Question

basic measures of center -2 score: 5.94/23 answered: 0/4 progress saved done question 1 7 pts 0 - 1 details use the appropriate formulas and methods to answer the following questions. do not use technology as an aid, unless otherwise stated. part 1 of 6 hint 1 hint 2 hint 3 hint 4 hint 5 below are iq scores from 30 randomly selected adults. { 83, 85, 88, 89, 91, 92, 93, 95, 96, 96, 97, 100, 100, 101, 102, 103, 104, 106, 106, 109, 110, 110, 111, 111, 112, 120, 122, 122, 122, 130 }. first, give the mean of the data set. 104.2 part 2 of 6 next, give the median 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 $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here $n = 30$.

Step2: Calculate the sum of the data - set

$\sum_{i=1}^{30}x_i=83 + 85+88 + 89+91+92+93+95+96+96+97+100+100+101+102+103+104+106+106+109+110+110+111+111+112+120+122+122+122+130=3126$.

Step3: Calculate the mean

$\bar{x}=\frac{3126}{30}=104.2$.

Step4: Recall median formula for $n$ even

Since $n = 30$ (even), the median $M$ is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$ - th ordered data - values.

Step5: Identify the positions

$\frac{n}{2}=\frac{30}{2}=15$ and $\frac{n}{2}+1 = 16$.

Step6: Find the 15 - th and 16 - th ordered values

The 15 - th value is $102$ and the 16 - th value is $103$.

Step7: Calculate the median

$M=\frac{102 + 103}{2}=\frac{205}{2}=102.5$.

Answer:

102.5