Question

QuestionThe following datavalues represent the daily amount spent by a family during a 7 day summer vacation.Find the population standard deviation of this dataset:$96, $125, $80, $110, $75, $100, $121(Round your answer to 1 decimal place).

Answer 1

Answer:

17.7

Explanation:

Given the dataset:

$96, $125, $80, $110, $75, $100, $121

To find the population standard deviation, use the formula:

$\sigma=\sqrt{\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}}$

Step 1: Find the mean

$\begin{gathered} \text{Mean,}\mu=\frac{96+125+80+110+75+100+121}{7} \\ =\frac{707}{7} \\ =101 \end{gathered}$

Step 2: Subtract the mean from each data point, square it and add them up:

$\begin{gathered} (96-101)^2+(125-101)^2+(80-101)^2+(110-101)^2 \\ ^{}+\mleft(75-101\mright)^2+\mleft(100-101\mright)^2+\mleft(121-101\mright)^2 \\ =25+576+441+81+676+1+400 \\ \sum (x_i-\mu)^2=2200 \end{gathered}$

Step 3: Divide the sum by the number of data points in the population. The result is called the variance.

$\frac{\sum(x_i-\mu)^2}{N}=\frac{2200}{7}$

Step 4: Take the square root of the variance to get the standard deviation.

$\begin{gathered} \sigma=\sqrt[]{\frac{2200}{7}} \\ \sigma=17.7\text{ (to 1 decimal place)} \end{gathered}$