1.
| xi |
fi |
c.f |
|xi - 7| |
|xi - 7| fi |
| 5 |
8 |
8 |
2 |
16 |
| 7 |
6 |
14 |
2 |
4 |
| 10 |
2 |
18 |
3 |
6 |
| 12 |
2 |
20 |
5 |
10 |
| 15 |
6 |
26 |
8 |
48 |
|
26 |
|
|
84 |
\(\frac{\sum^{n}_{i=1}}{2}\) = \(\frac{26}{2}\) = 13
The c.f just greater than 13 is 14 and corresponding value of x is 7.
Therefore; median, M = 7
Hence; M.D about median
\(\frac{\displaystyle\sum_{i=1}^{n} f_i |x_i - M|}{\displaystyle\sum_{i = 1}^{n} f_i}\)
= \(\frac{84}{26} = 3.23\)
2.
| xi |
fi |
c.f |
|xi - 30| |
|xi - 30| fi |
| 15 |
3 |
3 |
15 |
45 |
| 21 |
5 |
8 |
9 |
45 |
| 27 |
6 |
14 |
3 |
18 |
| 30 |
7 |
21 |
0 |
0 |
| 35 |
8 |
29 |
5 |
40 |
|
29 |
|
|
148 |
\(\frac{\sum^{n}_{i=1}}{2}\) = \(\frac{29}{2} = 14.5\)
The c.f just greater than 14.5 is 21 and corresponding value of x is 30. Therefore; median, M = 30
Hence; M.D about median
\(\frac{\displaystyle\sum_{i=1}^{n} f_i |x_i - M|}{\displaystyle\sum_{i = 1}^{n} f_i}\)
\(\frac{148}{29} = 5.1\)
