Twelve college students were surveyed about the distance from their house to
the college they attended.
12 18 54
13 15 24
8 5 14
27 1 20
1. Using the data set above, find the percentile ranking for the data point 24.
2. Using the data set above, what distance corresponds to the 58th percentile?
3. Using the data set above, calculate the three quartiles. Q1, Q2, and Q3
1. Is this correct? 10/12=.83 =83rd percentile.
2. Is this correct? .58*12=6.9=7;7/12=58th percentile, 7th number = 15
15 corresponds to 58th percentile
3. Q1=10; Q2=14.5; Q3=22
To find the answers to these questions, you can follow the steps below:
1. To determine the percentile ranking for the data point 24, you need to calculate the percentage of data points that are less than or equal to 24. Follow these steps:
a. Sort the data set in ascending order:
1, 5, 8, 12, 13, 14, 15, 18, 24, 27, 54.
b. Count the number of data points that are less than or equal to 24. In this case, there are 8 data points.
c. Divide the count by the total number of data points (12) and multiply by 100 to get the percentile ranking:
(8/12) * 100 = 66.67%
Therefore, the percentile ranking for the data point 24 is approximately 66.67%.
2. To find the distance that corresponds to the 58th percentile, you need to identify the data point that separates the lower 58% of the data from the upper 42%. Follow these steps:
a. Calculate the index corresponding to the 58th percentile. To do this, multiply 58 by the total number of data points (12) and divide by 100:
(58 * 12) / 100 = 6.96
b. Round the index up to the next whole number. In this case, round up 6.96 to 7.
c. Locate the 7th data point in the sorted data set. In this case, it is 15.
Therefore, the distance that corresponds to the 58th percentile is 15.
3. To calculate the three quartiles (Q1, Q2, and Q3), you need to divide the sorted data set into four equal parts. Follow these steps:
a. Identify the index positions for the quartiles. Q1 corresponds to the 25th percentile, Q2 corresponds to the 50th percentile (or the median), and Q3 corresponds to the 75th percentile.
b. Calculate the index positions as follows:
- Q1: (25 * 12) / 100 = 3
- Q2: (50 * 12) / 100 = 6
- Q3: (75 * 12) / 100 = 9
c. Locate the data points corresponding to the calculated index positions in the sorted data set:
- Q1: 8
- Q2: 15
- Q3: 27
Therefore, the three quartiles are Q1 = 8, Q2 = 15, and Q3 = 27.