Averages and Range (Copy)

Q1 (Non-Calculator)
Find the mean of the data set: 4, 6, 8, 10, 12.

Solution:
Mean = (4 + 6 + 8 + 10 + 12) ÷ 5
= 40 ÷ 5
= 8

Answer:
8

Q2 (Non-Calculator)
Find the median of the data set: 7, 3, 5, 9, 1.

Solution:
First, order the data: 1, 3, 5, 7, 9
Median = middle value = 5

Answer:
5

Q3 (Non-Calculator)
Find the mode of the data set: 2, 4, 4, 5, 7, 7, 7, 9.

Solution:
Most frequent value = 7 (appears 3 times)

Answer:
7

Q4 (Non-Calculator)
Find the range of the data set: 15, 22, 17, 13, 19.

Solution:
Range = Largest – Smallest
Range = 22 – 13 = 9

Answer:
9

Q5 (Non-Calculator)
The table shows the number of books read by students:

Find the mean number of books read.

Solution:
Sum = (1×3) + (2×5) + (3×7) + (4×5)
= 3 + 10 + 21 + 20
= 54

Total frequency = 3 + 5 + 7 + 5 = 20

Mean = 54 ÷ 20
= 2.7

Answer:
2.7

Q6 (Non-Calculator)
Find the median number of books from Q5.

Solution:
Total students = 20
Median position = (20 + 1) ÷ 2 = 10.5th value → average of 10th and 11th values.

Cumulative frequencies:

• 1 book: 3 students
• 2 books: 8 students (3 + 5)
• 3 books: 15 students (8 + 7)

10th and 11th students are in the 3 books category.

Answer:
3 books

Q7 (Calculator)
Find the mode of the data in Q5.

Solution:
Highest frequency = 7 (for 3 books)

Answer:
3 books

Q8 (Calculator)
Find the range of number of books read from Q5.

Solution:
Highest number of books = 4
Lowest number of books = 1
Range = 4 – 1 = 3

Answer:
3

Q9 (Calculator)
A set of data has mean 15 and 8 values. Find the total sum of the data.

Solution:
Total = mean × number of values
Total = 15 × 8 = 120

Answer:
120

Q10 (Calculator)
The ages of five people are: 12, 15, 17, 20, 25.
Find the mean and range.

Solution:
Mean = (12 + 15 + 17 + 20 + 25) ÷ 5
= 89 ÷ 5
= 17.8

Range = 25 – 12 = 13

Answer:
Mean = 17.8, Range = 13