2 multiple choice 2.5 points a sample of 12 students was taken from a statistics class and their ages (in…

2 multiple choice 2.5 points a sample of 12 students was taken from a statistics class and their ages (in years) are given below. 18 22 21 19 23 31 19 23 20 18 19 25 find the five - number summary. min = 18, q1 = 19, m = 20, q3 = 23, max = 31 min = 18, q1 = 19.5, m = 21.5, q3 = 24, max = 31 min = 18, q1 = 19, m = 20.5, q3 = 23, max = 31 min = 18, q1 = 20, m = 25, q3 = 19, max = 31

2 multiple choice 2.5 points a sample of 12 students was taken from a statistics class and their ages (in years) are given below. 18 22 21 19 23 31 19 23 20 18 19 25 find the five - number summary. min = 18, q1 = 19, m = 20, q3 = 23, max = 31 min = 18, q1 = 19.5, m = 21.5, q3 = 24, max = 31 min = 18, q1 = 19, m = 20.5, q3 = 23, max = 31 min = 18, q1 = 20, m = 25, q3 = 19, max = 31

Answer

Explanation:

Step1: Order the data

First, we order the given data set: (18, 18, 19, 19, 19, 20, 21, 22, 23, 23, 25, 31)

Step2: Find the minimum (Min) and maximum (Max)

The smallest value is (18) (Min), and the largest is (31) (Max).

Step3: Find the median (M)

Since there are (n = 12) (even) data points, the median is the average of the (\frac{n}{2}=6)th and ((\frac{n}{2}+ 1)=7)th values. The 6th value is (20), the 7th is (21), so (M=\frac{20 + 21}{2}=20.5)

Step4: Find the first quartile (Q1)

The first quartile is the median of the lower half of the data (excluding the median if (n) is even? Wait, for (n = 12), the lower half is the first (6) values: (18, 18, 19, 19, 19, 20). The median of these (6) (even number) is the average of the 3rd and 4th values. The 3rd is (19), the 4th is (19), so (Q1=\frac{19+19}{2}=19)

Step5: Find the third quartile (Q3)

The upper half of the data is the last (6) values: (21, 22, 23, 23, 25, 31). The median of these (6) is the average of the 3rd and 4th values. The 3rd is (23), the 4th is (23), so (Q3=\frac{23 + 23}{2}=23)

Answer:

Min = 18, Q1 = 19, M = 20.5, Q3 = 23, Max = 31 (the third option: Min = 18, Q1 = 19, M = 20.5, Q3 = 23, Max = 31)