Measures of Central Tendency — Flashcards
Gujarat Board · Class 11 · Statistics
24 flashcards for Measures of Central Tendency (Gujarat Board Class 11 Statistics) to test yourself on key terms and facts.
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What is a measure of central tendency and why is it important?
Answer
A measure of central tendency is a single value that represents the center or typical value of a dataset. It is important because it: (1) Presents data in a concise form, (2) Shows special characteris…
List the six characteristics of an ideal measure of central tendency.
Answer
An ideal average should be: (1) Well defined and rigid, (2) Easy to understand and calculate, (3) Based on all observations, (4) Suitable for algebraic operations, (5) A stable measure across samples,…
What is arithmetic mean and what is its formula for raw data?
Answer
Arithmetic mean is the sum of all observations divided by the total number of observations. Formula: x̄ = Σx/n, where Σx is the sum of all observations and n is the number of observations.
Write the short-cut method formula for calculating mean in grouped data.
Answer
x̄ = A + (Σfd/n) × c, where A = assumed mean, d = (x-A)/c, f = frequency, c = class width, and n = total frequency (Σf).
State the important property: What is the sum of deviations of all observations from their mean?
Answer
The sum of deviations of all observations from their mean is always zero. Symbolically: Σ(x - x̄) = 0. This is a unique property of arithmetic mean - deviations from any other value will not sum to ze…
What is the formula for combined mean and when is it used?
Answer
Combined mean formula: x̄c = (n₁x̄₁ + n₂x̄₂ + ... + nₖx̄ₖ)/(n₁ + n₂ + ... + nₖ). It is used when we know the means of two or more separate groups and want to find the mean of the combined group.
Define weighted mean and give its formula.
Answer
Weighted mean is used when observations have different importance. Each observation is assigned a weight according to its importance. Formula: x̄w = Σwx/Σw, where w represents the weights assigned to …
What is geometric mean and when should it be used?
Answer
Geometric mean is the nth root of the product of n positive observations: G = ⁿ√(x₁ × x₂ × ... × xₙ). It should be used for calculating average rates of change, growth rates, or when dealing with rati…
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