hannahcornell77
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Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her
steps for finding the variance are shown below.
(87 - 78)2 + (46 - 78)? +(90- 78)2+(78-78)2 + (89 - 78) 2
(9)2-(32)? +(12)2+(0)+(11)2
81 - 1,024 + 144 + 0 + 121
-678
--135.6
What is the first error she made in computing the variance?
Emi failed to find the difference of 89 - 78 correctly
Emi divided by N-1 instead of N.
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Answer:

The first error she made in computing the variance was to have placed -1,024 instead of +1,024

Step-by-step explanation:

we have the data set

87, 46, 90, 78, and 89

step 1

Find the mean

[tex](87+46+90+78+89)/5[/tex]

[tex]390/5=78[/tex]

step 2

Subtract the Mean for each value of data set and square the result  and then adds the numbers

[tex](87-78)^{2}+(46-78)^{2}+(90-78)^{2}+(78-78)^{2}+(89-78)^{2}[/tex]

[tex](9)^{2}+(-32)^{2}+(12)^{2}+(0)^{2}+(11)^{2}[/tex]

[tex]81+1,024+144+0+121[/tex]

so

The first error she made in computing the variance was to have placed -1,024 instead of +1,024

[tex]1,370[/tex]

step 3

Work out the mean of those squared differences

[tex]1,370/5=274[/tex] ----> this value is called the "Variance"

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