MEASURES OF TENDENCY

Objectives: 

1. Find Mode

2. Find Median

3. Find Mean 

Introduction...

What is average?

Average is a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number, OR constituting the result obtained by adding together several amounts and then dividing this total by the number of amounts. 

How to find Average?

The mean is the average of the numbers. so the way how we find it is add up all the numbers, then divide by how many numbers there are, in other words, it is the sum divided by the number of counts.

By the way, there are few terms that you need to know:

1. Mode - The mode is the common value of the data. 

2. Median - The median is the middle value in a set of data. 

3. Mean - The mean is the average of the sum of numbers then divided by the number of counts.

Lets take some example..

Mode 

Find the mode of: 

black, grey, grey, red, white, grey 

mode = grey

why? because grey has 3 possible modes 

black, grey, grey, red, white, grey 

what if:

black, black, grey, red, white, grey 

mode = black, grey

why? because there is possible to have 2 modes 

black, black, grey, red, white, grey

what if: 

black, grey, red, white

mode = no mode

why? yes it is possible to have no mode. 

Median 

To find median: 

First step is to arrange the numbers in numerical order.

for example: 

9, 7, 6, 5, 2, 3, 1

Arrange it = 1, 2, 3, 5, 6, 7, 9

median = 5 

another example:
In a car company that sells car, there are 8 cars altogether with different prices.
$40, 000, $29, 000, $35, 500, $31, 000, $43 ,000, $30, 000, $27, 000, $32, 000

First step ; Arrange the data from least to Greatest. Then find the middle
= $27, 000, $29, 000, $30, 000, $31, 000, $32, 000, $35, 500, $40, 000, $43, 000

= $31,000, $32, 000 (if there is even number of counting in the middle, we take those two numbers and divide it by 2)

= 31000+32000 = 31,500
             2

= Median is $31,500 

Mean 

The mean is the average of the numbers, then dive by how many numbers there are. 

How to calculate? 

Just add all the numbers then divide by how many numbers there are.

for example: 

Find the mean of 2, 4, and 8? 

First Step: Add all the number = 2 + 4 + 8 = 14
Second Step: Divide the sum of all numbers by the number of counts : = 14 = 4.67 

                                                                                                                      3

= The mean is 4.67

LETS TAKE MORE EXAMPLES...

Example 1 : 

The weekly salaries of six employees at Burger King are $140, $220, $90, $180, $140, $200 

Find the Mean, Median and Mode

Mean : 

= $140 + $220 + $90 + $180 + $140 + $200 

                                  6

= $970

     6

= $161.67

Median : 

= $90, $140, $140, $180, $200, $220 

                             2

= $140 + $180 

             2

= $160 

Mode : 

= $140 

Example 2 :

Azwan trapped 10 rabbits, weighed them to the nearest pound, and recorded his results in groups as follows : 

Use the midpoints of the groups to estimate the mean weight of the rabbits Azwan trapped 

Example 3 : 

The populations of crocodiles in 7 national parks is below. Calculate the mean, median and mode.

Data : 14, 13, 8, 19, 13, 24, 15

Mean : 

= 14 + 13 + 8 + 19 + 13 + 24 + 15

                            7

= 106 

     7

= 15.1 Crocodiles 

Median :

= 8, 13, 13, 14, 15, 19, 24 

= 14 Crocodiles 

Mode :

= 13 Crocodiles 

Lets take an exercise...

Exercise 1 :

The number of graffiti convictions for 12 months of monthly data is below. Calculate the mean, the median and the mode. 

Data : 14, 25, 23, 15, 16, 16, 11, 23, 12, 13, 24, 7.