Question

multiple choice
for what value of x will the data set below have a mean of 33?
23, 26, 38, 42, 35, 31, x
a x = 36
b x = 39
c x = 33

Explanation:

Step1: Recall the formula for the mean

The mean $\bar{x}$ of a data set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 7$ and $\bar{x}=33$. So, $\sum_{i=1}^{7}x_i=33\times7$.

Step2: Calculate the sum of the known values

Sum of known values: $23 + 26+38 + 42+35+31=(23 + 26)+(38 + 42)+(35 + 31)=49+80 + 66=195$.

Step3: Solve for $x$

We know that $195+x=33\times7$. Since $33\times7 = 231$, then $x=231-195$. So, $x = 36$.

Answer:

A. $x = 36$