Question -
Answer -
(i) 3011, 2780, 3020, 2354, 3541, 4150, 5000
To calculate the Median (M), let us arrange the numbers in ascending order.
Median is the middle number of all the observation.
2354, 2780, 3011, 3020, 3541, 4150, 5000
So, Median = 3020 and n = 7
By using the formula to calculate Mean Deviation,
MD=
| xi | |di| = |xi – 3020| |
| 3011 | 9 |
| 2780 | 240 |
| 3020 | 0 |
| 2354 | 666 |
| 3541 | 521 |
| 4150 | 1130 |
| 5000 | 1980 |
| Total | 4546 |
MD=
= 1/7 × 4546
= 649.42
∴ The Mean Deviation is 649.42.
(ii) 38, 70, 48, 34, 42, 55, 63, 46, 54, 44
To calculate the Median (M), let us arrange the numbers in ascending order.
Median is the middle number of all the observation.
34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here the Number of observations are Even then Median = (46+48)/2 = 47
Median = 47 and n = 10
By using the formula to calculate Mean Deviation,
MD=
| xi | |di| = |xi – 47| |
| 38 | 9 |
| 70 | 23 |
| 48 | 1 |
| 34 | 13 |
| 42 | 5 |
| 55 | 8 |
| 63 | 16 |
| 46 | 1 |
| 54 | 7 |
| 44 | 3 |
| Total | 86 |
MD= = 1/10 × 86
= 8.6
∴ The Mean Deviation is 8.6.
(iii) 34, 66, 30, 38, 44, 50, 40, 60, 42, 51
To calculate the Median (M), let us arrange the numbers in ascending order.
Median is the middle number of all the observation.
30, 34, 38, 40, 42, 44, 50, 51, 60, 66
Here the Number of observations are Even then Median = (42+44)/2 = 43
Median = 43 and n = 10
By using the formula to calculate Mean Deviation,
MD= | xi | |di| = |xi – 43| |
| 30 | 13 |
| 34 | 9 |
| 38 | 5 |
| 40 | 3 |
| 42 | 1 |
| 44 | 1 |
| 50 | 7 |
| 51 | 8 |
| 60 | 17 |
| 66 | 23 |
| Total | 87 |
MD=
= 1/10 × 87
= 8.7
∴ The Mean Deviation is 8.7.
(iv) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42
To calculate the Median (M), let us arrange the numbers in ascending order.
Median is the middle number of all the observation.
22, 24, 25, 27, 28, 29, 30, 31, 41, 42
Here the Number of observations are Even then Median = (28+29)/2 = 28.5
Median = 28.5 and n = 10
By using the formula to calculate Mean Deviation,
MD=
| xi | |di| = |xi – 28.5| |
| 22 | 6.5 |
| 24 | 4.5 |
| 30 | 1.5 |
| 27 | 1.5 |
| 29 | 0.5 |
| 31 | 2.5 |
| 25 | 3.5 |
| 28 | 0.5 |
| 41 | 12.5 |
| 42 | 13.5 |
| Total | 47 |
MD= = 1/10 × 47
= 4.7
∴ The Mean Deviation is 4.7.
(v) 38, 70, 48, 34, 63, 42, 55, 44, 53, 47
To calculate the Median (M), let us arrange the numbers in ascending order.
Median is the middle number of all the observation.
34, 38, 43, 44, 47, 48, 53, 55, 63, 70
Here the Number of observations are Even then Median = (47+48)/2 = 47.5
Median = 47.5 and n = 10
By using the formula to calculate Mean Deviation,
MD= | xi | |di| = |xi – 47.5| |
| 38 | 9.5 |
| 70 | 22.5 |
| 48 | 0.5 |
| 34 | 13.5 |
| 63 | 15.5 |
| 42 | 5.5 |
| 55 | 7.5 |
| 44 | 3.5 |
| 53 | 5.5 |
| 47 | 0.5 |
| Total | 84 |
MD=
= 1/10 × 84
= 8.4
∴ The Mean Deviation is 8.4.