Statistics is part of Mathematics and holds 730 questions with answers, free to read and with no account needed.
Questions from this area appear in PPSC, FPSC and NTS papers. Each guide explains how that paper is built and which subjects carry it.
Attempt each question before revealing the answer, and keep a note of the ones you get wrong — those are the topics worth reading about properly. If an answer looks wrong, there is a link to report it on every question.
Answer: D. Both A and B
The geometric mean involves multiplying values and taking roots, which fails when zero is present. The harmonic mean requires dividing by data values, leading to division by zero errors if zero occurs. Therefore, the pre...
Answer: B. 4 Var(X)
Adding a constant shifts the mean but does not affect data dispersion. Multiplying a random variable by two scales its variance by two squared. Applying the linear variance rule gives four times the original variance of...
Answer: C. ∑Pn(Po + Pn)/∑Pn(Po + Pn) x100
Marshall's index formulas use sums of base and current periods as weighting factors. The volume index variant focuses specifically on measuring aggregate physical quantity changes. Therefore option C correctly formulates...
Answer: A. J- shaped
A J-shaped frequency distribution curve starts very low and rises sharply or drops sharply toward one extreme end. This pattern occurs when the maximum frequency of observations concentrates heavily at one boundary of th...
Answer: A. Less than mean
In a binomial distribution, the mean equals np and the variance equals npq. The parameter q represents the probability of failure, which must be a fraction less than one. Multiplying np by a fractional q ensures the vari...
Answer: C. Cube
A geometric cube has length width and height dimensions that are all completely equal. Multiplying equal side lengths x by x by x produces the algebraic expression x cubed. Volume formulas for cubes require raising the e...
Answer: A. A sample
A sample is a subset of a population selected to represent the entire group during analysis. Gathering data from this smaller group saves time and resources compared to complete enumeration. Statistical inference allows...
Answer: B. np (1 – p)
The binomial distribution models the number of successes in n independent trials. Each trial has a constant probability of success denoted by the variable p. Mathematical derivation shows its variance equals the product...
Answer: A. Mean
Variance measures dispersion by calculating squared deviations away from a central benchmark. Mathematical theory proves that this central benchmark must be the arithmetic mean. Therefore variance is consistently calcula...
Answer: E. Cannot be determined from given information
Calculating the probability of drawing a specific item requires knowing both the target count and the total number of items. The provided problem statement lacks crucial information regarding the population size and comp...
Answer: D. Number of classes
Frequency distributions organize raw data by grouping values into manageable class intervals. The total span of the data from minimum to maximum is known as the range. Dividing this total range by the chosen class width...
Answer: C. 216 outcomes
Each standard die possesses six distinct faces resulting in six possible individual outcomes. Rolling three dice means multiplying the six outcomes of each die together consecutively. Multiplying six by six by six yields...
Answer: C. Primary data
Primary data refers to information collected firsthand by researchers for a specific investigative purpose. A local Patwari collecting original agricultural crop statistics is gathering data directly from the source. Thi...
Answer: D. Cannot be determined without more information
Type II error probability depends heavily on the specific alternative hypothesis value. Knowing only the significance level alpha does not provide enough information to calculate beta. Sample size and effect size must al...
Answer: C. Continuous
Physical measurements can take on any numerical value within a continuous physical range. Instruments can measure quantities down to infinitely small decimal fractions given enough precision. Therefore direct physical me...
