Question

hint 1 hint 2 hint 3 hint 4 hint 5
below are iq scores from 30 randomly selected adults.
{ 60, 63, 78, 81, 83, 84, 85, 91, 92, 93, 94, 97, 98, 98, 98, 99, 101, 102, 103, 107, 109, 109, 110, 112, 113, 114, 114, 121, 121, 125 }.
first, give the mean of the data set.
103
×
part 2 of 6
next, give the median of the data set.
98.5
✓
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.
98
✓
part 4 of 6
finally, give the midrange of the data set.
92.5
✓
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.
×
part 6 of 6
suppose the first value in the data set is mistakenly recorded as 0.0.
how would this affect the mean?
the mean would get larger.
the mean would not change.
the mean would get smaller.
how would this affect the median?
the median would get smaller.
the median would not change.
the median would get larger.

Explanation:

Step1: Calculate the sum of data

Sum = $60 + 63+78 + 81+83+84+85+91+92+93+94+97+98+98+98+99+101+102+103+107+109+109+110+112+113+114+114+121+121+125=2880$

Step2: Calculate the mean

Mean = $\frac{2880}{30}=96$

Step3: Find the median

Since $n = 30$ (even), median is the average of the 15th and 16th - ordered values. The ordered data set: 60, 63, 78, 81, 83, 84, 85, 91, 92, 93, 94, 97, 98, 98, 98, 99, 101, 102, 103, 107, 109, 109, 110, 112, 113, 114, 114, 121, 121, 125. The 15th value is 98 and the 16th value is 99. Median=$\frac{98 + 99}{2}=98.5$

Step4: Find the mode

The mode is the most - frequently occurring value. Here, 98 occurs 3 times, more frequently than any other value, so mode = 98

Step5: Calculate the mid - range

Mid - range=$\frac{\text{Minimum value}+\text{Maximum value}}{2}=\frac{60 + 125}{2}=92.5$

Step6: Analyze the distribution shape

Since mean ($96$) < median ($98.5$), the distribution is probably skewed to the left.

Step7: Analyze the effect on the mean

The original sum is 2880. If the first value is changed from 60 to 0, the new sum is $2880-60 + 0=2820$. The new mean is $\frac{2820}{30}=94$. So the mean would get smaller.

Step8: Analyze the effect on the median

Since the median is the average of the 15th and 16th ordered values and changing the first value (the smallest value) does not change the 15th and 16th ordered values in the ordered data - set, the median would not change.

Answer:

Part 1: 96
Part 2: 98.5
Part 3: 98
Part 4: 92.5
Part 5: The distribution will probably be skewed to the left.
Part 6: The mean would get smaller.
Part 7: The median would not change.