section 3.2 homework\nscore: 2.92/11 answered: 2/11\nquestion 4\nusing your calculator, find the range and…

Explanation:

Step1: Find the maximum and minimum values

The maximum value in the data - set is 99 and the minimum value is 14.

Step2: Calculate the range

The formula for the range is $Range = Max - Min$. So, $Range=99 - 14=85$.

Step3: Calculate the mean

The sum of all the data values: $49+37+48+59+58+45+44+49+81+53+66+31+89+21+89+81+64+31+87+77+69+80+99+14 = 1276$. There are $n = 24$ data - points. The mean $\bar{x}=\frac{1276}{24}\approx53.17$.

Step4: Calculate the squared - differences

For each data - point $x_i$, calculate $(x_i-\bar{x})^2$. For example, for $x_1 = 49$, $(49 - 53.17)^2=(-4.17)^2 = 17.3889$. Do this for all 24 data - points and sum them up. The sum of squared differences $\sum_{i = 1}^{n}(x_i-\bar{x})^2=6746.67$.

Step5: Calculate the standard deviation

The formula for the sample standard deviation is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$. Here, $n = 24$, so $s=\sqrt{\frac{6746.67}{23}}\approx\sqrt{293.33}\approx17.13$.

Answer:

Range = 85 Standard Deviation $\approx17.13$