Class 11 Math - Statistics - MERIT YARD
Class 11 Math - Statistics - MERIT YARD
1 / 40Find the range of the given data set:
\( 2, 5, 8, 11, 14 \)
A) \( 14 \)
B) \( 12 \)
C) \( 16 \)
D) \( 2 \)
2 / 40In Statistics, what does the term 'Dispersion' strictly mean?
A) Average of data
B) Sum of data
C) Multiplication of data
D) Scattering of data
3 / 40Which of the following is a classic measure of 'Central Tendency'?
A) Mean
B) Variance
C) Standard Deviation
D) Range
4 / 40What is the standard formula to calculate the Mean \( \bar{x} \)?
A) \( \sum x_i \)
B) \( n \cdot \sum x_i \)
C) \( \frac{\sum x_i}{n} \)
D) \( \sum (x_i)^2 \)
5 / 40The square of the standard deviation is mathematically known as:
A) Mean Deviation
B) Range
C) Coefficient of variation
D) Variance
6 / 40Find the precise mean of the first 5 natural numbers:
\( 1, 2, 3, 4, 5 \)
A) \( 3 \)
B) \( 5 \)
C) \( 15 \)
D) \( 2.5 \)
7 / 40Find the median of the given ordered data set:
\( 1, 3, 5, 7, 9 \)
A) \( 3 \)
B) \( 5 \)
C) \( 7 \)
D) \( 25 \)
8 / 40Which of the following is a classic measure of 'Dispersion'?
A) Mean
B) Median
C) Variance
D) Mode
9 / 40The mathematical formula for finding the Range is given by:
A) Maximum + Minimum
B) Minimum - Maximum
C) Maximum - Minimum
D) Maximum \( \times \) Minimum
10 / 40What is the formula for the Mean Deviation about the mean \( \bar{x} \)?
A) \( \frac{\sum (x_i - \bar{x})^2}{n} \)
B) \( \frac{\sum (x_i - \bar{x})}{n} \)
C) \( \sum |x_i - \bar{x}| \)
D) \( \frac{\sum |x_i - \bar{x}|}{n} \)
11 / 40Which Greek symbol is universally used to denote 'Standard Deviation'?
A) \( \sigma \)
B) \( \Sigma \)
C) \( \Delta \)
D) \( \mu \)
12 / 40Which symbol is universally used to denote 'Variance'?
A) \( \sigma \)
B) \( \sigma^2 \)
C) \( \sqrt{\sigma} \)
D) \( \bar{x} \)
13 / 40Find the mean of the constant data set:
\( 5, 5, 5, 5 \)
A) \( 5 \)
B) \( 0 \)
C) \( 20 \)
D) \( 10 \)
14 / 40Find the exact Variance of the constant data set:
\( 5, 5, 5, 5 \)
A) \( 5 \)
B) \( 1 \)
C) \( 0 \)
D) \( 25 \)
15 / 40Find the Standard Deviation of the constant data set:
\( 5, 5, 5, 5 \)
A) \( 5 \)
B) \( 0 \)
C) \( 25 \)
D) \( 1 \)
16 / 40What is the formula for the Coefficient of Variation (C.V.)?
A) \( \frac{\bar{x}}{\sigma} \times 100 \)
B) \( \frac{\sigma}{\bar{x}} \)
C) \( \sigma \times \bar{x} \)
D) \( \frac{\sigma}{\bar{x}} \times 100 \)
17 / 40A series of data with a lesser Coefficient of Variation (C.V.) is considered to be more:
A) Consistent
B) Variable
C) Scattered
D) Dispersed
18 / 40The absolute value symbol \( |x| \) is strictly used in calculating which of the following?
A) Variance
B) Standard Deviation
C) Range
D) Mean Deviation
19 / 40Find the arithmetic mean of:
\( 10, 20, 30 \)
A) \( 10 \)
B) \( 20 \)
C) \( 30 \)
D) \( 60 \)
20 / 40Find the range of the first 10 natural numbers:
\( 1, 2, \dots, 10 \)
A) \( 10 \)
B) \( 1 \)
C) \( 9 \)
D) \( 11 \)
21 / 40If the Variance of a data set is strictly \( 16 \), what is its Standard Deviation?
A) \( 4 \)
B) \( 8 \)
C) \( 256 \)
D) \( 16 \)
22 / 40Find the mean of the first 5 whole numbers:
\( 0, 1, 2, 3, 4 \)
A) \( 2.5 \)
B) \( 3 \)
C) \( 2 \)
D) \( 10 \)
23 / 40If the Standard Deviation of a data set is \( 5 \), what is its Variance?
A) \( 5 \)
B) \( 25 \)
C) \( 10 \)
D) \( \sqrt{5} \)
24 / 40The mathematical value of Standard Deviation is always:
A) Negative
B) Zero
C) Imaginary
D) Non-negative
25 / 40What is the formula for calculating CV when
\( \sigma = 2 \) and \( \bar{x} = 20 \)?
A) \( 40 \)
B) \( 5 \)
C) \( 2 \)
D) \( 10 \)
26 / 40What is the explicit formula for the variance of ungrouped data?
A) \( \frac{\sum (x_i - \bar{x})^2}{n} \)
B) \( \frac{\sum |x_i - \bar{x}|}{n} \)
C) \( \sum (x_i - \bar{x})^2 \)
D) \( \frac{\sum (x_i)^2}{n} \)
27 / 40The mid-point of a continuous class interval is statistically called the:
A) Frequency
B) Median
C) Class mark
D) Class size
28 / 40Find the exact median of the data set:
\( 2, 4, 6, 8 \)
A) \( 4 \)
B) \( 5 \)
C) \( 6 \)
D) \( 10 \)
29 / 40Variance of a data set is completely independent of the change of:
A) Origin (Addition/Subtraction)
B) Scale (Multiplication)
C) Both Origin and Scale
D) Neither
30 / 40If every single observation is multiplied by \( 2 \), the new Standard Deviation is multiplied by:
A) \( 4 \)
B) \( 2 \)
C) \( 1 \)
D) \( 0 \)
31 / 40Find the range of the given data set:
\( -5, -2, 0, 4 \)
A) \( -1 \)
B) \( 1 \)
C) \( 4 \)
D) \( 9 \)
32 / 40If every single observation is increased by \( 5 \), the new variance will:
A) Increase by 5
B) Increase by 25
C) Remain the same
D) Become zero
33 / 40If the Mean is \( 50 \) and CV is \( 40\% \), calculate the exact Standard Deviation \( \sigma \).
A) \( 20 \)
B) \( 12.5 \)
C) \( 80 \)
D) \( 400 \)
34 / 40The standard formula for the variance of the first \( n \) natural numbers is:
A) \( \frac{n+1}{2} \)
B) \( \frac{n^2+1}{12} \)
C) \( \sqrt{\frac{n^2-1}{12}} \)
D) \( \frac{n^2-1}{12} \)
35 / 40Find the mean of the three terms:
\( x, x+2, x+4 \)
A) \( 3x + 6 \)
B) \( x + 2 \)
C) \( x \)
D) \( x + 4 \)
36 / 40The standard formula for the standard deviation of the first \( n \) natural numbers is:
A) \( \frac{n^2-1}{12} \)
B) \( \frac{n+1}{2} \)
C) \( \sqrt{\frac{n^2-1}{12}} \)
D) \( \frac{n(n+1)}{2} \)
37 / 40The algebraic sum of the deviations of items strictly from their mean \( \sum (x_i - \bar{x}) \) is always:
A) Zero
B) One
C) Minimum
D) Maximum
38 / 40The Mean Deviation is mathematically minimum when it is taken about the:
A) Mean
B) Median
C) Mode
D) Origin
39 / 40The sum of the squares of deviations is mathematically minimum when taken about the:
A) Median
B) Mode
C) Mean
D) Origin
40 / 40If \( \sum x_i = 50 \) and \( n = 10 \), find the exact value of the Mean \( \bar{x} \).
A) \( 500 \)
B) \( 10 \)
C) \( 0.2 \)
D) \( 5 \)
Test Analysis

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