Answer to Question #160381 in Statistics and Probability for Abu Ubayda

Question #160381

Calculate the mean and standard deviation for the following data:


Neck circumference

(in inches)

12 12.5 13 13.5 14 14.5 15 15.5 16

Frequency

5 20 30 43 60 56 37 16 3


1
Expert's answer
2021-02-03T04:02:29-0500

To find the mean and standard deviation we will calculate the following table,



Here A=A= assumed mean =14=14

Now the formula for mean is, xˉ=A+ΣfdΣf\bar x = A+ \frac{\Sigma fd}{\Sigma f}

=14+3.5270=14.0129=14+\frac{3.5}{270}=14.0129

\therefore The required mean is =14.0129=14.0129

Again the formula for standard deviation is , σ=Σfd2Σf(ΣfdΣf)2\sigma =\sqrt{\frac {\Sigma fd^2}{\Sigma f}-(\frac {\Sigma fd}{\Sigma f})^2}

=204.75270(3.5270)2=\sqrt{\frac {204.75}{270}-(\frac {3.5}{270})^2}

=0.8707=0.8707

\therefore The required standard deviation is =0.8707=0.8707


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