Match each number to the letters of its location on the number line

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marian987

12.04.2023

Mathematics

The variance of the data set is 1.28, approximately.

Step-by-step explanation:

The variance is defined by

$\sigma^{2} =\frac{\sum (x-\mu)^{2} }{N-1}$

Where $\mu$ is the mean and is the total number of rings.

First, we find the mean

$\mu = \frac{9+7+6.5+7.5+7+8+5+6+7.5+8}{10}=\frac{71.5}{10}=7.15$

Then, we subtract the means with each element

$9-7.15=1.85\\7-7.15=-0.15\\6.5-7.15=-0.65\\7.5-7.15=0.35\\7-7.15=-0.15\\8-7.15=0.85\\5-7.15=-2.15\\6-7.15=-1.15\\7.5-7.15=0.35\\8-7.15=0.85$

Now, we elevate each difference to the square power

$(1.85)^{2} =3.4225\\(-0.15)^{2} =0.0225\\(-0.65)^{2} =0.4225\\(0.35)^{2} =0.1225\\(-0.15)^{2} =0.0225\\(0.85)^{2} =0.7225\\(-2.15)^{2} =4.6225\\(-1.15)^{2} =1.3225\\(0.35)^{2} =0.1225\\(0.85)^{2} =0.7225$

Then, we sum all these results

$\sum (x-\mu)^{2}= 11.525$

Now, we replace in the formula

$\sigma^{2} =\frac{\sum (x-\mu)^{2} }{N-1}=\frac{11.525}{10-1} \approx 1.28$

Therefore, the variance of the data set is 1.28, approximately.

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Match each number to the letters of its location on the number line​​