page : 72 , Block Name : Exercises
Q4 If the arithmetic mean of the data given below is 28, find (a) the missing
frequency, and (b) the median of the series :
Profit per 0-10 10-20 20-30 30-40 40-50 50-60
retail shop
(in Rs)
Number of 12 18 27 - 17 6
retail
shops
Answer. Let the missing frequency be f.
Then, the mean can be calculated as
Page 3 of 13
(i) The sum of deviation of items from median is zero.
(ii) An average alone is not enough to compare series.
(iii) Arithmetic mean is a positional value.
(iv) Upper quartile is the lowest value of top 25% of items.
(v) Median is unduly affected by extreme observations.
Answer.
(i) False. The sum of deviation of items from arithmetic mean is zero.
(ii) True.
(iii) False, arithmetic mean is not a positional value.
(iv) True.
(v) False, it is not much affected by extreme observations.
Page : 72 , Block Name : Exercises
Q4 If the arithmetic mean of the data given below is 28, find (a) the missing
frequency, and (b) the median of the series :
Profit per 0-10 10-20 20-30 30-40 40-50 50-60
retail shop
(in Rs)
Number of 12 18 27 - 17 6
retail
shops
Answer. Let the missing frequency be f.
Then, the mean can be calculated as
Page 3 of 13
Page 5
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Equating both the known and unknown means, we get:
=28
= 28
7f=140
f=20
Now, the number of observations is 100.
The median will be the mean of 50th and 51st observation, which falls in 20-30 class
range. Using formula,
Median = L+
= 20 +
= 20 + 0.741 10
= 27.41
(Ans. The value of missing frequency is 20 and value of the median is
Rs 27.41)
Page : 72 , Block Name : Exercises
Q5 The following table gives the daily income of ten workers in a factory.
Find the arithmetic mean.
Work A B C D E F G H I J
ers
Daily 120 150 180 200 250 300 220 350 370 260
incom
e
Page 4 of 13
Equating both the known and unknown means, we get:
=28
= 28
7f=140
f=20
Now, the number of observations is 100.
The median will be the mean of 50th and 51st observation, which falls in 20-30 class
range. Using formula,
Median = L+
= 20 +
= 20 + 0.741 10
= 27.41
(Ans. The value of missing frequency is 20 and value of the median is
Rs 27.41)
Page : 72 , Block Name : Exercises
Q5 The following table gives the daily income of ten workers in a factory.
Find the arithmetic mean.
Work A B C D E F G H I J
ers
Daily 120 150 180 200 250 300 220 350 370 260
incom
e
Page 4 of 13
Page 6
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Answer. Sum of daily incomes = 2400
Total number of workers = 10
Mean = Sum of daily incomes/Total number of workers
=
= 240
Page : 72 , Block Name : Exercises
Q6 Following information pertains to the daily income of 150 families.
Calculate the arithmetic mean.
Income (in Rs) Number of families
More than 75 150
More than 85 140
More than 95 115
More than 105 95
More than 115 70
More than 125 60
More than 135 40
More than 145 25
Answer. The data can be tabulated as:
Class interval Number of Frequency (f) Mid Value (m) Total Income
Families (fm)
75-85 150 10 80 800
85-95 140 25 90 2250
95-105 115 20 100 2000
105-115 95 25 110 2750
Page 5 of 13
Answer. Sum of daily incomes = 2400
Total number of workers = 10
Mean = Sum of daily incomes/Total number of workers
=
= 240
Page : 72 , Block Name : Exercises
Q6 Following information pertains to the daily income of 150 families.
Calculate the arithmetic mean.
Income (in Rs) Number of families
More than 75 150
More than 85 140
More than 95 115
More than 105 95
More than 115 70
More than 125 60
More than 135 40
More than 145 25
Answer. The data can be tabulated as:
Class interval Number of Frequency (f) Mid Value (m) Total Income
Families (fm)
75-85 150 10 80 800
85-95 140 25 90 2250
95-105 115 20 100 2000
105-115 95 25 110 2750
Page 5 of 13
Page 7
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
115-125 70 10 120 1200
125-135 60 20 130 2600
135-145 40 15 140 2100
145-155 25 25 150 3750
=150
=17450
Mean =
=
= Rs. 116.33
Page : 72 , Block Name : Exercises
Q7 The size of land holdings of 380 families in a village is given below. Find the median
size of land holdings.
Size of Land Less than 100-200 200-300 300-400 400 and
Holdings (in 100 above
acres)
Number of 40 89 148 64 39
families
Answer. The tabulated information can be given as:
Class Interval Frequency (f) Cumulative Frequency (cf)
0-100 40 40
100-200 89 129
200-300 148 277
300-400 64 341
Page 6 of 13
115-125 70 10 120 1200
125-135 60 20 130 2600
135-145 40 15 140 2100
145-155 25 25 150 3750
=150
=17450
Mean =
=
= Rs. 116.33
Page : 72 , Block Name : Exercises
Q7 The size of land holdings of 380 families in a village is given below. Find the median
size of land holdings.
Size of Land Less than 100-200 200-300 300-400 400 and
Holdings (in 100 above
acres)
Number of 40 89 148 64 39
families
Answer. The tabulated information can be given as:
Class Interval Frequency (f) Cumulative Frequency (cf)
0-100 40 40
100-200 89 129
200-300 148 277
300-400 64 341
Page 6 of 13
Page 8
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
400-500 39 380
∑f=380
Since the total number of observations is 380, the median will be the mean of 190th and
191st observation. Using formula,
Median = L+
= 200 +
= 200 + 0.4121 100
= 241.21
Page : 72 , Block Name : Exercises
Q8 The following series relates to the daily income of workers employed in
a firm. Compute (a) highest income of lowest 50% workers (b) minimum
income earned by the top 25% workers and (c) maximum income earned
by lowest 25% workers.
Daily 10-14 15-19 20-24 25-29 30-34 35-39
Income (in
Rs)
Number of 5 10 15 20 10 5
workers
Answer. The information can be tabulated as :
Class Interval Frequency (f) Cumulative Frequency (cf)
9.5-14.5 5 5
14.5-19.5 10 15
19.5-24.5 15 30
Page 7 of 13
400-500 39 380
∑f=380
Since the total number of observations is 380, the median will be the mean of 190th and
191st observation. Using formula,
Median = L+
= 200 +
= 200 + 0.4121 100
= 241.21
Page : 72 , Block Name : Exercises
Q8 The following series relates to the daily income of workers employed in
a firm. Compute (a) highest income of lowest 50% workers (b) minimum
income earned by the top 25% workers and (c) maximum income earned
by lowest 25% workers.
Daily 10-14 15-19 20-24 25-29 30-34 35-39
Income (in
Rs)
Number of 5 10 15 20 10 5
workers
Answer. The information can be tabulated as :
Class Interval Frequency (f) Cumulative Frequency (cf)
9.5-14.5 5 5
14.5-19.5 10 15
19.5-24.5 15 30
Page 7 of 13
Page 9
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
24.5-29.5 20 50
29.5-34.5 10 60
34.5-39.5 5 65
=65
Median = L+
= 24.5 +
= 24.5 + 0.125 5
= 26.13
Minimum income earned by top 25% workers =
= L+
= 24.5 +
= 24.5 + 4.68
= 29.18
Minimum income earned by lowest 25% workers =
= L+
= 19.5 +
= 19.5 + 0.416
= 19.92
Page : 72 , Block Name : Exercises
Q9 The following table gives production yield in kg. per hectare of wheat of
150 farms in a village. Calculate the mean, median and mode values.
Page 8 of 13
24.5-29.5 20 50
29.5-34.5 10 60
34.5-39.5 5 65
=65
Median = L+
= 24.5 +
= 24.5 + 0.125 5
= 26.13
Minimum income earned by top 25% workers =
= L+
= 24.5 +
= 24.5 + 4.68
= 29.18
Minimum income earned by lowest 25% workers =
= L+
= 19.5 +
= 19.5 + 0.416
= 19.92
Page : 72 , Block Name : Exercises
Q9 The following table gives production yield in kg. per hectare of wheat of
150 farms in a village. Calculate the mean, median and mode values.
Page 8 of 13
Page 10
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Produ 50-53 53-56 56-59 59-62 62-65 65-68 68-71 71-74 74-77
ction
yield
(kg.
Per
hectar
e)
Numb 3 8 14 30 36 28 16 10 5
er of
farms
Answer. To calculate Mean :
Production No. of farms Mid A = 63.5 fd’
Yield value
50 – 53 3 51.5 –12 –4 –12
53 – 56 8 54.5 –9 –3 –24
56 – 59 14 57.5 –6 –2 –28
59 – 62 30 60.5 –3 –1 –30
62 – 65 36 63.5 0 0 0
65 – 68 28 66.5 +3 +1 28
68 – 71 16 69.5 +6 +2 32
71 – 74 10 72.5 +9 +3 30
74 – 77 5 75.5 +12 +4 20
Page 9 of 13
Produ 50-53 53-56 56-59 59-62 62-65 65-68 68-71 71-74 74-77
ction
yield
(kg.
Per
hectar
e)
Numb 3 8 14 30 36 28 16 10 5
er of
farms
Answer. To calculate Mean :
Production No. of farms Mid A = 63.5 fd’
Yield value
50 – 53 3 51.5 –12 –4 –12
53 – 56 8 54.5 –9 –3 –24
56 – 59 14 57.5 –6 –2 –28
59 – 62 30 60.5 –3 –1 –30
62 – 65 36 63.5 0 0 0
65 – 68 28 66.5 +3 +1 28
68 – 71 16 69.5 +6 +2 32
71 – 74 10 72.5 +9 +3 30
74 – 77 5 75.5 +12 +4 20
Page 9 of 13
Page 11
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Total
Mean = A +
= 63.5 + 0.32
= 63.82 kg/hectare
(ii) Median
Class Interval Frequency Cumulative
(f) Frequency (CF)
50 – 53 3 3
53 – 56 8 11
56 – 59 14 25
59 – 62 30 55
62 – 65 36 91
65 – 68 28 119
68 – 71 16 135
71 – 74 10 145
74 – 77 5 150
Total ∑f=150
Median will be the 75th term, which is in the 62-65 interval.
Page 10 of 13
Total
Mean = A +
= 63.5 + 0.32
= 63.82 kg/hectare
(ii) Median
Class Interval Frequency Cumulative
(f) Frequency (CF)
50 – 53 3 3
53 – 56 8 11
56 – 59 14 25
59 – 62 30 55
62 – 65 36 91
65 – 68 28 119
68 – 71 16 135
71 – 74 10 145
74 – 77 5 150
Total ∑f=150
Median will be the 75th term, which is in the 62-65 interval.
Page 10 of 13
Page 12
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Median = L+
= 62 +
= 63.667 kg / hectare
(iii) Mode
Class Interval I II III IV V VI
50 – 53 3
11 22 25 52
53 – 56 8
56 – 59 14
44
59 – 62 30
62 – 65
44 54
65 – 68 28
68 – 71 16
26 15 31
71 – 74 10
Page 11 of 13
Median = L+
= 62 +
= 63.667 kg / hectare
(iii) Mode
Class Interval I II III IV V VI
50 – 53 3
11 22 25 52
53 – 56 8
56 – 59 14
44
59 – 62 30
62 – 65
44 54
65 – 68 28
68 – 71 16
26 15 31
71 – 74 10
Page 11 of 13
Page 13
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
74 – 77 5
Analysis Table
Column 50 – 53 – 56 – 59 – 62 – 65 – 68 – 71 – 74 –
53 56 59 62 65 68 71 74 77
I ✓
II ✓ ✓
III ✓ ✓
IV ✓ ✓ ✓
V ✓ ✓ ✓
VI ✓ ✓ ✓
Total – – 1 3 6 3 1 – –
Modal class = 62 – 65
Mode = L +
Mode = 62 +
= 62 + 1.28
= 63.28 kg / hectare
Page : 73 , Block Name : Exercises
Page 12 of 13
74 – 77 5
Analysis Table
Column 50 – 53 – 56 – 59 – 62 – 65 – 68 – 71 – 74 –
53 56 59 62 65 68 71 74 77
I ✓
II ✓ ✓
III ✓ ✓
IV ✓ ✓ ✓
V ✓ ✓ ✓
VI ✓ ✓ ✓
Total – – 1 3 6 3 1 – –
Modal class = 62 – 65
Mode = L +
Mode = 62 +
= 62 + 1.28
= 63.28 kg / hectare
Page : 73 , Block Name : Exercises
Page 12 of 13
Page 14
Book : Statistics for Economics Ncert Solutions | Chapter - 5 Statistics
Page 13 of 13
Page 13 of 13
Document Details
| Board / Org | NCERT |
| Exam | Class 11 |
| Type | Solution |
| Pages | 14 |
| Updated | 30 Apr 2026 |