Question

three students found the mean of the data set given. their work is shown below. choose the student who correctly found the mean.
10, 10, 13, 14, 16, 19, 23
naeem’s work
10 + 10 + 13 + 14 + 16 + 19 + 23
7
= 105
7 = 15
preston’s work
10 + 13 + 14 + 16 + 19 + 23
6
= 95
6 = 15.8
calida’s w
10 - 23
2
= 33
2 =

Explanation:

Step1: Recall the formula for mean

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

Step2: Count the number of data points

The data set is \(10,10,13,14,16,19,23\). The number of data points \(n = 7\).

Step3: Calculate the sum of the data points

\(\sum_{i=1}^{7}x_i=10 + 10+13 + 14+16+19+23=(10 + 10)+(13 + 14)+(16 + 19)+23=20+27+35+23=105\).

Step4: Calculate the mean

Using the formula \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), with \(n = 7\) and \(\sum_{i=1}^{7}x_i = 105\), we get \(\bar{x}=\frac{105}{7}=15\).

Answer:

Naeem's Work is correct.