Question

section 3.2 homework
score: 2.92/11 answered: 2/11
question 4
using your calculator, find the range and standard deviation, round to two decimal places.
the table below gives the number of hours spent watching tv last week
49 37 48 59 58 45
44 49 81 53 66 31
89 21 89 81 64 31
87 77 69 80 99 14
range =
standard deviation =

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 $\approx17.13$