Question -
| xi | 5 | 7 | 9 | 10 | 12 | 15 |
| fi | 8 | 6 | 2 | 2 | 2 | 6 |
(ii)
| xi | 5 | 10 | 15 | 20 | 25 |
| fi | 7 | 4 | 6 | 3 | 5 |
(iii)
| xi | 10 | 30 | 50 | 70 | 90 |
| fi | 4 | 24 | 28 | 16 | 8 |
Answer -
(i)
To find the mean deviation from the mean, firstly let uscalculate the mean.
By using the formula,
| xi | fi | Cumulative Frequency (xifi) | |di| = |xi – Mean| | fi |di| |
| 5 | 8 | 40 | 4 | 32 |
| 7 | 6 | 42 | 2 | 12 |
| 9 | 2 | 18 | 0 | 0 |
| 10 | 2 | 20 | 1 | 2 |
| 12 | 2 | 24 | 3 | 6 |
| 15 | 6 | 90 | 6 | 36 |
| Total = 26 | Total = 234 | | Total = 88 |
= 234/26
= 9
= 88/26
= 3.3
∴ Themean deviation is 3.3
(ii)
To find the mean deviation from the mean, firstly let uscalculate the mean.
By using the formula,
| xi | fi | Cumulative Frequency (xifi) | |di| = |xi – Mean| | fi |di| |
| 5 | 7 | 35 | 9 | 63 |
| 10 | 4 | 40 | 4 | 16 |
| 15 | 6 | 90 | 1 | 6 |
| 20 | 3 | 60 | 6 | 18 |
| 25 | 5 | 125 | 11 | 55 |
| | | | |
| Total = 25 | Total = 350 | | Total = 158 |
= 350/25
= 14
= 158/25
= 6.32
∴ Themean deviation is 6.32
(iii)
To find the mean deviation from the mean, firstly let uscalculate the mean.
By using the formula,
| xi | fi | Cumulative Frequency (xifi) | |di| = |xi – Mean| | fi |di| |
| 10 | 4 | 40 | 40 | 160 |
| 30 | 24 | 720 | 20 | 480 |
| 50 | 28 | 1400 | 0 | 0 |
| 70 | 16 | 1120 | 20 | 320 |
| 90 | 8 | 720 | 40 | 320 |
| | | | |
| Total = 80 | Total = 4000 | | Total = 1280 |
= 4000/80
= 50
= 1280/80
= 16
∴ Themean deviation is 16