medium difficulty6 min

Comparing central tendency measures

Comparing central tendency measures means deciding whether mean, median, or mode best describes a data set for a given situation.

In one line: Mean for balance, median for extremes, mode for popularity.

Practice This Concept

Understand it

Each measure has a different use.
Mean is useful when data is balanced and every value should contribute.
Median is useful when extreme values may distort the average.
Mode is useful when we want the most common value.
Good exam answers compare the situation before choosing the measure.

Example

For income data with one very large value, the median may describe the centre better than the mean.

Formula and rule

Mean uses all values, median uses the middle position, and mode uses the most frequent value.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1For house-price data with one very expensive house, the mean rises sharply.
2The median remains closer to the centre of the usual houses, so it gives a fairer central value.

Method you can reuse

1Check whether the data is balanced or skewed.
2See whether extreme values are present.
3Decide if the question asks for average, middle, or most common value.
4Choose the measure that fits the situation.
5Support the choice with one reason.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

When is the median often better than the mean?

Think first, then show answer

The median is often better when the data has very large or very small values that can pull the mean away from the centre. In such cases, the median gives a more stable central value.

Common wrong answer

A common wrong answer is to choose the mean automatically even when the data contains extreme values that distort it.

Don't mix this up

Students often pick the mean for every data set without checking whether the data has extreme values.

Exam tip

Read the situation first: balanced data often suits mean, skewed data often suits median, and most common item questions often suit mode.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask which measure is most suitable for a real-life situation and why.

1
Enough for 1 mark
Comparing central tendency measures means deciding whether mean, median, or mode best describes a data set for a given situation.
2
Add for 2 marks
Example: For income data with one very large value, the median may describe the centre better than the mean.
3
Add for 3 marks
Each measure has a different use.

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