four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. which student found the correct…

four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. which student found the correct mean?\nashritas work:\n$\frac{26 + 31+39 + 30+16 + 16+18 + 38}{8}=\frac{214}{8}=26.75$\ncollettes work:\n$\frac{26 + 38}{2}=\frac{64}{2}=32$\ndaniels work:\n$\frac{26+31 + 39+30 + 16+18 + 38}{7}=\frac{198}{7}=28.29$\nloras work:\n$\frac{30 + 16}{2}=\frac{46}{2}=23$

four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. which student found the correct mean?\nashritas work:\n$\frac{26 + 31+39 + 30+16 + 16+18 + 38}{8}=\frac{214}{8}=26.75$\ncollettes work:\n$\frac{26 + 38}{2}=\frac{64}{2}=32$\ndaniels work:\n$\frac{26+31 + 39+30 + 16+18 + 38}{7}=\frac{198}{7}=28.29$\nloras work:\n$\frac{30 + 16}{2}=\frac{46}{2}=23$

Answer

Answer:

Ashrita's work: $\frac{26 + 31+39+30 + 16+16+18+38}{8}=\frac{214}{8}=26.75$

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ 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 and $\sum_{i = 1}^{n}x_i$ is the sum of the data points.

Step2: Count number of data points

The data - set is $26,31,39,30,16,16,18,38$. Here $n = 8$.

Step3: Calculate sum of data points

$26+31+39+30+16+16+18+38=214$.

Step4: Calculate the mean

$\bar{x}=\frac{214}{8}=26.75$. Ashrita correctly used the formula for the mean by adding all 8 data points and dividing by 8. Collette only averaged two values, Daniel divided by 7 instead of 8, and Lora only averaged two values.