Why grouping needs an assumption
The values are gone
A class tells you how many observations fell in it, not what they were.
↳ Grouping trades detail for readability.
📚 Chapter Learning Kit
Statistics · Class 10 Mathematics
English 3 topics 174 leveled MCQs 66 flashcards 2 games Free
Shared by a Veda teacher · Generated with Veda AI · Sep 2026
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The class mark
Stand them at the middle
↳ Every observation in a class is treated as sitting here.
The direct method
Method 1
↳ Multiply, add, divide by the total frequency.
What a mode is
The most common value
The observation that occurs most often.
↳ Counting, not arithmetic.
The modal class
The tallest bar
The class with the largest frequency.
↳ Easy to spot in a histogram.
Modal class against mode
The class is not the answer
The modal class is an interval; the MODE is a single value inside it.
↳ Name the class, then interpolate.
📖 Smart notes
What you'll study, topic by topic
1
Mean of Grouped Data
Once data are grouped, the individual values are gone. The mean is recovered by treating every observation in a class as sitting at the class mark — and there are three ways to do the arithmetic, all giving the same answ…
- Grouping loses the individual values, so each class is represented by its CLASS MARK.
- Class mark $= \frac{\text{lower limit} + \text{upper limit}}{2}$.
- DIRECT method: $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.
~50 min · full explanation, examples & memory tricks in the app
2
Mode of Grouped Data
The mode is the most common value. Once data are grouped you can only name the most common class — and then interpolate inside it, using how much taller it is than each of its neighbours.
- The MODE is the value that occurs most often.
- For grouped data the MODAL CLASS is the class with the largest frequency.
- Mode $= l + \left(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$.
~45 min · full explanation, examples & memory tricks in the app
3
Median of Grouped Data
The median is the middle observation. For grouped data you first find which class the middle falls in, then walk the right fraction of the way into it — and a single empirical relation ties all three averages together.
- The MEDIAN is the middle observation when the data are arranged in order.
- CUMULATIVE FREQUENCY of a class is the total frequency up to and including it.
- The MEDIAN CLASS is the first class whose cumulative frequency reaches $\frac{n}{2}$.
~50 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
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174 questions laddered from warm-up to topper-level, each with an explanation. A taste:
The mean of grouped data must be estimated because
Beginner
A the frequencies are approximate
B class marks are irrational
C the individual values are lost in grouping
D the classes overlap
Show answer & explanation
the individual values are lost in grouping
Only the counts per class survive.
The class mark of a class is
Beginner
A its lower limit
B half the sum of its limits
C its upper limit
D its frequency
Show answer & explanation
half the sum of its limits
The midpoint of the interval.
The class mark of 20–30 is
Beginner
A 20
B 25
C 30
D 10
Show answer & explanation
25
$\frac{20+30}{2}$.
The class mark of 45–60 is
Intermediate
A 52.5
B 45
C 60
D 15
Show answer & explanation
52.5
$\frac{45+60}{2}$.
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