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. next, give the median of the data set. now give the mode of the data set. if there is more than one, write them in order, separated by commas. finally, give the mid - range of the data set. given the relationship between the mean and median above, what shape is the distribution likely to be? suppose the first value in the data set is mistakenly recorded as 0.0. how would this affect the mean? how would this affect the median?

Explanation:

Step1: Calculate the original mean

The sum of the original data set $\sum x = 60+70 + 79+79+81+82+83+84+91+94+95+96+99+101+101+104+104+106+107+107+108+110+111+112+114+115+118+124+124+124=3009$. There are $n = 30$ data - points. The original mean $\bar{x}=\frac{\sum x}{n}=\frac{3009}{30}=100.3$.

Step2: Analyze the effect on the mean when the first value changes

The original first - value is $60$. If it is changed to $0$, the new sum $\sum x_{new}=3009 - 60+0=2949$. The new mean $\bar{x}_{new}=\frac{2949}{30}=98.3$. Since $98.3<100.3$, the mean would get smaller.

Step3: Analyze the effect on the median when the first value changes

The original data set has $n = 30$ data - points. The median is the average of the 15th and 16th ordered data - points. Changing the first value from $60$ to $0$ does not change the position of the 15th and 16th ordered data - points. So the median would not change.

Answer:

For the question "How would this affect the mean?": The mean would get smaller.
For the question "How would this affect the median?": The median would not change.