15. an electric bill is an essential expense. the following is a list of jack’s months: $110, $125, $140…

Explanation:

Step1: Find the range

The range is the difference between the maximum and minimum values. Let the data - set be (x={110, 125, 140, 142, 148, 150}). The maximum value (x_{max}=150) and the minimum value (x_{min}=110). Range (=x_{max}-x_{min}=150 - 110=40)

Step2: Calculate the mean

The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (n = 6) and (\sum_{i=1}^{6}x_{i}=110 + 125+140+142+148+150=715). (\bar{x}=\frac{715}{6}\approx119.17)

Step3: Calculate the squared - differences

((x_1-\bar{x})^2=(110 - 119.17)^2=(- 9.17)^2 = 84.09) ((x_2-\bar{x})^2=(125 - 119.17)^2=(5.83)^2 = 34.00) ((x_3-\bar{x})^2=(140 - 119.17)^2=(20.83)^2 = 433.89) ((x_4-\bar{x})^2=(142 - 119.17)^2=(22.83)^2 = 521.21) ((x_5-\bar{x})^2=(148 - 119.17)^2=(28.83)^2 = 831.17) ((x_6-\bar{x})^2=(150 - 119.17)^2=(30.83)^2 = 950.49)

Step4: Calculate the variance

The variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}) (\sum_{i = 1}^{6}(x_i-\bar{x})^2=84.09+34.00 + 433.89+521.21+831.17+950.49=2854.85) (s^2=\frac{2854.85}{6 - 1}=\frac{2854.85}{5}=570.97)

Step5: Calculate the standard deviation

The standard deviation (s=\sqrt{s^2}) (s=\sqrt{570.97}\approx23.90)

Answer:

a) Range: (40) Standard deviation: (23.90)