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Phrases Previous Year Questions (PYQs)

Phrases Statistics Measures Of Central Tendency PYQ


Phrases PYQ
List I List II
A. Dog : Rabies :: Mosquito : I. Bacteria
B. Amnesia : Memory :: Paralysis : II. Liver
C. Meningitis : Brain :: Cirrhosis : III. Movement
D. Influenza : Virus :: Typhoid : IV. Malaria






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Phrases Previous Year PYQPhrases CUET 2023 PYQ

Solution

Dog causes Rabies, Mosquito causes Malaria → A-IV
Amnesia affects Memory, Paralysis affects Movement → B-III
Meningitis affects Brain, Cirrhosis affects Liver → C-II
Influenza is caused by Virus, Typhoid is caused by Bacteria → D-I

Correct matching: A-IV, B-III, C-II, D-I

Phrases PYQ
If each of $n$ numbers $x_i = i$ is replaced by $(i+1)x_i$, then the new mean is





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

Original numbers: $1,2,3,\dots,n$

New values:
$(i+1)i = i^2+i$

Sum of new values:
$\sum i^2 + \sum i = \dfrac{n(n+1)(2n+1)}{6} + \dfrac{n(n+1)}{2}$

$= \dfrac{n(n+1)(2n+1+3)}{6}
= \dfrac{n(n+1)(2n+4)}{6}
= \dfrac{n(n+1)(n+2)}{3}$

New mean:
$\dfrac{(n+1)(n+2)}{3}$

Phrases PYQ
The mean deviation from the mean of the A.P. $a, a+d, a+2d, \ldots, a+2nd$ is





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

The A.P. is symmetric with $2n+1$ terms. Mean deviation from mean for such A.P. is $\dfrac{n(n+1)d}{2n+1}$.

Phrases PYQ
If each observation of raw data whose variance is $\sigma^2$ is multiplied by $h$, then the variance of the new set is





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

If all observations are multiplied by a constant $h$, then variance becomes $h^2$ times the original variance. So, new variance $=h^2\sigma^2$.

Phrases PYQ
Which of the following are true: 
(A) Ogive graph is used to measure the median of the collection of datas. 

(B) Two events A and B are such that P(A) = 1/2 and P(B) = 7/12 and P(not A not B) = 1/4 then A and B are independent events. 

(C) Relation for mean, mode and median is given by Mode = 3 Median – 2 Mean. 

(D) The number of two–digits even number formed from digits 1,2,3,4,5 is 10

Choose the correct answer from the options given below:





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Phrases Previous Year PYQ Phrases CUET 2024 PYQ

Solution

Solution:

(A) Ogive is used to determine the Median. ✅ True

(B) Given:
\( P(A) = \tfrac{1}{2}, \; P(B) = \tfrac{7}{12}, \; P(\text{not A and not B}) = \tfrac{1}{4} \)

\( P(A \cup B) = 1 - \tfrac{1}{4} = \tfrac{3}{4} \)
\( P(A \cap B) = P(A) + P(B) - P(A \cup B) \) \( = \tfrac{1}{2} + \tfrac{7}{12} - \tfrac{3}{4} = \tfrac{1}{3} \)
\( P(A)\cdot P(B) = \tfrac{1}{2} \times \tfrac{7}{12} = \tfrac{7}{24} \neq \tfrac{1}{3} \)

So, A and B are not independent. ❌ False

(C) Empirical relation: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] ✅ True

(D) Two–digit even numbers from {1,2,3,4,5}:
- Units digit must be even → {2, 4} → 2 choices.
- Tens digit (if repetition allowed) → 5 choices.
\[ \text{Total} = 5 \times 2 = 10 \] ✅ True (with repetition allowed)

✔ Final Answer: (A), (C), and (D) are correct.


Phrases PYQ
Mean and variance of 12 observations are $ \frac{9}{2} $ and $4$ respectively. Later it was observed that two observations were considered $9$ and $10$ instead of $7$ and $14$ respectively. If the correct variance is $ \frac{m}{n} $ where $m$ and $n$ are coprime, then $m+n$ is





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Phrases Previous Year PYQ Phrases CUET MCA 2026 PYQ

Solution


Phrases PYQ
Arrange the following in sequence to find variance of individual observation. 
(A) compute $ \bar{X} $ of observation $x_1, x_2 \dots x_n$ 
(B) square the deviation obtain sum $ \sum_{i=1}^{n} (x_i-\bar{X})^2 $ 
(C) divide the sum $ \sum_{i=1}^{n} (x_i-\bar{X})^2 $ by $n$ 
(D) take deviation of observation from mean that is $(x_i-\bar{X})$ 

(a) A, B, C, D 
(b) A, D, B, C 
(c) A, C, B, D 
(d) B, C, D, A





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Phrases Previous Year PYQ Phrases CUET MCA 2026 PYQ

Solution


Phrases PYQ
The mean of 5 data is 5.2 and their variance is 27.296. If there of the data are 1, 3 and 6 then other two data are





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Phrases Previous Year PYQ Phrases CUET 2024 PYQ

Solution


Phrases PYQ
The arithmetic mean and standard deviation of series of 20 items were calculated by a student as 20 cm and 5 cm respectively. But while calculating them an item 15 was misread as 30. Find the correct standard deviation.





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
Given the marks of 25 students in the class as $\{m_1,m_2,m_3,..m_{25}\}$. Marks lie in the range of [1-100] and $\overline{m}$ is the mean. Which of the following quantity has the value zero?





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution



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