Skip to page content

Measures of Central Tendency — Part 2: Short-cut methods, missing frequencies and classes

Beta

Lesson

Measures of Central Tendency, Part 2

Shorter arithmetic, same mean; then the median class and modal class.

In this lesson you will

Find the mean by the assumed-mean and step-deviation methods
Check that all three methods agree
Find a missing frequency when the mean is given
Identify the median class and the modal class

Smaller numbers, same mean.
Quantity	Meaning	Formula
$a$	assumed mean, chosen near the middle (a class mark)
$d$	deviation of a class mark from $a$	$d = x - a$
$\sum fd$	total of $f \times d$ (may be negative)
Mean	assumed mean plus the average deviation	$\bar{x} = a + \dfrac{\sum fd}{\sum f}$

Concept

What you will be able to do

Use the assumed-mean method
Use the step-deviation method
Find a missing frequency from the mean
Identify the median class and the modal class

Choosing the right tool.
Situation	Method to prefer
Small class marks, few classes	direct method
Large class marks, unequal-looking numbers	assumed mean
Equal class widths and large values	step deviation
A frequency is missing but the mean is given	mean equation in $y$
Only the class containing the centre is wanted	median class by cumulative frequency
Only the most crowded class is wanted	modal class by highest frequency

Concept

The assumed-mean method

Choose a class mark near the middle as $a$ . Then $d = x - a$ and $\bar{x} = a + \dfrac{\sum fd}{\sum f}$ .

Smaller numbers, same mean.
Quantity	Meaning	Formula
$a$	assumed mean, chosen near the middle (a class mark)
$d$	deviation of a class mark from $a$	$d = x - a$
$\sum fd$	total of $f \times d$ (may be negative)
Mean	assumed mean plus the average deviation	$\bar{x} = a + \dfrac{\sum fd}{\sum f}$