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Maths Statistics Class 11 Assertion and Reason Questions

Assertion Reasoning Quiz · Class 11 · Maths · CBSE

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Chapter 13 Class 11 Statistics | 7 questions | about 6 minutes

Practise Statistics Class 11 with Teachoo's Assertion Reasoning Quiz (Class 11 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 7
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Question 1 of 7
Assertion (A): The sum of algebraic deviations \(\sum_{i=1}^n (x_i - \bar{x})\) of a dataset from its arithmetic mean \(\bar{x}\) is equal to \(n\bar{x}\).
Reason (R): By definition of arithmetic mean \(\bar{x} = \frac{\sum x_i}{n}\), we have \(\sum_{i=1}^n x_i = n\bar{x}\).
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Question 2 of 7
Assertion (A): If the mean of five observations is \(4.4\) and three observations are \(1, 2, 6\), then the sum of the remaining two observations \(x + y\) is equal to \(13\).
Reason (R): The variance of a dataset depends solely on the sum of observations \(\sum x_i\) and is independent of individual squared values.
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Question 3 of 7
Assertion (A): If an additional \(10^{\text{th}}\) observation equal to the dataset's mean \(\bar{x}\) is added to a dataset of \(n=9\) observations with variance \(\sigma^2 = 20\), the new variance becomes \(18.0\).
Reason (R): The sum of squared deviations of original dataset is given by \(\sum_{i=1}^n (x_i - \bar{x})^2 = n \cdot \sigma^2\).
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Question 4 of 7
Assertion (A): The mean deviation about median for the dataset \(3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21\) is equal to \(5.27\).
Reason (R): For an odd number of observations \(n\), the median is given by the \((\frac{n+1}{2})^{\text{th}}\) observation when ordered.
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Question 5 of 7
Assertion (A): For the dataset \(\{2, 4, 6, 8, 10\}\), the Mean Deviation about mean is \(2.4\).
Reason (R): For any non-constant dataset, the Mean Deviation about mean is strictly greater than the Standard Deviation.
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Question 6 of 7
Assertion (A): A standardized variable \(z_i = \frac{x_i - \bar{x}}{\sigma_x}\) created from dataset \(X\) has mean \(\bar{z} = 0\) and variance \(\sigma_z^2 = 1\).
Reason (R): Standardizing a variable converts raw observations into standard deviation units measured relative to the mean.
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Question 7 of 7
Assertion (A): The variance of \(15\) identical observations, all equal to \(7\), is equal to \(0\).
Reason (R): The standard deviation of \(n\) identical observations equal to \(k\) is equal to \(k\).
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