Phrases Statistics Measures of Central Tendency Previous Year Question Paper and Solution with PDF

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Phrases Statistics Measures Of Central Tendency PYQ

The mean of 5 observation is 5 and their variance is 12.4. If three of the observations are 1,2 and 6; then the mean deviation from the mean of the data is:

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 2Phrases PYQ

If the mean deviation 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then d is equal to

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 3Phrases PYQ

and

, then a possible value of n is among the following is

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 4Phrases PYQ

Not Available

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 5Phrases PYQ

The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 6Phrases PYQ

The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 7Phrases PYQ

If ${{a}}_1,{{a}}_2,\ldots,{{a}}_n$ are any real numbers and $n$ is any positive integer, then

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 8Phrases PYQ

The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 9Phrases PYQ

Given a set A with median $m_1 = 2$ and set B with median $m_2 = 4$

What can we say about the median of the combined set?

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 10Phrases PYQ

If the mean of the squares of first n natural numbers be 11, then n is equal to?

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 11Phrases PYQ

The standard deviation of 20 numbers is 30. If each of the numbers is increased by 4, then the new standard deviation will be

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 12Phrases PYQ

If a variable takes values 0, 1, 2,…, 50 with frequencies $1,\, {{50}}_{{{C}}_1},{{50}}_{{{C}}_2},\ldots..,{{50}}_{{{C}}_{50}}$, then the AM is

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 13Phrases PYQ

Consider the following frequency distribution table.

Class Interval	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	180	$f_1$	34	180	136	$f_2$	50

If the total frequency is 686 and the median is 42.6, then the value of $f_1$;and $f_2$ are

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 14Phrases PYQ

A, B, C are three sets of values of x:

A: 2,3,7,1,3,2,3

B: 7,5,9,12,5,3,8

C: 4,4,11,7,2,3,4

Select the correct statement among the following:

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

A: 2, 3, 7, 1, 3, 2, 3

Increasing Order : A: 1, 2, 2, 3, 3, 3, 7

Mode = 3 (occurs maximum number of times)

Median = 3 (the middle term)

Mean =$\frac{(1+2+2+3+3+3+7)}{7}$

$=\frac{21}{7} = 3$

Hence. Mean=Median=Mode

Qus : 15Phrases PYQ

Standard deviation for the following distribution is

Size of item	6	7	8	9	10	11	12
Frequency	3	6	9	13	8	5	4

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Total number of items in the distribution = Σ f_i = 3 + 6 + 9 + 13 + 8 + 5 + 4 = 48.

The Mean (x̅) of the given set = $\rm \dfrac{\sum f_i x_i}{\sum f_i}$.

⇒ x̅ = $\rm \dfrac{6\times3+7\times6+8\times9+9\times13+10\times8+11\times5+12\times4}{48}=\dfrac{432}{48}$ = 9.

Let's calculate the variance using the formula: $\rm \sigma^2 =\dfrac{\sum x_i^2}{n}-\bar x^2$.

$\rm \dfrac{\sum {x_i}^2}{n}=\dfrac{6^2\times3+7^2\times6+8^2\times9+9^2\times13+10^2\times8+11^2\times5+12^2\times4}{48}=\dfrac{4012}{48}$ = 83.58.

∴ σ² = 83.58 - 9² = 83.58 - 81 = 2.58.

And, Standard Deviation (σ) = $\rm \sqrt{\sigma^2}=\sqrt{Variance}=\sqrt{2.58}$ ≈ 1.607.

Qus : 16Phrases PYQ

The mean of 5 observation is 5 and their variance is 124. If three of the observations are 1,2 and 6; then the mean deviation from the mean of the data is:

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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Qus : 17Phrases PYQ

For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures are

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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Qus : 18Phrases PYQ

Consider the following frequency distribution table.

Class interval	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	180	$f_1$	34	180	136	$f_2$	50

If the total frequency is 685 & median is 42.6 then the values of $f_1$ and $f_2$ are

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

Solution

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