Question

15 students received the following scores on a quiz. 6, 7, 2, 10, 8, 6, 7, 3, 9, 5, 5, 8, 9, 8, 4

1. What is the cumulative frequency for students who scored 6?

2. How many students scored between 7 and 10?

3. What is the cumulative percentage for students who scored 9?

4. A student who received a score of 7 would be at what percentile? (approximately)

Answer 1

Sorting the given data in an ascending order:

2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10

Total frequency = n =15

Frequency distribution table:

Score	Frequency
2	1
3	1
4	1
5	2
6	2
7	2
8	3
9	2
10	1
Total	15

1.

The cumulative frequency for students who scored 6 =The sum of frequencies up to 6 =7

2.

The number of students who scored between 7 and 10(inclusive) = n - cumulative frequency up to 6 = 15 - 7 =8

3.

The cumulative percentage for students who scored 9 =The cumulative frequency for students who scored 9 ÷ n =The sum of frequencies up to 9 ÷ 15 =14 ÷ 15 =0.9333

4.

Percentile for x =7 =(number of scores below 7/total number of scores)*100 =(cumulative frequency up to 6/n)*100 =(7/15)*100 =46.6667 rounded to 47.

Thus, a student who received a score of 7 would be at 47^th percentile.