The mean deviation about the mean for the data x_i, 5, 7, 9, 10, 12, 15 | ---|---|---|---|…

Question

The mean deviation about the mean for the data
 $x_i$, 5, 7, 9, 10, 12, 15 |
---|---|---|---|---|---|---|
 $f_i$, 8, 6, 2, 2, 2, 6 |

is equal to:

Accepted Answer

$$\sum f_i = 8+6+2+2+2+6 = 26, \qquad \sum f_ix_i = 40+42+18+20+24+90 = 234$$

$$\bar{x} = \frac{234}{26} = 9$$

, $x_i$, $f_i$, $\|x_i-9\|$, $f_i\|x_i-9\|$ |
---|---|---|---|
 5, 8, 4, 32 |
 7, 6, 2, 12 |
 9, 2, 0, 0 |
 10, 2, 1, 2 |
 12, 2, 3, 6 |
 15, 6, 6, 36 |

$$\sum f_i|x_i-\bar{x}| = 32+12+0+2+6+36 = 88$$

$$\text{M.D.} = \frac{88}{26} = \frac{44}{13}$$

Solutions · 1