alleryStart learning →Mean of n numbers x₁, x₂, ..., x_n:
- Product
- Σ x_i / n (arithmetic mean)
- Σ x_i
- Max - Min
Show answer and solution
Correct answer: B. Σ x_i / n (arithmetic mean)
Arithmetic mean = Σxi/n.
Most common measure of central tendency. Sensitive to outliers.
UPCET / UPSEE Statistics and Probability — practice questions
Explore 70 free Statistics and Probability questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 70.
Mean of n numbers x₁, x₂, ..., x_n:Read the answer and worked solution →Median of sorted data with odd count n:Read the answer and worked solution →Mode of data set is:Read the answer and worked solution →Probability of certain event:Read the answer and worked solution →Total probability of all mutually exclusive outcomes:Read the answer and worked solution →Standard deviation of n numbers with mean x̄:Read the answer and worked solution →Variance:Read the answer and worked solution →For independent events A and B:Read the answer and worked solution →Mutually exclusive events A and B:Read the answer and worked solution →Conditional probability:Read the answer and worked solution →Bayes' theorem:Read the answer and worked solution →Expected value E(X) of discrete random variable:Read the answer and worked solution →Bernoulli trial has:Read the answer and worked solution →Binomial distribution: P(X = k) =Read the answer and worked solution →Mean of binomial distribution with n trials, success probability p:Read the answer and worked solution →Variance of binomial:Read the answer and worked solution →Mean of 10 numbers is 8. If a new value 30 is added, new mean:Read the answer and worked solution →Box has 5 red, 7 blue balls. Draw 2 without replacement. P(both red):Read the answer and worked solution →P(both red OR both blue) in 2 draws without replacement from 5R 7B box:Read the answer and worked solution →A coin tossed 10 times. P(exactly 5 heads):Read the answer and worked solution →If P(A) = 0.4, P(B) = 0.5, P(A ∩ B) = 0.2: A and B independent?Read the answer and worked solution →For random variable X uniform on [0, 1]: E(X²) =Read the answer and worked solution →For uniform U[0,1]: variance =Read the answer and worked solution →E[X² + Y²] when X, Y are independent identically distributed with E(X) = 0, Var(X) = σ²:Read the answer and worked solution →Cov(X, X) =Read the answer and worked solution →Correlation coefficient r:Read the answer and worked solution →5 cards from deck of 52. P(all spades):Read the answer and worked solution →Coefficient of variation (CV):Read the answer and worked solution →Mean of frequency distribution Σf_i x_i / Σf_i. Find mean of: 2(×3), 4(×5), 6(×2): values 2,4,6 with frequencies 3, 5, 2:Read the answer and worked solution →Standard deviation property: σ(aX + b) =Read the answer and worked solution →
Worked practice questions
Median of sorted data with odd count n:
- First value
- Mean
- Mode
- Middle value (((n+1)/2)-th term)
Show answer and solution
Correct answer: D. Middle value (((n+1)/2)-th term)
**Median:** middle value of sorted data. Robust to outliers.
**For odd n:** just the ((n+1)/2)-th value.
**For even:** mean of two middle values.
Mode of data set is:
- Range
- Median
- Average
- Most frequent value
Show answer and solution
Correct answer: D. Most frequent value
**Mode:** value occurring with highest frequency.
Distribution can have 0, 1, or multiple modes (unimodal, bimodal, etc.).
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