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Table for finding mean
$\therefore \bar{x}=\mathrm{A}+\frac{\sum_{i=1}^{n} f_{i} d_{i}}{\sum_{i=1}^{n} f_{i}} \times h=20+\frac{0}{115} \times 5=20$
Table for finding first four moments
$\mu_{2}=\frac{1}{\mathrm{~N}} \sum_{i=1}^{n} f_{i}\left(x_{i}-20\right)^{2}=\frac{1}{115} \times 7150=62.17 ; \mu_{4}=\frac{1}{\mathrm{~N}} \sum_{i=1}^{n} f_{i}\left(x_{i}-20\right)^{4}=\frac{1}{115} \times 1003750=8728.26$
$\beta_{2}=\frac{\mu_{4}}{\mu_{2}^{2}}=\frac{8728.26}{(62.17)^{2}}=2.26<3$; Nature of kurtosis is platykurtic.
$\therefore \bar{x}=\mathrm{A}+\frac{\sum_{i=1}^{n} f_{i} d_{i}}{\sum_{i=1}^{n} f_{i}} \times h=20+\frac{0}{115} \times 5=20$
Table for finding first four moments
| $x _{ i }$ | $f _{ i }$ | $x_i-20$ | $I _{ i }\left( x _{ i }-20\right)$ | $f_i\left(x_i 20\right)^2$ | $f_i\left(x_i-20\right)^3$ | $f_i\left(x_i-20\right)^4$ |
| 5 | 8 | -15 | -120 | 1800 | -27000 | 405000 |
| 10 | 15 | -10 | -150 | 1500 | -15000 | 150000 |
| 15 | 18 | -5 | -90 | 450 | -2250 | 11250 |
| 20 | 29 | 0 | 0 | 0 | 0 | 0 |
| 25 | 23 | 5 | 115 | 575 | -2875 | 14375 |
| 30 | 17 | 10 | 170 | 1700 | 17000 | 170000 |
| 35 | 5 | 15 | 75 | 1125 | 16875 | 253125 |
| 115 | 0 | 7150 | 10000 | 1003750 |
$\mu_{2}=\frac{1}{\mathrm{~N}} \sum_{i=1}^{n} f_{i}\left(x_{i}-20\right)^{2}=\frac{1}{115} \times 7150=62.17 ; \mu_{4}=\frac{1}{\mathrm{~N}} \sum_{i=1}^{n} f_{i}\left(x_{i}-20\right)^{4}=\frac{1}{115} \times 1003750=8728.26$
$\beta_{2}=\frac{\mu_{4}}{\mu_{2}^{2}}=\frac{8728.26}{(62.17)^{2}}=2.26<3$; Nature of kurtosis is platykurtic.
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