Q.For the following frequency distribution, find the mean and variance: Class: $0$-$30$, $30$-$60$, $60$-$90$, $90$-$120$, $120$-$150$, $150$-$180$, $180$-$210$
Frequency: $2$, $3$, $5$, $10$, $3$, $5$, $2$ OR The sum and sum of squares of the length $x$ (in cm) and weight $y$ (in gm) of 50 plant products are given below: $\sum_{i=1}^{50}x_i=212$, $\sum_{i=1}^{50}x_i^2=902.8$, $\sum_{i=1}^{50}y_i=261$, $\sum_{i=1}^{50}y_i^2=1457.6$. In which is there more variation — length or weight?

Standard deviation is defined as the positive square root of variance.

By definition, standard deviation $\sigma = \sqrt{\text{variance}}$. Given variance $= 144$:

$\sigma = \sqrt{144} = 12$ …

The square of the standard deviation is called the variance, option (c).

Standard deviation ($\sigma$) measures the spread of data about the mean. By definition, variance ($\sigma^2$) is exactly the square of the standard deviation: $\text{Variance} = \sigma^2 = (\text{Standard Deviation})^2$.

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Standard deviation $=\sqrt{\text{Variance}}$; here $\sqrt{225}=15$.

By definition, variance is the square of the standard deviation, so standard deviation $=\sqrt{\text{variance}}$.

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Variance is defined as the square of the standard deviation.

By definition, variance $= (\text{standard deviation})^2$.

Given standard deviation $= 0.012$: …

Given standard deviation $=1.6$, the variance is $2.56$.

By definition, variance $=(\text{standard deviation})^2$. Here standard deviation $=1.6$ …

This difference is called the range of the series, the simplest measure of dispersion.

Step 1. Range is defined as: Range $=$ Maximum value $-$ Minimum value.

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