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Worked Examples · Example 11
Q.

Find the standard deviation for the following data:

xix_ifif_i
37
810
1315
1810
236
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The mean is 61448≈12.79\dfrac{614}{48} \approx 12.79; the variance is ≈37.46\approx 37.46 and the standard deviation is 37.46≈6.12\sqrt{37.46} \approx 6.12.

Understanding Standard Deviation

Standard deviation measures the typical spread of the data about the mean. For a frequency distribution it is the square root of the frequency-weighted average of the squared deviations. The shortcut form avoids rounding the mean before subtracting.

σ=∑fixi2N−(∑fixiN)2\sigma = \sqrt{\frac{\sum f_i x_i^2}{N} - \left(\frac{\sum f_i x_i}{N}\right)^2}

Step-by-Step Solution

1. Totals

xix_ifif_ifixif_i x_ifixi2f_i x_i^2
372163
81080640
13151952535
18101803240
2361383174

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