Question -
Answer -
(i) 4, 7,8, 9, 10, 12, 13, 17
We know that,
MD=
Where, |di| = |xi – x|
So, let ‘x’ be the mean of the given observation.
x = [4 + 7 + 8 + 9 + 10 + 12 + 13 + 17]/8
= 80/8
= 10
Number of observations, ‘n’ = 8
| xi | |di| = |xi – 10| |
| 4 | 6 |
| 7 | 3 |
| 8 | 2 |
| 9 | 1 |
| 10 | 0 |
| 12 | 2 |
| 13 | 3 |
| 17 | 7 |
| Total | 24 |
MD=
= 1/8 × 24
= 3
∴ TheMean Deviation is 3.
(ii) 13, 17,16, 14, 11, 13, 10, 16, 11, 18, 12, 17
We know that,
MD=
Where, |di| = |xi – x|
So, let ‘x’ be the mean of the given observation.
x = [13 + 17 + 16 + 14 + 11 + 13 + 10 + 16 + 11 + 18 + 12 +17]/12
= 168/12
= 14
Number of observations, ‘n’ = 12
| xi | |di| = |xi – 14| |
| 13 | 1 |
| 17 | 3 |
| 16 | 2 |
| 14 | 0 |
| 11 | 3 |
| 13 | 1 |
| 10 | 4 |
| 16 | 2 |
| 11 | 3 |
| 18 | 4 |
| 12 | 2 |
| 17 | 3 |
| Total | 28 |
MD=
= 1/12 × 28
= 2.33
∴ TheMean Deviation is 2.33.
(iii) 38, 70,48, 40, 42, 55, 63, 46, 54, 44
We know that,
MD=
Where, |di| = |xi – x|
So, let ‘x’ be the mean of the given observation.
x = [38 + 70 + 48 + 40 + 42 + 55 + 63 + 46 + 54 + 44]/10
= 500/10
= 50
Number of observations, ‘n’ = 10
| xi | |di| = |xi – 50| |
| 38 | 12 |
| 70 | 20 |
| 48 | 2 |
| 40 | 10 |
| 42 | 8 |
| 55 | 5 |
| 63 | 13 |
| 46 | 4 |
| 54 | 4 |
| 44 | 6 |
| Total | 84 |
MD=
= 1/10 × 84
= 8.4
∴ TheMean Deviation is 8.4.
(iv) 36, 72,46, 42, 60, 45, 53, 46, 51, 49
We know that,
MD=
Where, |di| = |xi – x|
So, let ‘x’ be the mean of the given observation.
x = [36 + 72 + 46 + 42 + 60 + 45 + 53 + 46 + 51 + 49]/10
= 500/10
= 50
Number of observations, ‘n’ = 10
| xi | |di| = |xi – 50| |
| 36 | 14 |
| 72 | 22 |
| 46 | 4 |
| 42 | 8 |
| 60 | 10 |
| 45 | 5 |
| 53 | 3 |
| 46 | 4 |
| 51 | 1 |
| 49 | 1 |
| Total | 72 |
MD=
= 1/10 × 72
= 7.2
∴ TheMean Deviation is 7.2.
(v) 57, 64,43, 67, 49, 59, 44, 47, 61, 59
We know that,
MD=
Where, |di| = |xi – x|
So, let ‘x’ be the mean of the given observation.
x = [57 + 64 + 43 + 67 + 49 + 59 + 44 + 47 + 61 + 59]/10
= 550/10
= 55
Number of observations, ‘n’ = 10
| xi | |di| = |xi – 55| |
| 57 | 2 |
| 64 | 9 |
| 43 | 12 |
| 67 | 12 |
| 49 | 6 |
| 59 | 4 |
| 44 | 11 |
| 47 | 8 |
| 61 | 6 |
| 59 | 4 |
| Total | 74 |
MD=
= 1/10 × 74
= 7.4
∴ TheMean Deviation is 7.4.