Question

Help please and Thank you.

A classroom full of statistics students took an exam. This data is a random sample of 19 student exam scores from that class:
59, 92, 66, 46, 90, 98, 95, 79, 70, 92, 75, 90, 63, 80, 92, 89, 85, 79, 63
Give the five number summary of this data set.
a. 46, 66, 80, 92, 98
b. 46, 14.52, 79.16, 80, 98
c. 46, 66, 79.16, 92, 98
d. 0, 1, 79.16, 99, 100

Answer 1

The five number summary of the 19 student exam scores is a)46, 66, 80, 92, and 98, which corresponds to the minimum, first quartile, median, third quartile, and maximum of the data set.

Step-by-step explanation:

The five number summary of a data set includes the minimum value, first quartile (Q1), median (second quartile or Q2), third quartile (Q3), and the maximum value. To compute this for the provided data set of 19 student exam scores, we first need to arrange the scores in ascending order and then find the various quartiles.

1. Firstly, arrange the scores: 46, 59, 63, 63, 66, 70, 75, 79, 80, 85, 89, 90, 90, 92, 92, 92, 95, 98.
2. Minimum value (Min) is the smallest number in the data set, which is 46.
3. Maximum value (Max) is the largest number in the data set, which is 98.
4. The median (Q2) is the middle score, for an odd number of data points, which in this case is the 10th score: 80.
5. Q1 is the median of the first half of the data (excluding the median if odd number of scores), so the 5th score for 19 data points: 66.
6. Q3 is the median of the second half of the data (excluding the median if odd number of scores), so the 15th score for 19 data points: 92.

The five number summary is 46, 66, 80, 92, and 98; hence, the correct answer is option (a).