If the variance of a data set is correctly computed with the formula using n -1 in the denominator, which of the following is true? a. the data set is a population. b. the data set is a sample. c. the data set could be either a sample or a population. d. the data set is from a census.

B. . the data set is a sample

Step-by-step explanation:

Given that the variance of a data set is correctly computed with the formula using n -1 in the denominator

We know by central limit theorem, that for large samples randomly drawn, the mean of the samples follow a normal distribution.

Here variance of the mean would be variance of population divided by degrees of freedom.

when sample size is n, we have degree of freedom n-1.

Hence only for samples of sizes n, where degree of freedom is n-1 we divide variance by n-1.

Answer is

B. . the data set is a sample

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.