Question

section 3.2 homework score: 3.42/11 answered: 3/11 question 4 score on last try: 0.5 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changable > next question get a similar question you can using your calculator, find the range and standard deviation, ro the table below gives the number of hours spent watching tv la 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 = 85 standard deviation = enter an integer or decimal number more...

Explanation:

Step1: Recall range formula

Range = Max - Min

Step2: Find maximum value

Max = 99

Step3: Find minimum value

Min = 14

Step4: Calculate range

Range = 99 - 14 = 85

Step5: Recall standard - deviation formula for sample

For a sample of data \(x_1,x_2,\cdots,x_n\), the sample standard - deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\), where \(\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}\)
First, find the mean \(\bar{x}\):
\(n = 24\)
\(\sum_{i=1}^{24}x_i=49+37+48+59+58+45+44+49+81+53+66+31+89+21+89+81+64+31+87+77+69+80+99+14\)
\(\sum_{i=1}^{24}x_i = 1338\)
\(\bar{x}=\frac{1338}{24}=55.75\)
Then, find \((x_i-\bar{x})^2\) for each \(i\) and sum them up:
\(\sum_{i = 1}^{24}(x_i - 55.75)^2=(49 - 55.75)^2+(37 - 55.75)^2+\cdots+(14 - 55.75)^2\)
\(\sum_{i = 1}^{24}(x_i - 55.75)^2=10779.5\)
\(s=\sqrt{\frac{10779.5}{24 - 1}}=\sqrt{\frac{10779.5}{23}}\approx\sqrt{468.6739}\approx21.64\)

Answer:

Range = 85
Standard Deviation \(\approx21.64\)