68 free MCQs on Statistics, each with its own worked answer and explanation. Mean, median, mode, standard deviation, and data interpretation
Take the timed Statistics chapterwise test →68 practice questions on Statistics, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Statistics notes.
In a perfectly normal (bell-shaped) distribution, mean, median, and mode all coincide at the centre; about 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 - the empirical rule used to judge how typical or extreme a value is.
Q2.
The middle value of an ordered data set is:
Q3.
The value that appears most often in a data set is:
Q9.
Data presented as a bar graph shows:
Q10.
What does a histogram show?
Q12.
Standard deviation measures:
Q13.
Which of these is a measure of central tendency?
Q14.
The cumulative frequency graph is also called:
Q16.
In a class of 10 students, the average score is 75. Total marks =
Q17.
Variance is the _____ of standard deviation.
Q18.
Which graphical representation uses sectors of a circle?
Q19.
If median > mean, the distribution is:
Q21.
Coefficient of variation is used to:
Q22.
The median of grouped data uses the formula:
Q23.
In grouped data, the mode formula is:
Q24.
Pearson's correlation coefficient r = 1 means:
Q25.
IQR (Interquartile Range) = Q<sub>3</sub> - Q<sub>1</sub> measures:
Q26.
Standard deviation is preferred over mean deviation because:
Q27.
If all values in a dataset are multiplied by 2, the standard deviation:
Q29.
Ogive is used to find:
Q30.
For data 3, 6, 9, 12, 15, the mean deviation from mean is:
Q31.
If adding a constant k to each observation, mean:
Q32.
The empirical relation between mean, median, and mode is:
Q33.
For a negatively skewed distribution:
Q34.
Step-deviation method for mean uses:
Q35.
Spearman's rank correlation is used when:
Q36.
The box-plot whiskers extend to:
Q37.
For data with high variability, standard deviation is:
Q39.
In a frequency distribution, class mark (midpoint) of interval 30-40 is:
Q40.
Mean of 10 numbers is 15. If one number 20 is replaced by 30, new mean is:
Q41.
For grouped data, Pearson's first coefficient of skewness is:
Q42.
The regression line y on x passes through:
Q43.
If byx × bxy = r², where byx and bxy are regression coefficients, then r =
Q44.
For a normal distribution N(μ, σ²), about 95% of data lies within:
Q45.
Partial correlation measures:
Q46.
The variance of combined data of two groups (n₁, x̄₁, σ₁²) and (n₂, x̄₂, σ₂²) is:
Q47.
Moment generating function M(t) of a random variable X is defined as:
Q48.
Stratified random sampling ensures:
Q49.
The harmonic mean of 2, 4, 8 is approximately:
Q50.
Laspeyres price index uses base year quantities. It tends to:
Q51.
In regression analysis, R² (coefficient of determination) measures:
Q52.
Tchebychev (Chebyshev) inequality states that for any distribution, P(|X - μ| ≥ kσ) ≤:
Q53.
The standard error of mean (SEM) for sample size n from population with SD σ is:
Q58.
If the mean of five observations is 10, their total sum is:
Q59.
The standard deviation of a data set is the ___ of its variance:
Q60.
The variance of a set of data is always:
Q62.
If every observation in a data set is increased by 5, the variance:
Q63.
The mean of 100 observations is 50. Later one observation 100 was found to be misread as 10. The corrected mean is:
Q65.
If the standard deviation of x₁, x₂, ..., xₙ is σ, the standard deviation of 3x₁, 3x₂, ..., 3xₙ is:
Q66.
For a data set with standard deviation 5 and mean 25, the coefficient of variation is:
Q67.
For a moderately skewed distribution with mean 10 and median 8, the mode is:
Q68.
Two groups have sizes 20 and 30 with means 30 and 20 respectively. Their combined mean is:
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