Question

7 average each group of numbers.
a. 110; 99; 125; 59;
175; 113; 121; 90; 89
b. 57; 48; 59; 41; 70

Explanation:

Step1: Recall the formula for the average

The formula for the average (mean) of a set of numbers \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), where \(\sum_{i=1}^{n}x_i=x_1 + x_2+\cdots+x_n\) and \(n\) is the number of data - points.

Step2: Calculate the average for part a

For the set of numbers \(a:110,99,125,59\), \(n = 4\) and \(\sum_{i=1}^{4}x_i=110 + 99+125 + 59\).

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Using the formula \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), we have \(\bar{x}=\frac{393}{4}=98.25\)

Step3: Calculate the average for part b

For the set of numbers \(b:57,48,59,41,70\), \(n = 5\) and \(\sum_{i=1}^{5}x_i=57 + 48+59+41+70\).

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Using the formula \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), we have \(\bar{x}=\frac{275}{5}=55\)

Answer:

a. \(98.25\)
b. \(55\)