Tesla (a car company) is developing a new vehicle that is very expensive. The marketing team is working on how to advertise this niche product to their market. Since the car is so expensive, their population is very small so they are able to interview all people in the population. The team is interested in the age of the users that may potentially buy the product. Let Y be the ages of the person being interviewed.

The data is below

Y = {40, 50, 56, 41, 28, 39, 66, 47}

What is the variance of Y?

(Note: you must use the formula in Ch 1 of the Text, or in the "Population & Sample Introduction" Video)

Submit your answer as a number rounded to 3 decimals. So 540.12357 would be input as 540.124

Question

Tesla (a car company) is developing a new vehicle that is very expensive. The marketing team is working on how to advertise this niche product to their market. Since the car is so expensive, their population is very small so they are able to interview all people in the population. The team is interested in the age of the users that may potentially buy the product. Let Y be the ages of the person being interviewed.

The data is below

Y = {40, 50, 56, 41, 28, 39, 66, 47}

What is the variance of Y?

(Note: you must use the formula in Ch 1 of the Text, or in the "Population & Sample Introduction" Video)

Submit your answer as a number rounded to 3 decimals. So 540.12357 would be input as 540.124

BlackTom AI · Accepted Answer

We have Y = {40, 50, 56, 41, 28, 39, 66, 47} with N = 8.
First, compute the mean: sum = 40+50+56+41+28+39+66+47 = 367; mean = 367/8 = 45.875.
Next, compute each deviation from the mean and square it:
- 40: (40 - 45.875) = -5.875; squared = 34.515625
- 50: (50 - 45.875) = 4.125; squared = 17.015625
- 56: (56 - 45.875) = 10.125; squared = 102.515625
- 41: (41 - 45.875) = -4.875; squared = 23.765625
- 28: (28 - 45.875) = -17.875; squared = 319.515625
- 39: (39 - 45.875) = -6.875; squared = 47.265625
- 66: (66 - 45.875) = 20.125; squared = 405.015625
- 47: (47 - 45.875) = 1.125; squared = 1.265625

Sum of squared deviations = 34.515625 + 17.015625 + 102.515625 + 23.765625 + 319.515625 + 47.265625 + 405.015625 + 1.265625 = 950.875.
Now decide which variance to use:
- Population variance uses divide-by-N: 950.875 / 8 = 118.859375, which rounds to 118.859.
- Sample variance uses divide-by-(N-1): 950.875 / 7 = 135.8392857..., which rounds to 135.839 (to three decimals) or 135.8393 (to four decimals).
The problem statement references a formula from Chapter 1 or the Population & Sample Introduction video, so both definitions could be relevant depending on whether you treat the data as the entire population or a sample of a larger population. In this dataset, since the set appears to be the entire population of interest, the population variance would be 118.859, while if treated as a sample the variance would be 135.8393 (approximately).
If you were required to match a specific rounding convention used by the course (three decimals), you would report 118.859 for population variance or 135.839 for sample variance, noting that the latter corresponds to the sample variance calculation.

STA304H1 S Module 3 Practice Problems

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