How to Pass Numerical Reasoning (6 page)

Worked example

In her aptitude test, Emma scores 77, 81 and 82 in each section. What is her average (arithmetic mean) score?

Arithmetic mean
= 80

Worked example

What is the arithmetic mean of the following set of numbers: 0, 6, 12, 18?

The arithmetic mean of the set is 36 ÷ 4 = 9.

Tip:
remember to include the zero as a value in your sum of the number of values.

Worked example

What is the value of q if the arithmetic mean of 3, 6, 9 and q = 5.5?

Step 1: Rearrange the formula to help you to find the sum of values

Sum of values = arithmetic mean × number of values

Step 2: Now plug in the numbers

(Don’t forget to count the fourth value
q
in the number of values.)

Sum of values = 22

Step 3: Subtract the sum of known values from the sum of values

Answer
: q = 4

The mode

The mode is the number (or numbers) that appear(s) the most frequently in a set of numbers. There may be more than one mode in a given set of numbers.

Worked example

What is the mode in the following set of numbers?

21, 22, 23, 22, 22, 25, 25, 22, 21

21 appears twice.

22 appears four times.

23 appears once.

25 appears twice.

So the mode is 22 as it appears most frequently.

Worked example

What is the mode in the following set of numbers?

–0.01, 0.01, –0.01, –0.1, 0.01, –0.01, 0.1, 0.01, –0.1

0.1 appears once.

0.01 appears three times.

–0.1 appears twice.

–0.01 appears three times.

So the mode numbers are 0.01 and –0.01.

The median

The median is the value of the middle number in a set of numbers, when the numbers are put in ascending or descending order.

Worked example

What is the median in the following set of numbers?

82, 21, 34, 23, 12, 46, 65, 45, 37

First order the numbers in ascending (or descending) order.

12, 21, 23, 34, 37, 45, 46, 65, 82

As there are nine numbers in the set, the fifth number in the series is the median.

37 is the median value.

Worked example

What is the median in the following set of numbers?

0, 2, 6, 10, 4, 8, 0, 1

First put the numbers of the set in order (either ascending or descending).

0, 0, 1, 2, 4, 6, 8, 10

This time there is an even number of values in the set.

Draw a line in the middle of the set:

The median of the series is the average of the two numbers on either side of the dividing line. Therefore, the median number in the series is the arithmetic mean of 2 and 4: (2 + 4) ÷ 2 = 3.

Averages: practice drill

Set a stopwatch and aim to complete the following drill in 60 seconds.

What is the arithmetic mean of the following sets of numbers?

Q1
17, 18, 21, 23, 21

Q2
0.1, 0.2, 0.2, 0.3, 0.3, 0.1

Q3
0, 2, 4, 6

Q4
–2, –4, –6, –10

Q5
–0.2, 0.1, 0.3, 0.6, 0.7, 0.9

What is the median of the following sets of numbers?

Q6
8, 1, 6, 2, 4

Q7
–6, –2.5, 0, –1, –3

Q8
82, 73, 72, 72, 71

Q9
6, 0, 3, 9, 15, 12

Q10
36, 32, 37, 41, 39, 39

What is the mode in the following sets of numbers?

Q11
21, 22, 23, 23, 22, 23

Q12
–2, –7, –2, –7, –7, –4, –4, –2, –3, –2

Q13
0, 1, 1, 1, 0, 0, 0, 1, 1

Q14

Q15
–0.1, 0.001, 0.01, –0.1, 0.001, –0.1, 0.001

Answers to Chapter 1

Multiplication tables: practice drill 1

Multiplication tables: practice drill 2