Answer :
The number of terms is 15.
The means is defined as the ratio of sum of terms by number of terms.
Mean:
Determine the mean of the data.
[tex]\begin{gathered} \mu=\frac{3.5+4.0+3.6+4.0+2.6+2.4+6.8+4.9+4.5+5.4+3.7+2.9+3.7+4.7+3.4}{15} \\ =\frac{60.1}{15} \\ =4.0066 \\ \approx4.01 \end{gathered}[/tex]Standard deviation:
Determine the sum of square of difference between each observation and mean of the data.
[tex]\begin{gathered} \sum ^n_{i\mathop=1}(x_i-\mu)^2=(3.5-4.01)^2+(4.0-4.01)^2+(3.6-4.01)^2+(4.0-4.01)^2+(2.6-4.01)^2 \\ +(2.4-4.01)^2+(6.8-4.01)^2+(4.9-4.01)^2+(4.5-4.01)^2+(5.4-4.01)^2 \\ +(3.7-4.01)^2+(2.9-4.01)^2+(3.7-4.01)^2+(4.7-4.01)^2+(3.4-4.01)^2 \end{gathered}[/tex][tex]\begin{gathered} =0.2601+0.0001+0.1681+0.0001+1.9881+2.5921+7.7841+0.7921+0.2401 \\ +1.9321+0.0961+1.2321+0.0961+0.4761+0.3721 \end{gathered}[/tex][tex]=18.0295[/tex]The formula for the statndard deviation is,
[tex]\sigma=\sqrt[]{\frac{\sum ^n_{i\mathop=1}(x_i-\mu)^2}{n-1}}[/tex]Substitute the values in the formula to determine the standard deviation of the data.
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{18.0295}{15-1}} \\ =\sqrt[]{\frac{18.0295}{14}} \\ =1.1348 \\ \approx1.13 \end{gathered}[/tex]Answer:
Mean: 4.01
Standard deviation: 1.13