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 =∑ [tex](x_{i} -\bar{x})^{2}[/tex]/ (n-1)
[tex]x_{i}[/tex] = value of each observation
[tex]\bar{x}=[/tex] mean of the given observation
n= number of observation
σ² = variance
Mean =∑ [tex]x_{i}[/tex] / 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,
[tex]\bar{x} = \frac{(23+32+20+43+41+66+63+59+54+36+45+61+55+44+47)}{15}[/tex]
[tex]=\frac{689}{15}\\ \\=45.93[/tex]
Substitute the value in the formula of variance from the table we get,
n= 15
∑[tex](x_{i} -\bar{x})^{2}[/tex]= 2768.95
[tex]\sigma^{2} = \frac{2768.95}{(15-1)}[/tex]
[tex]= \frac{2768.95}{(14)}[/tex]
= 197.78
Hence, variance for the given set of data is equals to 197.78.
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