Question

Sixty students were given a history exam. Their scores are shown below, sorted from smallest to largest

16 28 29 34 35

37 37 39 39 40

41 42 43 43 46

47 53 65 70 72

73 74 74 74 74

75 76 77 78 78

78 79 79 79 79

79 80 81 81 81

81 81 82 82 82

82 82 82 83 83

83 83 83 83 85

86 87 87 88 94

1) Compute the 5-number summary for this data:

Answer 1

The 5-number summary refers to:

1. Minimum = 16
2. First Quartile (Q1) = 46.5
3. Median = 78
4. Third Quartile (Q3) = 82
5. Maximum = 94

See the explanation section for details

Explanation:

The 5-number summary refers to:

1. Minimum = 16
2. First Quartile (Q1) = 46.5
3. Median = 78
4. Third Quartile (Q3) = 82
5. Maximum = 94

1. Minimum is 16. Since the number is already arranged in ascending order.

2. First Quartile is defined as the median of the lower half.

`Q1 = (46 + 47)/(2)  = 46.5`

46 and 47 are the median of the first half of the score, that is 15th and 16th score.

3. Median is the sum of the 30th and 31th score divide by two, which is 78 and 78.

Median =
`(78 + 78)/(2)  = (156)/(2)  = 78`

4. Third quartile is define as the median of the upper half.

`Q3 = (82 + 82)/(2)  = 82`

82 and 82 are the median of the upper half of the score, that is 45th and 46th score.

5. Maximum is 94.