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Comparing central tendency measures

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Mean for balance, median for extremes, mode for popularity.

Examples and method

Worked example

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

Method to apply

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

Diagram support

A comparison chart with three columns for mean, median, and mode helps students choose the right measure quickly.

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

When is the median often better than the mean?

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

Comparing central tendency measures means deciding whether mean, median, or mode best describes a data set for a given situation. Mean uses all values, median uses the middle position, and mode uses the most frequent value. For income data with one very large value, the median may describe the centre better than the mean.

3-mark answer

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. Mean uses all values, median uses the middle position, and mode uses the most frequent value. For house-price data with one very expensive house, the mean rises sharply. The median remains closer to the centre of the usual houses, so it gives a fairer central value. Questions may ask which measure is most suitable for a real-life situation and why. A common wrong answer is to choose the mean automatically even when the data contains extreme values that distort it.
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