The following data represents Total Credit Hours from our class survey.
90 54 98 45 65 43 12 48 56 12 15 60 38 18 67 125 50 43 26 64 22 52 69
You may use your calculator to find the following statistics:
Considering the Total Credit Hours data from our class survey:
(A1) What percent of the data should be less than Q3 on all box plots? ___________
(A2) What percent of this data is actually less than Q3 ? ___________
(B1) What percent of the data should be between Q1 and Q3 on all box plots? ___________
(B2) What percent of this data is actually between Q1 and Q3? ___________
If the percentages are not the same in (A) or (B) above, why is this happening?
To find the answers to these questions, we will first need to determine the quartiles (Q1, Q3) for the Total Credit Hours data. Once we have the quartiles, we can then calculate the percentages.
Let's start by finding the quartiles:
Step 1: Sort the data in ascending order:
12 12 15 18 22 26 38 43 43 45 48 50 52 54 56 60 64 65 67 69 90 98 125
Step 2: Find the median (Q2), which is the middle value of the data set:
Q2 = 52 (the 11th value in the sorted data set)
Step 3: Find Q1, which is the median of the lower half of the data set:
Q1 = 26 (the median of the first half of the sorted data set: 12 12 15 18 22 26)
Step 4: Find Q3, which is the median of the upper half of the data set:
Q3 = 65 (the median of the second half of the sorted data set: 43 43 45 48 50 52 54 56 60 64 65)
Now that we have the quartiles, we can calculate the percentages:
(A1) What percent of the data should be less than Q3 on all box plots?
To find this percentage, we need to count the number of data points that are less than Q3. In this case, all the data points less than Q3 (65) should be included. Counting the data points, we find that there are 11 data points less than Q3.
The total number of data points is 23 (from the sorted data set). To find the percentage, divide the number of data points less than Q3 (11) by the total number of data points (23), and then multiply by 100:
(11/23) * 100 = 47.83%
So, the answer to (A1) is 47.83%.
(A2) What percent of this data is actually less than Q3?
To find this percentage, we need to count the number of data points in the original data set that are less than Q3 (65). Counting the data points, we find that there are 17 data points less than Q3.
The total number of data points in the original data set is 23. To find the percentage, divide the number of data points less than Q3 (17) by the total number of data points (23), and then multiply by 100:
(17/23) * 100 = 73.91%
So, the answer to (A2) is 73.91%.
(B1) What percent of the data should be between Q1 and Q3 on all box plots?
To find this percentage, we need to count the number of data points between Q1 (26) and Q3 (65). Counting the data points, we find that there are 17 data points between Q1 and Q3.
The total number of data points is 23. To find the percentage, divide the number of data points between Q1 and Q3 (17) by the total number of data points (23), and then multiply by 100:
(17/23) * 100 = 73.91%
So, the answer to (B1) is 73.91%.
(B2) What percent of this data is actually between Q1 and Q3?
To find this percentage, we need to count the number of data points in the original data set that are between Q1 (26) and Q3 (65). Counting the data points, we find that there are 17 data points between Q1 and Q3.
The total number of data points in the original data set is 23. To find the percentage, divide the number of data points between Q1 and Q3 (17) by the total number of data points (23), and then multiply by 100:
(17/23) * 100 = 73.91%
So, the answer to (B2) is 73.91%.
If the percentages are the same in (A) and (B) above, it means that all the data points in the original data set are between Q1 and Q3. However, if the percentages are different, it indicates that there are outliers present in the data set (data points outside the range of Q1 and Q3), which is causing the difference in percentages.