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Questions › IIT JAM › IIT JAM 2025 › Q33
2 marksStatistics › Descriptive statistics and dispersion › Geometric and harmonic meansHardabout 3 min

IIT JAM 2025 Question 33: Descriptive statistics and dispersion

Which of the following is/are NOT TRUE?

(A) Arithmetic mean is always greater than or equal to the geometric mean of a set of positive values.

(B) Correlation coefficient between two variables varies between 0 and 1.

(C) Exact middle point of −∞-\infty−∞ and ∞\infty∞ on the real line is 0.

(D) Domain of a random variable that follows χ2\chi^2χ2 distribution with degree of freedom one is [0,∞][0,\infty][0,∞].

Select all that apply.

Answer and worked solution

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Plain-text version

Which of the following is/are NOT TRUE? (A) Arithmetic mean is always greater than or equal to the geometric mean of a set of positive values. (B) Correlation coefficient between two variables varies between 0 and 1. (C) Exact middle point of -∞ and ∞ on the real line is 0. (D) Domain of a random variable that follows χ² distribution with degree of freedom one is [0,∞]. (A) Arithmetic mean is always greater than or equal to the geometric mean of a set of positive values. (B) Correlation coefficient between two variables varies between 0 and 1. (C) Exact middle point of -∞ and ∞ on the real line is 0. (D) Domain of a random variable that follows χ² distribution with degree of freedom one is [0,∞].

Also written as: Which of the following is/are NOT TRUE? (A) Arithmetic mean is always greater than or equal to the geometric mean of a set of positive values. (B) Correlation coefficient between two variables varies between 0 and 1. (C) Exact middle point of - inf and inf on the real line is 0. (D) Domain of a random variable that follows chi^2 distribution with degree of freedom one is [0, inf ].

Descriptive statistics and dispersion has come up 117 times in 6 exams since 2004.

What this question tests

This question is on Geometric and harmonic means, part of Descriptive statistics and dispersion in Statistics.

Averages for rates, ratios and growth, and how they compare with the arithmetic mean.

TestStop has 13 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Geometric and harmonic means

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Question from the IIT JAM 2025 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.