Find the variance and standard deviation of the following frequency distribution.

$x_i$: 4, 8, 11, 17, 20, 24, 32
$f_i$: 3, 5, 9, 5, 4, 6, 1

Question

Find the variance and standard deviation of the following frequency distribution.

$x_i$: 4, 8, 11, 17, 20, 24, 32
$f_i$: 3, 5, 9, 5, 4, 6, 1

Accepted Answer

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> [!TLDR]
> Use the direct formula $\sigma^2=\dfrac{\sum f_ix_i^2}{n}-\left(\dfrac{\sum f_ix_i}{n}\right)^2$ on the given frequency table, then take the square root for the standard deviation.
>
> *(Note: this row's source scan flagged one frequency-table cell as visually uncertain. The table transcribed here — $x_i:4,8,11,17,20,24,32$ with $f_i:3,5,9,5,4,6,1$ — is complete and internally consistent, so it is used as given; if the printed paper's cell differs, …

Q.Find the variance and standard deviation of the following frequency distribution. $x_i$ : 4, 8, 11, 17, 20, 24, 32
$f_i$ : 3, 5, 9, 5, 4, 6, 1

Q.Find the variance and standard deviation of the following frequency distribution. $x_i$ : 4, 8, 11, 17, 20, 24, 32
$f_i$ : 3, 5, 9, 5, 4, 6, 1

Q.Find the variance and standard deviation of the following frequency distribution. xix_ixi​: 4, 8, 11, 17, 20, 24, 32 fif_ifi​: 3, 5, 9, 5, 4, 6, 1

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Q.Find the variance and standard deviation of the following frequency distribution. xix_ixi​: 4, 8, 11, 17, 20, 24, 32 fif_ifi​: 3, 5, 9, 5, 4, 6, 1

🔒Unlock the full solution

Q.Find the variance and standard deviation of the following frequency distribution. $x_i$ : 4, 8, 11, 17, 20, 24, 32
$f_i$ : 3, 5, 9, 5, 4, 6, 1

Unlock the full solution

Q.Find the variance and standard deviation of the following frequency distribution. $x_i$ : 4, 8, 11, 17, 20, 24, 32
$f_i$ : 3, 5, 9, 5, 4, 6, 1

Unlock the full solution