Question

below are iq scores from 30 randomly selected adults. { 60, 70, 79, 79, 81, 82, 83, 84, 91, 94, 95, 96, 99, 101, 101, 104, 104, 106, 107, 107, 108, 110, 111, 112, 114, 115, 118, 124, 124, 124 }. first, give the mean of the data set. part 2 of 6 next, give the median of the data set. 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. part 4 of 6 finally, give the midrange of the data set. part 5 of 6 given the relationship between the mean and median above, what shape is the distribution likely to be? the distribution will be roughly symmetric. the distribution will probably be skewed to the right. the distribution will probably be skewed to the left.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 30$ and $x_{i}$ are the data - points.
$\sum_{i=1}^{30}x_{i}=60 + 70+79+79+81+82+83+84+91+94+95+96+99+101+101+104+104+106+107+107+108+110+111+112+114+115+118+124+124+124=3009$
$\bar{x}=\frac{3009}{30}=100.3$

Step2: Recall median formula

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 101 and the 16 - th value is 104. Median$=\frac{101 + 104}{2}=102.5$

Step3: Recall mode definition

The mode is the data - point that appears most frequently. 124 appears 3 times, more frequently than any other number, so the mode is 124.

Step4: Recall mid - range formula

The mid - range is calculated as $\frac{\text{Minimum value}+\text{Maximum value}}{2}$. The minimum value is 60 and the maximum value is 124. Mid - range$=\frac{60 + 124}{2}=92$

Step5: Analyze shape based on mean and median

Since the mean ($100.3$) is less than the median ($102.5$), the distribution will probably be skewed to the left.

Answer:

Part 1: 100.3
Part 2: 102.5
Part 3: 124
Part 4: 92
Part 5: The distribution will probably be skewed to the left.