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. (2 points)
To find the Mean, Median, Mode, and Quartiles of the data set, let's begin by arranging the data set in ascending order:
11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23
Mean:
To find the mean, we add up all the numbers and divide by the total number of values:
Mean = (11 + 15 + 15 + 15 + 16 + 17 + 18 + 19 + 20 + 22 + 23) / 11
Mean = 191 / 11
Mean = 17.36
Median:
The median is the middle number of the set when arranged in ascending order. Since we have an odd number of values, the median would be the middle value, which is the 6th value in the data set:
Median = 17
Mode:
The mode is the number that appears most frequently in the data set. In this case, 15 appears most frequently (3 times) compared to other numbers in the data set:
Mode = 15
Quartiles:
To find the quartiles, we need to first find the median of the lower half (Q1) and upper half (Q3) of the data set.
Q1 is the median of the lower half: 11, 15, 15, 15, 16
Q1 = 15
Q3 is the median of the upper half: 18, 19, 20, 22, 23
Q3 = 20
Therefore, the Mean is 17.36, the Median is 17, the Mode is 15, Q1 is 15, and Q3 is 20.