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Class 10 Maths · Chapter 13 · NCERT (jemh113)

Statistics: common misconceptions

See the tempting mistake students make in Statistics, why it feels right at first glance, and a worked visual example that shows the right idea.

The tempting mistake & worked visual

Can you ignore frequencies in the mean?

Wrong

If scores are 1 and 5, the mean is 3.

Why it feels right. I average the two score labels.

Right

Each score contributes as many times as it occurs.

Worked example

All scores
1
1
1
5
Average
Sum 8
4 students
2
The mean counts all four students. A score of 1 is counted three times.

If three students score 1 and one scores 5, the mean is (1 + 1 + 1 + 5) ÷ 4 = 2.

If your child says… (5 concept checks in this chapter)

As you work through Statistics, listen for these everyday misunderstandings and use the prompt alongside each one.

1. Mean of Grouped Data See how to teach this step →

If your child says… “There are three rows, so I divide by three.”

Ask together
How many people do these three rows count altogether?
What’s true
These three rows represent four people, so divide the estimated total by four.
2. Mode of Grouped Data See how to teach this step →

If your child says… “The tallest bar is three, so the mode is three minutes.”

Ask together
Does the vertical scale measure people or minutes?
What’s true
Bar height counts people, while the horizontal position gives their waiting time.
3. Cumulative Frequency and Median Class See how to teach this step →

If your child says… “No class count exceeds four, so there is no median class.”

Ask together
How many waits have you counted altogether by the end of each class?
What’s true
The middle position counts waits across earlier classes too.
4. Median of Grouped Data See how to teach this step →

If your child says… “I can add three-quarters straight to the class's start.”

Ask together
How many minutes is three-quarters of this two-minute interval?
What’s true
Multiply the fraction by the class width to turn it into minutes.
5. Mean, Median and Mode See how to teach this step →

If your child says… “The mean always tells us the most common amount.”

Ask together
Which original pile had the equal-share count of four?
What’s true
Here, four is the equal share; two is the most frequent original pile size.

Use this chapter three ways