Question

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.
102
part 3 of 6
now give the mode of the data set. if there is more than one, write them in order, separated by commas.
122
part 4 of 6
finally, give the midrange of the data set.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 30$ and $x_{i}$ are the data - points.
$\sum_{i=1}^{30}x_{i}=83 + 85+88 + 89+91+92+93+95+96+96+97+100+100+101+102+103+104+106+106+109+110+110+111+111+112+120+122+122+122+130=3126$.
$\bar{x}=\frac{3126}{30}=104.2$.

Step2: Calculate the median

Since $n = 30$ (an even number), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered data - points.
The 15 - th value is 102 and the 16 - th value is 103.
Median$=\frac{102 + 103}{2}=102.5$.

Step3: Calculate the mid - range

The mid - range is calculated as $\frac{\text{Minimum value}+\text{Maximum value}}{2}$.
The minimum value is 83 and the maximum value is 130.
Mid - range$=\frac{83+130}{2}=\frac{213}{2}=106.5$.

Answer:

Part 1 of 6: 104.2
Part 2 of 6: 102.5
Part 3 of 6: 122
Part 4 of 6: 106.5