Cara computes the mean and variance for the set 87, 46, 90, 78, and 89. She finds the mean to be 78. Her steps for finding the variance are shown below.
Variance squared = StartFraction (87 minus 78) squared + (46 minus 78) squared + (90 minus 78) squared + (78 minus 78) squared + (89 minus 78) squared Over 5 EndFraction
Variance squared = StartFraction (9) squared minus (32) squared + (12) squared + 0 squared + (11) squared Over 5 EndFraction
Variance squared = StartFraction 81 minus 1,024 + 144 + 0 +121 Over 5 EndFraction
Variance squared = StartFraction negative 678 Over 5 EndFraction = negative 135.6
What is the first error Cara made in computing the variance?

Population variance (σ²) describes the way data points in a given population are distributed. It is the aggregate of the distances from each data set in the population towards the mean squared.

The population variance is a population parameter that is independent of research methodologies or sampling practices.

Mathematically, The correct calculation can be done by using the formula:

[tex]\mathbf{\sigma^2 = \dfrac{ \sum(x_i-\bar x)^2}{N}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{ (87-78)^2 + (46-78)^2+ (90-78)^2+(78-78)^2+(89-78)^2}{5}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{ (9)^2 + (-32)^2+ (12)^2+(0)^2+(11)^2}{5}}[/tex]

We can now see that the minus 32 is supposed to be in the bracket.

[tex]\mathbf{\sigma^2 = \dfrac{81+1024+ 44+0+121}{5}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{1270}{5}}[/tex]

[tex]\mathbf{\sigma^2 = 254}[/tex]

Learn more about population variance here:
https://brainly.com/question/26520946