Question

The data represents the semester exam scores of 8 students in a math course. {51,91,46,30,36,50,73,80} What is the five-number summary?

Answer 1

minimum = 30, Q1 = 36, median = 50.5, Q3 = 80, and maximum = 91.

Explanation:

We are given the following data set for the exam scored of 8 students in a math course and we are to find the five number summary:

51, 91, 46, 30, 36, 50, 73, 80

Step 1: For that, we first need to rearrange in an ascending order:

30, 36, 46, 50, 51, 73, 80, 91

Step 2: Now we will spot the smallest and largest number in the data.

Smallest number: 30

Largest number: 91

Step 3: Finding the median (middle number) now:

Median = 50+51/2 = 50.5

Step 4: Placing parenthesis around the number before and after the median values:

(30, 36, 46) 50, 51 (73, 80, 91)

Find Q1 (median in the lower half of the data) and Q3 (median for the upper half of data):

Q1 = 36

Q3 = 80

Five step summary:

minimum = 30, Q1 = 36, median = 50.5, Q3 = 80, and maximum = 91.

Answer 2

Minimum = 30, Maximum = 91, Median = 50.5, Q₁ = 36, Q₃ = 80

Explanation:

We have to find the five-number summary of the given data represents the semester exam scores of 8 students in a math course.

The five-number summary includes 5 items:

1. The minimum

2. Q₁ (First quartile)

3. Median

4. Q₃ (Third quarlile)

5. The maximum

First we put the numbers in ascending order (lowest to highest)

30, 36, 46, 50, 51, 73, 80, 91

Now find the minimum and maximum from your data set.

Minimum = 30 and Maximum = 91

Now find the median, median is the middle number. But we have 50, 51 two middle numbers so we take the median of those numbers =

Median =
`((50+51))/(2)` = 50.5

Median = 50.5

Now place parenthesis around the numbers before and after the median values

30, 36, 46, 50, 51, 73, 80, 91

Median of lower half of the data Q₁ = 36

Median of upper half of the data Q₃ = 80

Five-number summary found

Minimum = 30, Maximum = 91, Median = 50.5, Q₁ = 36, Q₃ = 80