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Maths Statistics Class 11 MCQ and Assertion Questions

10 Question MCQ (including Assertion) · Class 11 · Maths · CBSE

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Chapter 13 Class 11 Statistics | 10 questions | about 8 minutes

Practise Statistics Class 11 with Teachoo's 10 Question MCQ (including Assertion) (Class 11 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 10
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Question 1 of 10
Calculate the mean deviation about mean for the continuous distribution: $$\begin{array}{|c|c|c|c|c|} \hline \text{Class} & 0-10 & 10-20 & 20-30 & 30-40 \\ \hline \text{Frequency } f_i & 2 & 3 & 3 & 2 \\ \hline \end{array}$$
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Question 2 of 10
Assertion (A): If Celsius temperature values have standard deviation \(\sigma_C = 5^\circ\text{C}\), converting them to Fahrenheit via \(F = \frac{9}{5}C + 32\) results in a variance \(\sigma_F^2 = 81\).
Reason (R): Under linear transformation \(F = aC + b\), variance transforms as \(\sigma_F^2 = a^2 \sigma_C^2\), where here \(a = \frac{9}{5}\).
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Question 3 of 10
The mean of \(5\) observations is \(4.4\) and their variance is \(8.24\). If three observations are \(1, 2,\) and \(6\), calculate the product of the remaining two observations.
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Question 4 of 10
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 10
Calculate standard deviation \(\sigma\) for the continuous distribution: $$\begin{array}{|c|c|c|c|c|} \hline \text{Class} & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency } f_i & 2 & 3 & 3 & 2 \\ \hline \end{array}$$
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Question 6 of 10
Assertion (A): If every observation \(x_i\) in a dataset with standard deviation \(\sigma_x = 3\) is multiplied by \(k = -4\), the standard deviation of the new dataset becomes \(-12\).
Reason (R): Standard deviation is defined as the non-negative square root of variance, so under transformation \(y = kx\), \(\sigma_y = |k|\sigma_x\).
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Question 7 of 10
A financial analyst defines a portfolio return \(Y = 4X + 7\), where \(X\) represents daily asset returns with a variance \(\sigma_X^2 = 5\). Calculate the variance of \(Y\) (\(\sigma_Y^2\)).
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Question 8 of 10
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 9 of 10
Find the mean deviation about the mean for the dataset: \(6, 7, 10, 12, 13, 4, 8, 12\).
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Question 10 of 10
Assertion (A): In the step-deviation method with class width \(h = 10\), if the standard deviation of step-deviations \(y_i = \frac{x_i - A}{h}\) is \(\sigma_y = 1.42\), then the standard deviation of original data is \(\sigma_x = 14.2\).
Reason (R): Changing scale by factor \(h\) scales the standard deviation proportionally such that \(\sigma_x = h \cdot \sigma_y\).
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This 10 Question MCQ (including Assertion) covers Statistics Class 11 for Class 11 · Maths · CBSE. Practise the questions in the interactive quiz and check your answers.

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