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# T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode

Exercise/Page

## T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 237

Solution SAQ 1

Arranging data in ascending order:

Solution SAQ 2

Arranging data in ascending order:

Solution SAQ 3

Median value corresponds to the 37th item in the series. Thus, median value is 6 as it corresponds to cumulative frequency 40.

Solution SAQ 4

Solution SAQ 5

Arranging data in the ascending order:

 S. No Ages 1 2 2 9 3 10 4 11 5 13 6 14 7 16 8 18

N = 8

Solution SAQ 6

 No. of person in a House No. of House (f) Cumulative Frequency (c.f.) 1 26 26 2 113 139 3 120 259 4 95 354 5 60 414 6 42 456 7 21 477 8 14 491 9 5 496 10 4 500 ∑f =500

Median value corresponds to the 250.5th item in the series. Thus, median value is 3 as it corresponds to cumulative frequency 259.

Solution SAQ 7

 Size Frequency (f) Cumulative Frequency (c.f.) 15 10 10 20 15 25 25 25 50 30 5 55 35 5 60 40 20 80 N = 80

Median value corresponds to the 40.5th item in the series. Thus, median value is 25 as it corresponds to cumulative frequency 50.

Solution SAQ 8

 Marks No. of Student (f) Cumulative Frequency (c.f.) 0 4 4 5 6 10 10 15 25 15 5 30 20 8 38 25 12 50 30 28 78 35 14 92 40 3 95 45 5 100 N = 100

Median value corresponds to the 50.5th item in the series. Thus, median value is 30 as it corresponds to cumulative frequency 78.

Solution SAQ 9

Solution SAQ 10

Arranging the data in ascending order:

## T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 238

Solution SAQ 11

Solution SAQ 12

Solution SAQ 13

Solution SAQ 14

Solution SAQ 15

Lower limits and upper limits of class intervals are calculated using the following formula.

where m is mid value and i is the difference between mid-values.

Solution SAQ 16

Solution SAQ 17

Mode of the given series is 75 as it has the highest frequency of 9.

Solution SAQ 18

Solution SAQ 19

Analysis Table

 Column Size of items containing maximum frequency 40 44 48 52 56 60 64 68 72 76 I ✓ ✓ II ✓ ✓ III ✓ ✓ IV ✓ ✓ ✓ V ✓ ✓ ✓ VI ✓ ✓ ✓ Total - - 1 3 4 5 2 - - -

Mode is 60 as it repeats itself maximum number of times.

## T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 239

Solution SAQ 20

Solution SAQ 21

Solution SAQ 22

 Wages No. of Wages 0 - 10 15 10 - 20 35 - 15 =20 20 - 30 60 - 35 =25 30 - 40 84 - 60 =24 40 - 50 97 - 84 =12 50 - 60 127- 96 = 31 60 - 70 198 - 127= 71 70 - 80 250 - 198 = 52

By inspection, we can say that the modal class is 60 - 70 as it has the highest frequency of 71.

Solution SAQ 23

Mode of the given series is 5 as it has the highest frequency of 20 times.

Solution SAQ 24

 No. of person per House (X) No. of House (f) fx Cumulative Frequency (c.f.) 1 26 26 26 2 113 226 139 3 120 360 259 4 95 380 354 5 60 300 414 6 42 252 456 7 21 147 477 8 14 112 491 9 5 45 496 10 4 40 500 N=∑f = 500 ∑fx = 1888

Solution SAQ 25

 Marks No. of Workers (f) Cumulative Frequency (c.f.) 0 - 10 2 2 10 - 20 18 20 20 - 30 30 50 30 - 40 45 95 40 - 50 35 130 50 - 60 20 150 60 - 70 6 156 70 - 80 3 159 N = ∑f = 159

Solution SAQ 26

 Age No. of Student (f) Cumulative Frequency (c.f) 20 - 25 50 50 25 - 30 70 120 30 - 35 100 220 35 - 40 180 400 40 - 45 150 550 45 - 50 120 670 50 - 55 70 740 55 - 60 60 800 ∑f = 800

Solution SAQ 27

 Marks Mid Value (m) No. of Workers  (f) Cumulative Frequency (c.f.) fm 0 - 10 5 5 5 25 10 - 20 15 7 12 105 20 - 30 25 15 27 375 30 - 40 35 25 52 875 40 - 50 45 20 72 900 50 - 60 55 15 87 825 60 - 70 65 8 95 520 70 - 80 75 5 100 375 N = ∑f =100 ∑fm = 4000

Solution SAQ 28

Given:

Mode = 83

Mean = 92

Median =?

We know:

Mode = 3(Median) - 2(Mean)

83 = 3 (Median) - 2(92)

3 (Median) = 83 + 184

## T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 240

Solution SAQ 29

Given:

Mean = 146

Median = 130

Mode =?

Mode = 3(Median) - 2(Mean)

Mode = 3(130) - 2(146)

Mode = 390 - 292

Solution SAQ 30

Given:

Mode = 63

Median = 77

Mean =?

We know:

Mode = 3(Median) - 2(Mean)

63 = 3 (77) - 2 (Mean)

2 (Mean) = 231 - 63

Solution SAQ 31

 Marks Mid Point (m) Cumulative Frequency Frequency fm 0 - 10 5 12 12 60 10 - 20 15 26 14 210 20 - 30 25 40 14 350 30 - 40 35 58 18 630 40 - 50 45 80 22 990 50 - 60 55 110 30 1650 60 - 70 65 138 28 1820 70 - 80 75 150 12 900 ∑f = 150 ∑fm = 6610

# Text Book Solutions

CBSE XI Commerce - Statistics for Economics

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