Class 10 • Maths • Chapter 13
STATISTICS
True & False Quiz
Mean. Median. Mode.
✓True
✗False
25
Questions
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Ch.13
Chapter
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X
Class
Why True & False for STATISTICS?
How this format sharpens your conceptual clarity
🔵 Statistics provides tools to summarise data — the three averages (mean, median, mode) and their formulas are directly tested.
✅ T/F questions distinguish between the three methods for mean (Direct, Assumed Mean, Step-Deviation) and the correct formula for each central tendency.
🎯 Median uses cumulative frequency and the class containing n/2 — it is NOT simply the middle observation in grouped data.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
Statistics is a branch of mathematics that deals with the collection, organisation, analysis and interpretation of data.
Q 2
In Class X, statistics deals only with ungrouped (raw) data and does not consider grouped data.
Q 3
A frequency distribution table shows each observation together with the number of times it occurs.
Q 4
For continuous grouped data, class intervals in a frequency distribution must not overlap.
Q 5
The sum of the frequencies in a grouped frequency distribution is equal to the total number of observations.
Q 6
The mean of a set of observations is always one of the given observations.
Q 7
For grouped data, the mean can be calculated using the assumed mean method to simplify calculations.
Q 8
In a grouped frequency distribution, the mean is computed using the mid-point of each class interval.
Q 9
The median of a data set is the arithmetic average of all observations.
Q 10
For ungrouped data, if the number of observations is odd, the median is the \(\frac{n+1}{2}\)th observation in the ordered list.
Q 11
For grouped data, the median always coincides with the mid-point of the median class.
Q 12
To find the median of grouped data, the class whose cumulative frequency is just greater than \(\frac{n}{2}\) is taken as the median class.
Q 13
The mode of a data set is the value that occurs most frequently.
Q 14
In a grouped frequency distribution, the modal class is the class interval with the smallest class width.
Q 15
For grouped data, the mode can be estimated using a formula involving the frequencies of the modal class and its neighbouring classes.
Q 16
A data set can have more than one mode.
Q 17
In the context of this chapter, cumulative frequency is obtained by successively adding frequencies down the table.
Q 18
A “less than” cumulative frequency curve (ogive) is drawn by plotting upper class boundaries against their corresponding cumulative frequencies.
Q 19
The point of intersection of “less than” and “more than” ogives gives a graphical estimate of the mean.
Q 20
In many real-life distributions treated in this chapter, mean, median and mode need not have the same value.
Q 21
For grouped data in Class X, the relationship \(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\) may be used under certain conditions.
Q 22
When data are given in grouped form, the exact original observations can be uniquely recovered from the frequency distribution table.
Q 23
In a frequency distribution, if all observations have the same value, then mean, median and mode are equal.
Q 24
While drawing a histogram for continuous data, the area of each rectangle is proportional to the frequency of the corresponding class.
Q 25
For grouped data with equal class intervals, choosing different origins (assumed means) changes the actual value of the mean.
Key Takeaways — STATISTICS
Core facts for CBSE Boards & exams
1
Mean (Direct): x̄ = Σfᵢxᵢ / Σfᵢ.
2
Mean (Assumed Mean): x̄ = a + (Σfᵢdᵢ / Σfᵢ), where dᵢ = xᵢ − a.
3
Median = l + [(n/2 − cf) / f] × h, where l = lower class limit of median class.
4
Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h.
5
Empirical relationship: Mode ≈ 3 Median − 2 Mean.
6
For a symmetric distribution: Mean = Median = Mode.