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What is the variance of the data set 49, 2, 52, 15, 25, 9, 3, 5 to the nearest hundredth?

Answer 1

Audrey Allen

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Answer 2

Liam Burke

To find the variance of a data set, follow these steps:

Find the mean (average) of the data set.
Subtract the mean from each data point, and square the result.
Find the mean of the squared differences obtained in step 2. This is the variance.

For the data set {49, 2, 52, 15, 25, 9, 3, 5}:

Mean ((\bar{x})) = (\frac{49 + 2 + 52 + 15 + 25 + 9 + 3 + 5}{8} = \frac{160}{8} = 20).
Squared differences from the mean: ((49 - 20)^2 = 841), ((2 - 20)^2 = 324), ((52 - 20)^2 = 1089), ((15 - 20)^2 = 25), ((25 - 20)^2 = 25), ((9 - 20)^2 = 121), ((3 - 20)^2 = 289), ((5 - 20)^2 = 225).
Mean of squared differences = (\frac{841 + 324 + 1089 + 25 + 25 + 121 + 289 + 225}{8} = \frac{2949}{8} \approx 368.63).

Therefore, the variance of the data set is approximately 368.63 to the nearest hundredth.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.