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Chapter 13 · Kerala SSLC Class 10 Maths

Statistics

Two ways to learn — a crisp formula reference, or a story that makes data analysis feel natural.

Mean · Median · ModeGrouped dataStep-deviationCumulative frequency
Kerala SSLCClass 10MathsChapter 13 · Statistics12 min read

Three scenes that reveal the maths naturally.

How this works

Each scene is a real classroom situation that uses the maths from Chapter 13. Read the story, then open "The Maths" box to see the formula behind it.

1

The Class Test Scores

The maths teacher hands back test papers. Scores range from 0 to 50. Instead of listing all 40 scores, she writes them as a grouped frequency table on the board.

Score (Class)Frequency (f)Midpoint (x)f × x
0 – 104520
10 – 20815120
20 – 301625400
30 – 401035350
40 – 5024590
Total40980
Teacher

Add up the f × x column and divide by the total frequency. That gives you the mean score.

x̄ = Σfᵢxᵢ / Σfᵢ = 980 / 40 = 24.5

The class mean is 24.5. Notice the key step: each class is represented by its midpoint, not its boundary. Using 10 or 20 instead of 15 for the class 10–20 would be wrong.

For grouped data, we treat every observation in a class as if it equals the class midpoint. The midpoint is (lower boundary + upper boundary) / 2.
2

Where Is the Middle?

Arjun wants to know the median score — the score that exactly half the class is above and half is below. With 40 students, he needs to find the 20th value.

He builds a cumulative frequency column. The median class is the first class where the cumulative frequency reaches 20.

ScorefCumulative f (cf)
0 – 1044
10 – 20812
20 – 301628
30 – 401038
40 – 50240
Arjun

n/2 = 20. The cf jumps from 12 to 28 in the 20–30 class. So the median is somewhere inside 20–30.

The median class is 20–30. Now he uses the median formula, interpolating within that class.

Median = l + ((n/2 − cf) / f) × h

= 20 + ((20 − 12) / 16) × 10

= 20 + (8/16) × 10

= 20 + 5 = 25

The median score is 25. Exactly half the students scored below 25 and half scored above.

3

The Most Popular Score — and the Ogive

Diya wants to know which score range the largest group of students fell in — and whether she can find the median graphically without any formula.

Diya

The 20–30 class has the highest frequency — 16 students. So the mode is somewhere in that class. And there's a graph called an ogive that shows the median visually.

For the mode, she uses the modal class (20–30) with f₁ = 16, f₀ = 8 (class before), f₂ = 10 (class after), and h = 10.

Mode = l + ((f₁ − f₀) / (2f₁ − f₀ − f₂)) × h

= 20 + ((16 − 8) / (32 − 8 − 10)) × 10

= 20 + (8 / 14) × 10

≈ 20 + 5.7 = 25.7

The mode is approximately 25.7. For the ogive: plot points (upper boundary of each class, cumulative frequency). The curve is S-shaped. To read the median, find n/2 = 20 on the y-axis, draw a horizontal line to the curve, then drop a vertical to the x-axis.

Mean ≈ 24.5, Median = 25, Mode ≈ 25.7. For roughly symmetrical data these three are close. When data is skewed, they diverge — and which one you report depends on what you want to convey.

The Big Picture

Chapter 13 has three measures and several methods. Match the situation to the tool:

Q

Find mean from grouped data?

Direct: x̄ = Σfᵢxᵢ/Σfᵢ | Step-deviation for large midpoints

Q

Find the middle value?

Median = l + ((n/2 − cf)/f) × h

Q

Find the most common class?

Mode = l + ((f₁−f₀)/(2f₁−f₀−f₂)) × h

Q

Read median from a graph?

Ogive: plot (upper boundary, cf), read at y = n/2

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