The owner of a manufacturing plant employs eighty people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The distances for a random sample of six employees are listed below: 26 32 29 16 45 19 Find the variance for the given data.

The variance of the given data is 106.9667

Step-by-step explanation:

The variance, S² of a sample is given by the expression;

Where:

= One of the observations

= The mean of the observations

n = Number in the sample = 6

The mean = Σ/n = (26  + 32 + 29  + 16  + 45  + 19 )/6 = 167/6 = 27.833

Therefore, we have;

S² = ((26 - 27.833)²+(32 - 27.833)²+(29 - 27.833)²+(16 - 27.833)²+(45 - 27.833)²+(19 - 27.833)²)/(6 - 1) = 106.9667.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."