Question

complete the table. round values to the nearest tenth as needed. midpoint x 70.5 92.5 114.5 136.5 158.5 x - x̄ -39.6 -17.6 4.4 26.4 48.4 (x - x̄)² 1568.2 309.8 19.4 697.0 2342.6 (x - x̄)²f 4704.6 4337.2 504.4 2788.0 7027.8 σ(x - x̄)²f = 19362.0 find the sample standard deviation of the data set. s = □ (round to the nearest hundredth as needed.)

Explanation:

Step1: Recall sample - standard - deviation formula

The formula for the sample standard deviation $s$ is $s=\sqrt{\frac{\sum(x - \bar{x})^2f}{n - 1}}$, where $\sum(x - \bar{x})^2f$ is the sum of the weighted squared - deviations, and $n$ is the number of data points. Here, $\sum(x - \bar{x})^2f=19362.0$. Assume the number of data points $n = 5$ (since there are 5 mid - points).

Step2: Calculate the sample standard deviation

Substitute into the formula: $s=\sqrt{\frac{19362.0}{5 - 1}}=\sqrt{\frac{19362.0}{4}}=\sqrt{4840.5}\approx69.57$.

Answer:

$69.57$