Autotrade.com would like to estimate the number of years owners keep the cars th

Question

Autotrade.com would like to estimate the number of years owners keep the cars that they purchase as a new vehicle. The following data shows the age of seven vehicles that were sold for the first time by their owners.
9 3 5 1 8 5 3 Using this sample, the point estimate for the age of cars sold for the first time is? Autotrade.com would like to estimate the number of years owners keep the cars that they purchase as a new vehicle. The following data shows the age of seven vehicles that were sold for the first time by their owners.
9 3 5 1 8 5 3 Using this sample, the point estimate for the age of cars sold for the first time is?

Explanation / Answer

Mean = Sum of observations/ Count of observations
Mean = (9 + 3 + 5 + 1 + 8 + 5 + 3 / 7) = 4.8571
Variance
Step 1: Add them up
9 + 3 + 5 + 1 + 8 + 5 + 3 = 34
Step 2: Square your answer
34*34 =1156
…and divide by the number of items. We have 7 items , 1156/7 = 165.1429
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
9^2 + 3^2 + 5^2 + 1^2 + 8^2 + 5^2 + 3^2 = 214
Step 4: Subtract the amount in Step 2 from the amount in Step 3
214 - 165.1429 = 48.8571
Step 5: Subtract 1 from the number of items in your data set, 7 - 1 = 6
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
48.8571 / 6 = 8.1429
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
2.8536

point estimate = sample variance = 8.1429

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