Home
Class 11
MATHS
Pearson's coefficient of correlation r a...

Pearson's coefficient of correlation r always follow: (a)`rle1` (b)`rlt-1` (c)`|r|le1` (d)`|r|ge1`

A

`rle1`

B

`rlt-1`

C

`|r|le1`

D

`|r|ge1`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding Pearson's coefficient of correlation \( r \), we will analyze the properties of \( r \) step by step. ### Step 1: Understanding Pearson's Coefficient of Correlation Pearson's coefficient of correlation \( r \) is a statistical measure that describes the strength and direction of a linear relationship between two variables. ### Step 2: Range of \( r \) It is known that the value of \( r \) can range from -1 to +1. This means: \[ -1 \leq r \leq 1 \] ### Step 3: Analyzing the Options Now, let's evaluate the given options based on the range of \( r \): - **Option (a)**: \( r \leq 1 \) - This is true, but it does not account for the lower limit of \( r \). Therefore, it is not a complete representation of the range. - **Option (b)**: \( r < -1 \) - This is incorrect because \( r \) cannot be less than -1. - **Option (c)**: \( |r| \leq 1 \) - This is correct because it captures both the upper and lower bounds of \( r \). It states that the absolute value of \( r \) is always less than or equal to 1. - **Option (d)**: \( |r| \geq 1 \) - This is incorrect because it suggests that \( r \) can be equal to or greater than 1 in absolute value, which is not true. ### Step 4: Conclusion Based on the analysis, the correct answer is: \[ \text{(c) } |r| \leq 1 \]
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MODEL TEST PAPER -4

    ICSE|Exercise SECTION -B|10 Videos

  • MODEL TEST PAPER -3

    ICSE|Exercise Section B |7 Videos

  • MODEL TEST PAPER -5

    ICSE|Exercise SECTION -C|10 Videos

Similar Questions

Explore conceptually related problems

Prove that coefficient of x^(r ) in (1-x)^(-n) " is " ""^(n+r-1)C_(r )

The coefficient of x^(50) in the series sum_(r=1)^(101)rx^(r-1)(1+x)^(101-r) is

Knowledge Check

  • Two moles of oxygen are mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is a) 1.3 R b) 1.4 R c) 1.7 R d) 1.9 R

    A
    1.3 R
    B
    1.4R
    C
    1.7R
    D
    1.9R

    • Similar Questions

    Explore conceptually related problems

    Prove that the coefficient of x^r in the expansion of (1-2x)^(-1/2) is (2r!)/[(2^r)(r!)^2]

    The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+.... +(x+2)^(n-1) is a.^n C_r(3^r-2^n) b.^n C_r(3^(n-r)-2^(n-r)) c.^n C_r(3^r+2^(n-r)) d. none of these

    Two concentric uniformly charge spherical shells of radius R_(1) and R_(2) (R_(2) gt R_(1)) have total charges Q_(1) and Q_(2) respectively. Derive an expression of electric field as a function of r for following positions. (i) r lt R_(1) (ii) R_(1) le r lt R_(2) (iii) r ge R_(2)

    Given positive integers r gt 1, n gt 2 and that the coefficient of (3rd)th and (r+2)th terms in the binomial expansion of (1+x)^(2n) are equal. Then (a) n=2r (b) n=2r+1 (c) n=3r (d) non of these

    If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expansion of (1+x)^(14) are in A.P., then r is/are a. 5 b. 11 c. 10 d. 9

    If the coefficients of r,(r +1 ),(r+2) terms in (1+x)^14 are in A.P. then r =

    If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

    Home
    Profile