Find variance and standard deviation of the following frequency distribution

Question : Find variance and standard deviation of the following frequency distribution.xFrequency (f)1.5202.0253.5805.0505.5257.2105.35Solution : Sum of the frequencies \[N=\sum_{i=1}^{N}f_i=215\](i) Arithmetic average (mean) \[\bar{x}=\frac{\sum_{i=1}^{N}{f_i\ast x_i}}{N}=\frac{30+50+280+250+137.5+72+26.5}{215}=\frac{846}{215}=3.93\]frequency distribution tablexFrequency (f)(x-x ̅)(x-x ̅)^2f*(x-x ̅)^21.520-2.435.92118.572.025  -1.93    3.74    93.593.580  -0.43    0.18    15.125.050   1.06    1.13    56.725.525   1.56    2.44    61.237.210   3.26  …

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