Question

The list contains 42 Test 3 scores from a section of MA 110.

35, 43, 44, 44, 45, 46, 48, 50, 53, 54, 54, 55, 56, 57, 62, 64, 65, 66, 67, 69, 75, 76, 77, 78, 78, 81, 83, 84, 85, 86, 86, 89, 89, 92, 93, 94, 97, 98, 100, 100, 100, 100

1. How do I divide the scores into four equal parts, and draw three lines to show this ?

2. How do I calculate the values for each of the three lines?

3. If I scored an 85, what percent of the class did I do better than?

Answer 1

The list can be divided into the following

Since there are 42 data points and we need to divide into 4 equal parts

We follow the quartile sytem where the data is divided into

First quartile = 54.25

Second Quartile = 75.5

Third Quartile = 88.25

Question 1

We have marked the lines where the quartiles divide into 4 parts

Queston 2

The formula for calculating quartiles is

Q1 = 1/4 * (n+1) th data point = 1/4 *43 =10.75 th data point = 54.25

Q2 = 2/4 *(n +1) th data point = 1/2*43 = 21.5 th data point = 75.5

Q3 = 3/4*(n+1) th data point = 3/4*43 = 32.25 th data point = 88.25

Question 3

Score = 85

As the score of 85 is the 29 th data point we have

32.25		75%
29		0.674419

Hence a score of 85 means that you  did better than 67.44% of the class