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प्रश्न
Calculate the mean deviation about the mean for the following frequency distribution:
| Class interval: | 0–4 | 4–8 | 8–12 | 12–16 | 16–20 |
| Frequency | 4 | 6 | 8 | 5 | 2 |
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उत्तर
Let the assumed mean A = 10 and h = 4.
| Class Interval | Mid-Value(xi) | Frequency(fi) |
\[d_i = \frac{x_i - 10}{4}\]
|
\[f_i d_i\]
|
\[\left| x_i - X \right|\]
\[ = \left| x_i - 9 . 2 \right|\] |
\[f_i \left| x_i - X \right|\]
|
| 0–4 | 2 | 4 | −2 | −8 | 7.2 | 28.8 |
| 4–8 | 6 | 6 | −1 | −6 | 3.2 | 19.2 |
| 8–12 | 10 | 8 | 0 | 0 | 0.8 | 6.4 |
| 12–16 | 14 | 5 | 1 | 5 | 4.8 | 24 |
| 16–20 | 18 | 2 | 2 | 4 | 8.8 | 17.6 |
| N = 25 |
\[\sum f_i d_i\]=-5
|
\[\sum f_i |x_i-\bar{x}|=96\]
|
Here, N = 25 and
\[ = 10 + 4\left( \frac{1}{25} \times \left( - 5 \right) \right)\]
\[ = 10 - \frac{20}{25}\]
\[ = 10 - 0 . 8\]
\[ = 9 . 2\]
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