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Statistics & Probability Quiz - CBSE Class 10 Mathematics

Free practice quiz: Statistics & Probability (CBSE Class 10 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 10 Mathematics practice quiz has 18 multiple-choice questions on Statistics & Probability, and 18 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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About this topic

Statistics finds one central value (mean, median, mode) to represent data. Probability measures how likely an event is, from 0 to 1. Both use simple counting and ratios.

Mean = sum of all values ÷ number of values. Sum = mean × n.
Median is the middle value after arranging data in order.
For even n, median is the average of the two middle values.
Mode is the value that occurs most often.
Probability = favourable outcomes ÷ total equally likely outcomes.
Probability of any event lies between 0 and 1, both included.
P(E) + P(not E) = 1. 'At least one' is easiest via the complement.

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Mean, Median, Mode, Range

Mean is the total of all values divided by how many values there are.
Median is the middle value after sorting. Mode is the most frequent value.
Range is the largest value minus the smallest value. It shows how spread out the data is.

Mean of n values

\[\bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n}\]

Total from mean

\[\sum x_i = n \times \bar{x}\]

Median position (n odd)

\[\left(\frac{n+1}{2}\right)^{\text{th}} \text{ value}\]

Range

\[\text{Range} = x_{\max} - x_{\min}\]

Common mistake: Finding the median without first arranging the data in ascending order. For an even n, forgetting to average the two middle values.

Mean and Median of Grouped Data

For class intervals, use each class mark (midpoint) as the value x_i for that class.
For the median, find the class where the cumulative frequency first reaches or exceeds n/2. That is the median class.

Class mark

\[x_i = \frac{\text{lower limit} + \text{upper limit}}{2}\]

Mean (direct method)

\[\bar{x} = \frac{\sum f_i x_i}{\sum f_i}\]

Median

\[\text{Median} = l + \left(\frac{\frac{n}{2} - cf}{f}\right) \times h\]

Common mistake: Using cf of the median class itself instead of the cumulative frequency of the class just before the median class.

Mode of Grouped Data

The modal class is the class with the highest frequency.
f_0 and f_2 are the frequencies of the classes just before and just after the modal class.

Mode

\[\text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h\]

Common mistake: Taking l as the lower limit of the first class instead of the lower limit of the modal class.

Basic Probability and Complement

Probability is the number of favourable outcomes divided by the total number of equally likely outcomes.
An event and its complement (the event not happening) have probabilities that add up to 1.

Classical probability

\[P(E) = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}\]

Complement rule

\[P(\text{not } E) = 1 - P(E)\]

Range of probability

\[0 \le P(E) \le 1\]

Common mistake: Counting outcomes incorrectly. With two dice, (a, b) and (b, a) are different outcomes when a ≠ b.

Combining Events and Counting Outcomes

Mutually exclusive events cannot happen together, so their probabilities simply add.
If events overlap, subtract the overlap once so it is not counted twice.
For 'at least one' questions, use 1 minus the probability of 'none'.

Mutually exclusive events

\[P(A \cup B) = P(A) + P(B)\]

General addition rule

\[P(A \cup B) = P(A) + P(B) - P(A \cap B)\]

Counting with overlap

\[n(A \cup B) = n(A) + n(B) - n(A \cap B)\]

Outcomes for n coin tosses

\[\text{Total outcomes} = 2^n\]

Common mistake: Adding the counts of two overlapping groups without subtracting the common part, which counts those items twice.

Exam tips

A standard deck has 52 cards in four suits of 13. Each suit has one king, queen, jack and ace.
Two dice give 36 equally likely outcomes. List the pairs systematically to count favourable ones.
For a grouped mean, check that the class marks and the f_i x_i column are correct before dividing.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

A coin is tossed 3 times. What is the probability of getting at least one head?
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Answer: C. 7/8
The total number of possible outcomes when a coin is tossed 3 times is 2^3 = 8. The outcomes with no heads is only 1 (TTT). Hence, the probability of getting at least one head is 1 - (1/8) = 7/8.
If an experiment has outcomes with probabilities P(A) = 0.3 and P(B) = 0.6, what is the probability of A or B occurring assuming they are mutually exclusive?
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Answer: B. 0.9
For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.3 + 0.6 = 0.9.
What is the probability of drawing a king from a standard deck of cards?
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Answer: A. 1/13
There are 4 kings in a deck of 52 cards. Hence, the probability of drawing a king is 4/52 = 1/13.
A bag contains 3 red balls, 4 blue balls, and 5 green balls. What is the probability of picking a blue ball?
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Answer: A. 1/3
The probability is the number of favorable outcomes divided by the total number of outcomes. So, P(blue) = 4/(3+4+5) = 4/12 = 1/3.
Find the mean of the following frequency distribution: Class: 0-10, 10-20, 20-30, 30-40, 40-50 | Frequency: 5, 8, 12, 10, 5
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Answer: B. 25.5
Class marks are 5, 15, 25, 35, 45, so Σfx = 25 + 120 + 300 + 350 + 225 = 1020 and Σf = 40. Mean = Σfx / Σf = 1020 / 40 = 25.5.