Variance for the given set of data is equals to 197.78.
What is variance?
" Variance is defined as the measurement which gives information about spreading of data variation in the given data set."
Formula used
Variance, σ² =∑ \((x_{i} -\bar{x})^{2}\)/ (n-1)
\(x_{i}\) = value of each observation
\(\bar{x}=\) mean of the given observation
n= number of observation
σ² = variance
Mean =∑ \(x_{i}\) / n
According to the question,
Given data set ,
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
Substitute in the formula to get mean of the given data set,
\(\bar{x} = \frac{(23+32+20+43+41+66+63+59+54+36+45+61+55+44+47)}{15}\)
\(=\frac{689}{15}\\ \\=45.93\)
Substitute the value in the formula of variance from the table we get,
n= 15
∑\((x_{i} -\bar{x})^{2}\)= 2768.95
\(\sigma^{2} = \frac{2768.95}{(15-1)}\)
\(= \frac{2768.95}{(14)}\)
= 197.78
Hence, variance for the given set of data is equals to 197.78.
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