medium difficulty5 min

Median from ogive

The median from an ogive is found by using the total frequency, locating N/2 on the cumulative frequency axis, and reading the corresponding class boundary value.

In one line: Half the total on y-axis, then read across and down.

Practice This Concept

Understand it

To get the median from an ogive, we first find N/2 on the y-axis. From that point, we move horizontally to the curve and then vertically down to the x-axis. The value read on the x-axis is the median estimate.

Example

If total frequency is 40, we locate 20 on the cumulative frequency axis and read the matching x-value from the ogive.

Formula and rule

Median from ogive is read at the x-value corresponding to N/2 on the y-axis of the less-than curve.

See it worked out

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

Worked example

1If the total frequency is 50, then N/2 = 25.
2Mark 25 on the cumulative frequency axis, meet the ogive, and drop a perpendicular to the x-axis to read the median value.

Method you can reuse

1Find total frequency N.
2Compute N/2.
3Mark N/2 on the cumulative frequency axis.
4Move horizontally to the ogive.
5Drop vertically to read the median on the x-axis.

Sketch it in your answer

Draw the ogive, mark N/2 on the y-axis, move horizontally to the curve, then vertically to the x-axis.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why do we use N/2 while finding the median from an ogive?

Think first, then show answer

We use N/2 because the median divides the data into two equal parts. On the ogive, this middle position helps us locate the value that separates the lower half from the upper half.

Common wrong answer

A common wrong answer is to read the median from the y-axis or to use the highest point of the curve.

Don't mix this up

Students sometimes read the median from the wrong axis or forget to use half of the total frequency.

Exam tip

Use a ruler and mark the horizontal and vertical steps carefully; one small reading error changes the answer.

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

Students may be given an ogive and asked to estimate the median directly from the graph.

1
Enough for 1 mark
The median from an ogive is found by using the total frequency, locating N/2 on the cumulative frequency axis, and reading the corresponding class boundary value.
2
Add for 2 marks
Example: If total frequency is 40, we locate 20 on the cumulative frequency axis and read the matching x-value from the ogive.
3
Add for 3 marks
To get the median from an ogive, we first find N/2 on the y-axis.

MCQ Quiz

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