Question

look at the graph below. calculate the standard deviation from the numbers on the graph and enter that number in the box provided. 29 41 53 65 77 89 101 standard deviation σ = ____________

Explanation:

Step1: Identify the mean

The data appears to be symmetrically distributed. The middle - value (mean $\mu$) of the data set $\{29,41,53,65,77,89,101\}$ is 65.

Step2: Calculate the differences from the mean

For 29: $29 - 65=-36$; for 41: $41 - 65=-24$; for 53: $53 - 65=-12$; for 65: $65 - 65 = 0$; for 77: $77 - 65 = 12$; for 89: $89 - 65 = 24$; for 101: $101 - 65 = 36$.

Step3: Square the differences

$(-36)^2=1296$, $(-24)^2 = 576$, $(-12)^2=144$, $0^2 = 0$, $12^2=144$, $24^2 = 576$, $36^2=1296$.

Step4: Calculate the variance

The variance $\sigma^{2}=\frac{1296 + 576+144 + 0+144 + 576+1296}{7}=\frac{4032}{7}=576$.

Step5: Calculate the standard deviation

The standard deviation $\sigma=\sqrt{576}=24$.

Answer:

24