Question

score: 5.94/23 answered: 0/4 progress saved done √0 use the appropriate formulas and methods to answer the following questions. do not use technology as an aid, unless otherwise stated. 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 next, give the median of the data set. 102 now give the mode of the data set. if there is more than one, write them in order, separated by commas.

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 $\frac{30}{2}=15$ - th and $15 + 1=16$ - th ordered data - points are 102 and 103.
Median $=\frac{102 + 103}{2}=102.5$.

Step3: Calculate the mode

The mode is the data - point(s) that occur most frequently.
The number 122 appears 3 times, which is more frequently than any other number. So the mode is 122.

Answer:

Part 1: 104.2
Part 2: 102.5
Part 3: 122