AP EAPCET (Engineering) Statistics — practice questions
92 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Statistics in the app →$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $$\cos 2\theta$ equals:If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals:sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:sin(A + B) equals:cos(A + B) equals:sin(60°) cos(30°) + cos(60°) sin(30°) equals:If sin θ = 3/5 (θ in Q1), find cos θ:Find cos(75°) using cos(A + B):sin(2θ) equals:Find sin(15°):If tan θ = 1/2 (acute), find sin 2θ:For 0 ≤ θ < 2π, solutions of sin θ = 1/2:1 - cos²θ equals:sin(A) + sin(B) equals (sum-to-product):In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:tan(A + B) equals:sin(180° - θ) equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:If sin θ + cos θ = 1, then sin θ × cos θ equals:General solution of cos θ = 0:If tan θ + cot θ = 2, find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Minimum value of sin²θ + cos⁴θ:If sin θ = 12/13 (acute), find tan(θ/2):In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):General solution of sin θ = sin α:A batsman's highest score is 117 and lowest is 0. What is the range of his scores?The sum of the deviations of all observations from their arithmetic mean is alwaysMean deviation about a value a is the mean of which quantities?Variance of a set of observations is defined as the mean of theIf the variance of a data set is 49, its standard deviation isA data set has standard deviation 5. What is its variance?Find the variance of the observations 2, 4, 4, 4, 5, 5, 7, 9 (population variance).Find the mean deviation about the mean for 5, 7, 9, 11, 13.The population variance of the five numbers 1, 2, 3, 4, 5 isFind the population variance of 4, 8, 12, 16, 20.If 10 is added to every observation of a data set, its varianceEvery observation is multiplied by 3. The standard deviation becomesIf x has variance 4, the variance of y = 2x + 3 isThe range of the data 5, 9, 14 is 9. If 6 is added to each value, the range becomesWhen all observations in a data set are equal, the standard deviation isTwo batsmen have the same mean and median score. What extra idea tells their consistency apart?Which of these is NOT a measure of dispersion?In statistics, dispersion is also calledA data set measured in metres has standard deviation 3. The unit of that standard deviation isHeights are measured in cm. In what unit is the variance of the heights?Which of these dispersion measures has no units even when data have units?Mean 50 with SD 5, versus mean 20 with SD 4: which has more relative variation?Data have mean 20 and standard deviation 4. The coefficient of variation isFor normally distributed data, about what share of values lies within one standard deviation of the mean?Heights are normal with mean 100 cm and SD 10 cm. About 95% of heights lie betweenScores are normal with mean 100 and SD 10. Roughly what percent score above 110?Which result guarantees a minimum share of data within k standard deviations for any distribution?By Chebyshev's inequality, at least what fraction of any data lies within 2 standard deviations?Bessel's correction replaces the divisor N byA sample of 5 values has a sum of squared deviations 40. The unbiased sample variance isSame sum of squared deviations 40 for 5 values. Treated as a whole population, the variance isThe sets {0,0,14,14}, {0,6,8,14} and {6,6,8,8} share mean 7. Which has the smallest SD?What is the standard deviation of the values 0, 0, 14, 14?Variance of a random variable X is the expected value of theA random variable has E(X) = 3 and E(X squared) = 10. Its variance isFor n = 10 values, the sum of values is 50 and the sum of their squares is 290. The variance isWhich statement about variance is always true?A random variable has variance 0. This means itX takes values 0 and 1 with probability 1/2 each. The variance of X isFor independent X and Y with variances 3 and 5, the variance of X + Y isIf the SD of x is 4 and y = 2x + 3, the SD of y isFor which measure are absolute values of deviations used to avoid cancelling?A drawback of mean deviation is that, because of absolute values, itThe sum of absolute deviations of a set of values is least when taken about theFor grouped data with classes replaced by mid-points, the standard deviation usesValues 2, 4, 6 occur with frequencies 1, 2, 1. The variance of this distribution isClasses 0-10 and 10-20 have frequencies 3 and 1. The variance of the grouped data isIn the step-deviation method with class width h, variance of x equalsStep deviations y have variance 2.5 and class width h = 10. The variance of x isThe sum of squared deviations of 5, 15, 25, 35, 45, 55 from their mean 30 is 1750. The variance isWhy is the plain sum of squared deviations a poor dispersion measure for sets of unequal size?For the interquartile range, if Q1 = 20 and Q3 = 45, the IQR isWith Q1 = 20 and Q3 = 45, the quartile deviation (half the IQR) isWhy is range only a rough measure of dispersion?Population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9 isVariance is the mean of squared deviations, whereas standard deviation isA set has 8 equal observations. Its variance and range are