Find the Mean, Median, Mode, and Quartiles of the following data set. Show and explain all your steps in solving. Data Set: 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15 Note: You can do your work on paper and insert the picture by using the picture icon, or sending your work via webmail. (10 points)
To find the mean, add up all the numbers in the data set and then divide by the total number of values:
Mean = (15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15) / 11
Mean = 191 / 11
Mean = 17.36
To find the median, first arrange the numbers in ascending order:
11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23
Since there are 11 numbers, the median is the 6th value in the ordered list:
Median = 17
To find the mode, we look for the number that appears most frequently in the data set:
The number 15 appears three times, which is more than any other number in the set.
Mode = 15
To find the quartiles, we need to first find the median of the lower half (Q1) and the upper half (Q3) of the data set.
Q1 is the median of the lower half of the data set (11, 15, 15, 15, 16).
Q1 = 15
Q3 is the median of the upper half of the data set (18, 19, 20, 22, 23).
Q3 = 20
Therefore, the mean is 17.36, the median is 17, the mode is 15, and the quartiles are Q1=15 and Q3=20.