Final answer:
The mode of the data set is 7, the median is 7, the mean is 7.25, the range is 6, the 5-number summary is 4, 6.5, 7, 8.5, 10, and the IQR is 2.
Step-by-step explanation:
The given data set is:
4, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10
To find the mode, we look for the value(s) that appears most frequently. In this data set, the mode is 7, as it appears 6 times.
To find the median, we arrange the data set in ascending order. Since there are 16 data points, the median will be the average of the 8th and 9th values, which are both 7. Therefore, the median is 7.
To find the mean, we add up all the values and divide by the total number of values. The sum of the data set is 116, and there are 16 data points. Therefore, the mean is 7.25.
The range is found by subtracting the smallest value from the largest value. The smallest value is 4 and the largest value is 10, so the range is 6.
The 5-number summary consists of the minimum value (4), the first quartile (6.5), the median (7), the third quartile (8.5), and the maximum value (10).
To find the IQR (interquartile range), we subtract the first quartile from the third quartile. Therefore, the IQR is 2.