a) Mean = 76
b) Standard deviation = 6.728
Explanation:
The data set has frequency. So we will apply the formula:
[tex]\text{Mean = }\frac{\sum ^{}_{}fx}{\sum ^{}_{}f}[/tex][tex]\begin{gathered} \text{Mean = }\frac{(69\times7)\text{ + (70}\times1)+(75\times3)\text{ + (81}\times6)\text{ + (82}\times2)+\text{ (92}\times1)}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{483\text{ + 70}+225\text{ + 486 + 164}+\text{ 9}2}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{1520}{20} \\ \text{Mean = 76} \end{gathered}[/tex]
To get the standard deviation, we will apply the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum^{}_{}f(x_i-\mu)^2}{n\text{ - 1}}} \\ \text{where }\sigma\text{ = standard deviation} \\ \mu\text{ = mean, }x_i\text{ = values of x} \\ n\text{ = }\sum ^{}_{}f=20 \end{gathered}[/tex][tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{860}{20-1}} \\ \sigma\text{ = }\sqrt[]{\frac{860}{19}} \\ \sigma\text{ = }\sqrt[]{45.2632} \\ \sigma\text{ = 6.7}28 \\ \\ \text{Standard deviation = 6.7}28 \end{gathered}[/tex]
