Question

below are iq scores from 30 randomly selected adults. { 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 }. 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 probably be skewed to the right. the distribution will probably be skewed to the left. the distribution will be roughly symmetric.

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.