Question

b)Weight in k.g of 10 students are given as 38,40,45,53,47,43,55,48,52,49,Can we say that Variance of the distribution of weights of all students from which the above sample was taken isequal to 20 square k.g​

Answer 1

The variance = 31.11.

• In probability and statistics, variance is the expected value of the squared variation of a random variable from its mean value. Informally, variance calculates the degree to which a random group of numbers deviates from the mean value. Another essential tool, the value of variance is equal to the square of the standard deviation.
• Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a set of data (numbers) are from their mean (average) value. Finding the expected difference of deviation from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.
• Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data spread from mean.

According to the given information, it is given that,

Weight in k.g of 10 students are given as 38,40,45,53,47,43,55,48,52,49.

Now, we know that, Variance s² = ∑$(x_{i} -x) ^{2}$/(n - 1) = $\frac{280}{9} = 31.11$.

Hence, the variance = 31.11.

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