Qus : 8 MCA NIMCET PYQ 2024 2 In
a reality show, two judges independently provided marks base do the performance
of the participants. If the marks provided by the second judge are given by Y =
10.5 + 2x, where X is the marks provided by the first judge. If the variance of
the marks provided by the second judge is 100, then the variance of the marks provided
by the first judge is:
1 49.5 2 25 3 50
4 99 Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2024 PYQ Solution
Statistics Puzzle: Variance under Linear Transformation
Given:
Y = 10.5 + 2X
Var(Y) = 100
Formula: If Y = a + bX, then Var(Y) = b² × Var(X)
Apply:
100 = 2² × Var(X)
100 = 4 × Var(X)
Var(X) = 100 / 4 = 25
✅ Final Answer: The variance of the marks given by the first judge is 25 .
Qus : 10 MCA NIMCET PYQ 2024 4 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?
1 at most 1 2 at most 2 3 at least 1 4 at least 2 Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2024 PYQ Solution
Given two sets:
Set A has median m 1 = 2
Set B has median m 2 = 4
What can we say about the median of the combined set A ∪ B ?
✅ Answer:
The combined median depends on the size and values of both sets.
Without that information , we only know that:
Combined Median ∈ [ 2 , 4 ]
So, the exact median cannot be determined with the given data.
Qus : 11 MCA NIMCET PYQ 2024 1 It is given that the mean, median and mode of a data set is 1 , 3 x and 9 x respectively. The possible values of the mode is
1 1,4 2 1,9 3 3,9 4 9,8 Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2024 PYQ Solution
Mean, Median, and Mode Relation
Given:
Mean = 1
Median = 3 x
Mode = 9 x
Use empirical formula:
Mode = 3 ⋅ Median − 2 ⋅ Mean
9 x = 3 ⋅ 3 x − 2 ⇒ ( 3 x ) 2 = 3 ⋅ 3 x − 2
Let y = 3 x , then:
y 2 = 3 y − 2 ⇒ y 2 − 3 y + 2 = 0 ⇒ ( y − 1 ) ( y − 2 ) = 0
So, y = 1 or 2 ⇒ 9 x = y 2 = 1 or 4
✅ Final Answer: 1 or 4
Qus : 14 MCA NIMCET PYQ 2025 4 Which one of the following is NOT a correct statement?
1 The value of standard deviation changes by a change of scale 2 The standard deviation is greater than or equal to the mean deviation (about mean) 3 The sum of squares of deviations is minimum when taken from the mean 4 The variance is expressed in the same units as the units of observation Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2025 PYQ
Solution Qus : 20 MCA NIMCET PYQ 2020 4 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:
1 Mean of A is equal to Mode of C 2 Mean of C is equal to Median of B 3 Median of B is equal to Mode of A 4 Mean, Median and Mode of A are same Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET 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 =( 1 + 2 + 2 + 3 + 3 + 3 + 7 ) 7
= 21 7 = 3
Hence. Mean=Median=Mode
Qus : 21 MCA NIMCET PYQ 2020 1 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
1 1.607 2 9.0 3 5.0 4 1.88 Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2020 PYQ Solution Total number of items in the distribution = Σ fi = 3 + 6 + 9 + 13 + 8 + 5 + 4 = 48.
The Mean (x̅) of the given set = ∑ f i x i ∑ f i .
⇒ x̅ = 6 × 3 + 7 × 6 + 8 × 9 + 9 × 13 + 10 × 8 + 11 × 5 + 12 × 4 48 = 432 48 = 9.
Let's calculate the variance using the formula: σ 2 = ∑ x 2 i n − ˉ x 2 .
∑ x i 2 n = 6 2 × 3 + 7 2 × 6 + 8 2 × 9 + 9 2 × 13 + 10 2 × 8 + 11 2 × 5 + 12 2 × 4 48 = 4012 48 = 83.58.
∴ σ2 = 83.58 - 92 = 83.58 - 81 = 2.58.
And, Standard Deviation (σ) = √ σ 2 = √ V a r i a n c e = √ 2.58 ≈ 1.607 .
Qus : 23 MCA NIMCET PYQ 2023 3 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
1 39.9, 14.97 2 39.5, 14 3 39.55, 14.97 4 40.19, 15.1 Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2023 PYQ Solution
Corrected Mean and Standard Deviation
Original Mean: 40, Standard Deviation: 15
Two scores were misread: 25 → 52 and 35 → 53
Corrected Mean:
μ ′ = 3955 100 = 39.55
Corrected Standard Deviation:
σ ′ = √ 178837 100 − ( 39.55 ) 2 ≈ 14.96
✅ Final Answer:
Mean = 39.55, Standard Deviation ≈ 14.96
Qus : 24 MCA NIMCET PYQ 2023 4 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
1 80, 25 2 83, 22 3 79, 26 4 82, 23 Go to Discussion MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2023 PYQ Solution
Median & Frequency Table
Given: Median = 42.6, Total Frequency = 685
Using Median Formula:
Median = L + ( N / 2 − F f ) ⋅ h
Median Class: 40–50
Lower boundary L = 40
Frequency f = 180
Class width h = 10
Cumulative freq before median class F = 214 + f 1
Substituting values:
42.6 = 40 + ( 128.5 − f 1 180 ) ⋅ 10 ⇒ f 1 = 82
Using total frequency:
662 + f 2 = 685 ⇒ f 2 = 23
✅ Final Answer:
f 1 = 82 , f 2 = 23
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