below are iq scores from 30 randomly selected adults. { 78, 82, 88, 88, 89, 93, 97, 98, 98, 98, 100, 101…

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 30$ and $x_{i}$ are the data - points. $\sum_{i=1}^{30}x_{i}=78 + 82+88+88+89+93+97+98+98+98+100+101+101+102+103+104+106+106+107+109+110+115+116+118+118+119+119+122+128+130=3120$ $\bar{x}=\frac{3120}{30}=104$

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 15th and 16th ordered data - points are 103 and 104. So, median$=\frac{103 + 104}{2}=103.5$

Step3: Find the mode

The mode is the data - point that appears most frequently. The number 98 appears 3 times, more frequently than any other number, so the mode is 98.

Step4: Calculate the mid - range

The mid - range is calculated as $\frac{\text{Minimum value}+\text{Maximum value}}{2}$. The minimum value is 78 and the maximum value is 130. So, mid - range$=\frac{78 + 130}{2}=104$

Step5: Determine the shape of the distribution

The mean ($\bar{x}=104$) is greater than the median ($103.5$). In a right - skewed distribution, the mean is typically greater than the median because the long tail on the right pulls the mean in that direction.

Answer:

Part 1: 104 Part 2: 103.5 Part 3: 98 Part 4: 104 Part 5: The distribution will probably be skewed to the right.