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.
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.
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 – 10 | 4 | 5 | 20 |
| 10 – 20 | 8 | 15 | 120 |
| 20 – 30 | 16 | 25 | 400 |
| 30 – 40 | 10 | 35 | 350 |
| 40 – 50 | 2 | 45 | 90 |
| Total | 40 | — | 980 |
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.
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.
| Score | f | Cumulative f (cf) |
|---|---|---|
| 0 – 10 | 4 | 4 |
| 10 – 20 | 8 | 12 |
| 20 – 30 | 16 | 28 |
| 30 – 40 | 10 | 38 |
| 40 – 50 | 2 | 40 |
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.
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.
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.
The Big Picture
Chapter 13 has three measures and several methods. Match the situation to the tool:
Find mean from grouped data?
Direct: x̄ = Σfᵢxᵢ/Σfᵢ | Step-deviation for large midpoints
Find the middle value?
Median = l + ((n/2 − cf)/f) × h
Find the most common class?
Mode = l + ((f₁−f₀)/(2f₁−f₀−f₂)) × h
Read median from a graph?
Ogive: plot (upper boundary, cf), read at y = n/2
Want to go deeper?
Our tutors cover the full Kerala SSLC syllabus live, 1-on-1. If Chapter 13 still feels shaky after this, one session usually fixes it.
Book a Free Trial Class