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.

Explanation:

Step1: Calculate the sum of data

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

Step2: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 30$. So $\bar{x}=\frac{2880}{30}=96$

Step3: Recall the concept of median

For a data - set with $n = 30$ (an even number of data points), 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 98 and 99, so the median $M=\frac{98 + 99}{2}=98.5$

Step4: Determine the mode

The mode is the data value that appears most frequently. Here, 98 appears 3 times, more frequently than any other value, so the mode is 98.

Step5: Calculate the mid - range

The mid - range is $\frac{\text{min}+\text{max}}{2}$, where $\text{min}=60$ and $\text{max}=125$. So the mid - range $=\frac{60 + 125}{2}=92.5$

Step6: Analyze the distribution shape

Since the mean ($96$) is less than the median ($98.5$), the distribution will probably be skewed to the left.

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.