Sixty students were given a history exam. Their scores are shown below, sorted from smallest to largest.
6 36 36 38 38
39 39 40 41 41
42 42 42 45 49
50 53 65 66 71
72 72 72 73 74
76 76 76 78 78
79 79 80 80 81
81 81 81 81 82
82 82 82 83 83
83 84 84 85 86
86 87 87 88 88
89 89 89 89 94
1) Compute the 5-number summary for this data:
You have to be kidding.
http://www.easycalculation.com/statistics/five-number-summary.php
To compute the 5-number summary for this data, you need to find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
1) Minimum: The minimum value is the smallest score, which is 6.
2) Q1 (First Quartile): The first quartile (Q1) is the median of the lower half of the data. To find Q1, count halfway through the data set from the minimum, which gives the position (60 students, so the 30th position). Since the position is an integer, you can take the average of the scores at positions 30 and 31. So, Q1 is the average of 38 and 39, which is 38.5.
3) Q2 (Median): The median (Q2) is the middle value of the data set. Since there are 60 students, the median is the average of the scores at positions 30 and 31. So, Q2 is the average of 50 and 53, which is 51.5.
4) Q3 (Third Quartile): The third quartile (Q3) is the median of the upper half of the data. To find Q3, count halfway through the data set from the median, which gives the position (60 students, so the 45th position). Since the position is an integer, you can take the average of the scores at positions 45 and 46. So, Q3 is the average of 79 and 80, which is 79.5.
5) Maximum: The maximum value is the largest score, which is 94.
Therefore, the 5-number summary for this data set is:
Minimum: 6
Q1: 38.5
Q2: 51.5
Q3: 79.5
Maximum: 94
To compute the 5-number summary for this data, we need to find the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum.
1. Minimum: The minimum value is the smallest score, which is 6 in this case.
2. Q1 (First Quartile): The first quartile is the value that separates the bottom 25% of scores from the remaining 75%. To find Q1, we can use the formula (n + 1) / 4, where n is the number of scores. In this case, n = 60, so (60 + 1) / 4 = 15.25. Since we don't have a score corresponding to the exact position of 15.25, we can take the average of the 15th and 16th smallest scores. In this data set, the 15th and 16th smallest scores are both 38, so Q1 = 38.
3. Q2 (Median): The median is the middle value of the data set when it is arranged in ascending order. Since we have 60 scores, the median would be the average of the 30th and 31st smallest scores. In this case, the 30th and 31st smallest scores are both 72, so Q2 = 72.
4. Q3 (Third Quartile): The third quartile is the value that separates the bottom 75% of scores from the remaining 25%. Using the same formula as before (n + 1) / 4, (60 + 1) * 3 / 4 = 45.75. The 45th and 46th smallest scores are both 83, so Q3 = 83.
5. Maximum: The maximum value is the largest score, which is 94 in this data set.
Therefore, the 5-number summary for this data is:
Minimum: 6
Q1: 38
Q2 (Median): 72
Q3: 83
Maximum: 94.