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  • The following are the weights (in kg) of 7 students in a statistics class: 55, 63, 57, 58, 59, 61, and 60. What is the variance of the weights?Option:

The following are the weights (in kg) of 7 students in a statistics class: 55, 63, 57, 58, 59, 61, and 60. What is the variance of the weights?

Option: 1

5.29kg^{2}


Option: 2

7.71 kg^{2}
 


Option: 3

8.29kg^{2}


Option: 4

9.71kg^{2}


Answers (1)

best_answer

option (C) 8.29kg^{2}

To calculate the variance, first, we need to calculate the mean weight: Mean weight =

\mathrm{\frac{55+63+57+58+59+61+60}{7}=59}

Next, we need to find the deviation of each weight from the mean:

\mathrm{55-59=4 63-59=4 57-59=-2 58-59= -1 59-59=0 61-59=2 60-59=1}

Then, we square each deviation:

\mathrm{-4^{2}= 164^{2} = 16(-2^{2}) = 4 (-1^{2}) = 10^{2}=0^{2}=2^{2}=41^{2}=1}

Next, we add up the squared deviations:

\mathrm{16+16+4+1+0+4+1=42}

Finally, we divide the sum of squared deviations by the number of data points minus one

\mathrm{(n-1):\frac{42}{7-1} = 8.29}

Therefore, the variance of the weights is \mathrm{8.29kg^{2}}

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