Class 11: Economics Chapter 5 solutions. Complete Class 11 Economics Chapter 5 Notes.
Contents
NCERT Solutions for 11th Class Economics: Chapter 5-Measures of Central Tendency
NCERT 11th Economics Chapter 5, class 11 Economics chapter 5 solutions
Page No: 71
Exercises
1. Which average would be suitable in the following cases?
(i) Average size of readymade garments.
► Mode
(ii) Average intelligence of students in a class.
► Median
(iii) Average production in a factory per shift.
► Arithmetic average
(iv) Average wages in an industrial concern.
► Arithmetic average
(v) When the sum of absolute deviations from average is least.
► Median
(vi) When quantities of the variable are in ratios.
► Arithmetic average
(vii) In case of open-ended frequency distribution.
► Median
NCERT 11th Economics Chapter 5, class 11 Economics chapter 5 solutions
2. 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
► (b) median
(ii) Which average is affected most by the presence of extreme items?
(a) median
(b) mode
(c) arithmetic mean
(d) none of the above
► (c) arithmetic mean
(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
► (b) 0
3. Comment whether the following statements are true or false.
(i) The sum of deviation of items from median is zero.
► False
(ii) An average alone is not enough to compare series.
► True
(iii) Arithmetic mean is a positional value.
► False
(iv) Upper quartile is the lowest value of top 25% of items.
► True
(v) Median is unduly affected by extreme observations.
► False
NCERT 11th Economics Chapter 5, class 11 Economics chapter 5 solutions
4. 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 retail shop (in Rs) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Number of retail shops | 12 | 18 | 27 | – | 17 | 6 |
(a) Let the missing frequency be x
Arithmetic mean = 28 (given)
| Profit per retail shop (in Rs) Class Interval | No. of retail shops Frequency (f) | Mid Value (m) | fm |
| 0-10 | 12 | 5 | 60 |
| 10-20 | 18 | 15 | 270 |
| 20-30 | 27 | 25 | 675 |
| 30-40 | x | 35 | 35x |
| 40-50 | 17 | 45 | 765 |
| 50-60 | 6 | 55 | 330 |
| Σf = 80 + x | Σfx = 2100 + 35x |
Mean = Σfx/Σf
⇒ 28 = 2100 + 35x/80 + x
⇒ 2240 + 28x = 2100 + 35
⇒ 2240 – 2100 = 35x – 25x
⇒ 140 = 7x
⇒ x = 140/7 = 20
Missing frequency = 20
(b)
| Class Interval | Frequency (f) | Cumulative frequency (CF) |
| 0-10 | 12 | 12 |
| 10-20 | 18 | 30 |
| 20-30 | 27 | 57 |
| 30-40 | x | 77 |
| 40-50 | 17 | 94 |
| 50-60 | 6 | 100 |
| Total | Σf = 100 |
Median = Size of (N/2)th item
= 100/2 = 50th item
It lies in class 20-30.
NCERT 11th Economics Chapter 5, class 11 Economics chapter 5 solutions
5. The following table gives the daily income of ten workers in a factory. Find the arithmetic mean.
| Workers | A | B | C | D | E | F | G | H | I | J |
| Daily Income (in Rs) | 120 | 150 | 180 | 200 | 250 | 300 | 220 | 350 | 370 | 260 |
Answer
| Workers | Daily Income (in Rs) X |
| A | 120 |
| B | 150 |
| C | 180 |
| D | 200 |
| E | 250 |
| F | 300 |
| G | 220 |
| H | 350 |
| I | 370 |
| J | 260 |
| Total | ΣX = 2400 |
N = 10
Arithmetic Mean = ΣX/N
= 2400/10
= 240
Arithmetic Mean = 240
NCERT 11th Economics Chapter 5, class 11 Economics chapter 5 solutions
6. 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
| Income | No. of families Frequency (f) | Mid Class |
(x)
fx
75-85
10
80
800
85-95
25
90
2250
95-105
20
100
2000
105-115
25
110
2750
115-125
10
120
1200
125-135
20
130
2600 135-145 15
140
2100 145-155 25
150
3750
150
17450 Arithmetic Mean = Σfx/Σf
= 17450/150
= 116.33
7. The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.
| Size of Land Holdings (in acres) | Less than 100 | 100-200 | 200-300 | 300-400 | 400 and above |
| Number of families | 40 | 89 | 148 | 64 | 39 |
Answer
| Size of Land Holdings Class Interval | Number of families (f) | Cumulative frequency (CF) |
| 0-100 | 40 | 40 |
| 100-200 | 89 | 129 |
| 200-300 | 148 | 277 |
| 300-400 | 64 | 341 |
| 400-500 | 39 | 380 |
| Total | Σf = 380 |
Σf = N = 380
Median = Size of (N/2)th item
= 380/2 = 190th item
It lies in class 200-300.
Median size of land holdings = 241.22 acres
8. 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 Income (in Rs) | 10-14 | 15-19 | 20-24 | 25-29 | 30-34 | 35-39 |
| Number of workers | 5 | 10 | 15 | 20 | 10 | 5 |
(Hint: Compute median, lower quartile and upper quartile.)
Answer
| Daily Income (in Rs) Class Interval | No of workers (f) | Cumulative frequency (CF) |
| 9.5-14.5 | 5 | 5 |
| 14.5-19.5 | 10 | 15 |
| 19.5-24.5 | 15 | 30 |
| 24.5-29.5 | 20 | 50 |
| 29.5-34.5 | 10 | 60 |
| 34.5-39.5 | 5 | 65 |
| Total | Σf = 65 |
(a) Σf = N = 65
Median = Size of (N/2)th item
= 65/2 = 32.5th item
It lies in class 24.5-29.5.
Highest income of lowest 50% workers = Rs 25.12
(b) First, we need to find Q1
Class interval of Q1 = (N/4)th items
= (65/4)th items = 16.25th item
It lies in class 19.5-24.5.
Minimum income earned by the top 25% workers = Rs 19.92
(c) First, we need to find Q3
Class interval of Q3 = 3 (N/4)th items
= 3 (65/4)th items = 3 × 16.25th item
= 48.75th item
It lies in class 24.5-29.5.
Maximum income earned by lowest 25% workers = Rs 29.19
9. 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.
| Production yield (kg. per hectare) | 50-53 | 53-56 | 56-59 | 59-62 | 62-65 | 65-68 | 68-71 | 71-74 | 74-77 |
| Number of workers | 3 | 8 | 14 | 30 | 36 | 28 | 16 | 10 | 5 |
Answer
| Production Yield (kg. per hectare) | No. of farms Frequency (f) | Mid Class (x) | fx | Cumulative frequency (CF) |
| 50-53 | 3 | 51.5 | 154.5 | 3 |
| 53-56 | 8 | 54.5 | 436 | 11 |
| 56-59 | 14 | 57.5 | 805 | 25 |
| 59-62 | 30 | 60.5 | 1815 | 55 |
| 62-65 | 36 | 63.5 | 2286 | 91 |
| 65-68 | 28 | 66.5 | 1862 | 119 |
| 68-71 | 16 | 69.5 | 1112 | 135 |
| 71-74 | 10 | 72.5 | 725 | 145 |
| 74-77 | 5 | 75.5 | 377.5 | 150 |
| Σf = 150 | Σfx = 9573 |
Mean = Σfx/Σf = 9573/150 = 63.82 hectare
Modal Class = 62-65
NCERT Solutions for 11th Class Economics: Chapter 5: Download PDF
NCERT Solutions for 11th Class Economics: Chapter 5-Measures of Central Tendency
Download PDF: NCERT Solutions for 11th Class Economics: Chapter 5-Measures of Central Tendency PDF
Chapterwise NCERT Solutions for Class 11 Economics:
- Chapter 1 Introduction
- Chapter 2 Collection of Data
- Chapter 3 Organisation of Data
- Chapter 4 Presentation of Data
- Chapter 5 Measures of Central Tendency
- Chapter 6 Measures of Dispersion
- Chapter 7 Correlation
- Chapter 8 Index Numbers
About NCERT
The National Council of Educational Research and Training is an autonomous organization of the Government of India which was established in 1961 as a literary, scientific, and charitable Society under the Societies Registration Act. Its headquarters are located at Sri Aurbindo Marg in New Delhi. Visit the Official NCERT website to learn more.