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Test: Statistics- 2 - JEE MCQ


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25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Statistics- 2

Test: Statistics- 2 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Statistics- 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Statistics- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Statistics- 2 below.
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Test: Statistics- 2 - Question 1

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

Test: Statistics- 2 - Question 2

If the mean of the first n odd natural numbers be n itself, then n is equal to

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Test: Statistics- 2 - Question 3

The mean of the first n terms of the A.P. (a + d) + (a + 3d) + (a + 5d) +………..is

Test: Statistics- 2 - Question 4

If a, b, c be any three positive numbers, then the least value of  (a + b + c) 

Detailed Solution for Test: Statistics- 2 - Question 4

Test: Statistics- 2 - Question 5

The median of the data 13,14,16,18,20,22 is

Test: Statistics- 2 - Question 6

If the two lines of regression are at right angles, then ρ(X,Y) is equal to

Test: Statistics- 2 - Question 7

If COV(X,Y) = 0, then the two lines of the regression are

Test: Statistics- 2 - Question 8

If the variance of the data is V, then its S.D. is

Detailed Solution for Test: Statistics- 2 - Question 8

If the variance of the data is denoted by V, then the standard deviation (S.D.) is the square root of the variance.
Mathematically,
S.D. = √V
The correct answer is: a) √V

Test: Statistics- 2 - Question 9

If the two lines of regression are y = 3x – 5 and y = 2x – 4 , then ρ(X,Y) is equal t

Test: Statistics- 2 - Question 10

If the median = (mode + 2 mean) μ, then μ is equal to

Test: Statistics- 2 - Question 11

If mean = (3 median – mode) x , then the value of x is

Test: Statistics- 2 - Question 12

Least square lines of regression give best possible estimates, when ρ(X,Y) is equal to

Test: Statistics- 2 - Question 13

Quartile deviation is nearly equal to

Test: Statistics- 2 - Question 14

For a symmetrical distribution Q1 = 20 and Q3. = 40. The median of the data is

Test: Statistics- 2 - Question 15

Which of the following is not a measure of dispersion ?

Test: Statistics- 2 - Question 16

The mean and S.D. of 1,2,3,4,5,6 is

Detailed Solution for Test: Statistics- 2 - Question 16

We are given the data: 1, 2, 3, 4, 5, 6

Step 1: Calculate the Mean

The formula for the mean is:

Mean = (Sum of all values) / (Number of values)

Substituting the values:

Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 7/2

Step 2: Calculate the Variance

The formula for variance is:

Variance = Σ(xi - Mean)² / n

1. Subtract the mean (7/2) from each value and square the result:

  • (1 - 7/2)² = (-5/2)² = 25/4
  • (2 - 7/2)² = (-3/2)² = 9/4
  • (3 - 7/2)² = (-1/2)² = 1/4
  • (4 - 7/2)² = (1/2)² = 1/4
  • (5 - 7/2)² = (3/2)² = 9/4
  • (6 - 7/2)² = (5/2)² = 25/4

2. Sum the squared values:

(25/4) + (9/4) + (1/4) + (1/4) + (9/4) + (25/4) = 70/4 = 35/2

3. Divide by n (6):

Variance = (35/2) / 6 = 35/12

Step 3: Calculate the Standard Deviation

The standard deviation is the square root of the variance:

Standard Deviation = √(35/12)

Final Answer

The mean is 7/2, and the standard deviation is √(35/12).

Correct option: (c) 7/2, √(35/12)

Test: Statistics- 2 - Question 17

The range of the following set of observations 2,3,5,9,8,7,6,5,7,4,3 is

Test: Statistics- 2 - Question 18

Which of the following, in case of a discrete data, is not equal to the median?

Test: Statistics- 2 - Question 19

Mean deviation from the mean for the observations – 1, 0 ,4 is

Test: Statistics- 2 - Question 20

The mean of 50 observations is 36, if two observations are 30 and 42 are deleted , then the mean of the remaining observations is

Test: Statistics- 2 - Question 21

For a bivariate frequency distribution byx > 1, then byx is

Test: Statistics- 2 - Question 22

A man tavels at a speed of 20 km/hour and then return at a speed of 30 km/hour. His average speed of the whole journey is

Test: Statistics- 2 - Question 23

In a group of students, mean weight of boys is 80 kg and mean weight of girls is 50kg.If the mean weight of all the students taken together is 60kg, then the ratio of the number of boys to that of the girls is

Test: Statistics- 2 - Question 24

If the mean of 3,4,x,7,10, is 6, then the value of x is

Test: Statistics- 2 - Question 25

For a normal distribution, we have

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