The yield of wheat and rice per acre for 10 districts of a state is as under:

District

1

2

3

4

5

6

7

8

9

10

Wheat

12

10

15

19

21

16

18

9

25

10

Rice

22

29

12

23

18

15

12

34

18

12

 

Calculate for each crop,

(i) Range

(ii) Q.D.

(iii) Mean Deviation about Mean

(iv) Mean Deviation about Median

(v) Standard Deviation

(vi) Which crop has greater variation?

(vii) Compare the value of different measures for each crop.

(i) Range

a. Wheat

Highest value of distribution (H) = 25

Lowest value of distribution (L) = 9

Range = HL

          = 25 – 9

          =16

 

b. Rice

Highest value of distribution (H) = 34

Lowest value of distribution (L) = 12

Range = HL

           =34 – 12

= 22

 

(ii) Quartile Deviation

 

a. Wheat

Arranging the production of wheat in increasing order

9, 10, 10, 12, 15, 16, 18, 19, 21, 25

= 2.75th item

=Size of 2th item + 0.75 (size of 3rd item – size of 2nd item)

= 10 + 0.75 (10 – 10)

= 10 + 0.75 × 0

=10

= 8.25th

=Size of 8th item + 0.25 (size of 9th item – size of 8th item)

= 19 + 0.25 (21 – 19)

= 19 + 0.25 × 2

= 19 + 0.50 = 19.50

= 4.75

 

b. Rice

Arranging the data of production of rice

12, 12, 12, 15, 18, 18, 22, 23, 29, 34

= 2.75th item

= size of 2nd item + 0.75 (size of 3rd item – size of 2nd item)

= 12 + 0 .75 (12 – 12)

= 12 + 0.75 × 0

= 12

= 8.25th item

= Size of 8th item + 0.25 (size of 9th item – size of 8th item)

= 23 + 0.25 (29 – 23)

= 23 + 0.25 × 6

= 23 + 1.5

= 24.5

= 6.25

 

(iii) Mean Deviation about Mean

 

a. Wheat

Wheat Production

x

9

6

10

5

10

5

12

3

15

0

16

1

18

3

19

4

21

6

25

10

 

 

b. Rice

 

Rice Production

 x

12

6

12

6

12

6

15

3

18

0

18

0

22

4

23

5

29

11

34

16

 

(iv) Mean Deviation about Median

 

a. Wheat

 

Production of Wheat

x

09

6

10

5

10

5

12

3

15

0

16

1

18

3

19

4

21

6

25

10

 

 

 

 

 

b. Rice

Production of rice

d = X–18

12

6

12

6

12

6

15

3

0

18

0

22

4

23

5

29

11

34

16

 

Since n is even

 

 

(v) Standard Deviation

 

a. Wheat

Reduction of Wheat

x

Ax = 15

d= xAx

d2

9

–6

36

10

–5

25

10

–5

25

12

–3

9

15

0

0

16

1

1

18

3

9

19

4

16

21

6

36

25

10

100

 

 

 

b. Rice

Production of rice

 x

Ax = 18

d = xA x

d2

12

–6

36

12

–6

36

12

–6

36

15

–3

9

18

0

0

22

4

16

23

5

25

29

11

121

34

16

256

 

 

 

 

(vi) Coefficient of Variation

 

a. Wheat

 

 

b. Rice

 

(vi) Rice crop has greater variation as the coefficient of variation is higher for rice as compared to that of wheat.

(vii) Rice crop has higher Range, Quartile Deviation, Mean Deviation about mean, Mean Deviation about median, Standard Deviation and Coefficient of Variation.

 

  • 3
What are you looking for?