Question

below are iq scores from 30 randomly selected adults. { 77, 80, 84, 85, 86, 88, 93, 95, 96, 100, 104, 104, 105, 107, 107, 107, 108, 108, 108, 108, 110, 111, 112, 113, 114, 114, 118, 120, 132, 137 }. first, give the mean of the data set.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, where $n$ is the number of data points and $\sum_{i=1}^{n}x_i$ is the sum of the data points. Here $n = 30$.

Step2: Calculate the sum of data points

$\sum_{i=1}^{30}x_i=77 + 80+84 + 85+86+88+93+95+96+100+104+104+105+107+107+107+108+108+108+108+110+111+112+113+114+114+118+120+132+137$
$=3108$.

Step3: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{30}x_i}{30}=\frac{3108}{30}=103.6$.

Answer:

$103.6$