Question

A group of students were given a spelling test.

The table shows their marks.
a) Work out the range of the marks.
b) How many students are in the group?
c) Work out the mean mark of the group.
Mark
6
7
8
9
10
Frequency
5
4
7
10
4

Answer 1

1. 4
2. 30 students
3. 8.1

Explanation:

Range of data :

• Maximum value - Minimum value
• 10 - 6
• 4

Students in the group :

• Sum of frequencies
• 5 + 4 + 7 + 10 + 4
• 9 + 7 + 10 + 4
• 16 + 10 + 4
• 26 + 4
• 30 students

Mean mark :

• 6(5) + 7(4) + 8(7) + 9(10) + 10(4) / 30
• 30 + 28 + 56 + 90 + 40
• 160 + 84 / 30
• 244/30
• 8.1

Answer 2

a) 4

b) 30

c) 8

Explanation:

The range is the difference between the biggest and the smallest number. The biggest mark is 10, and the smallest mark is 6.

⇒ Range = 10 - 6 = 4

To calculate how many students are in the group, add the values in the frequency column:

⇒ Total number of students = 5 + 4 + 7 + 10 + 4 = 30

To calculate the mean mark of the group, multiply each mark by its frequency, add these up, then divide by the total number of students:

⇒ Mean Mark = [ (6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + (10 × 4) ] ÷ 30

= [ 30 + 28 + 56 + 90 + 40 ] ÷ 30

= 244 ÷ 30

= 8.1333333333...

= 8 (nearest whole number)