Analyze Data Shape and Context Practice

Question

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4 of 54 of 5 Items

Question
The ages (in years) of 10 randomly selected individuals are 24, 15, 18, 30, 32, 40, 22, 27, 33, and 35. Form a new dataset by replacing the maximum age with 50. In years, how much higher is the mean of the new dataset than the mean of the original dataset?(1 point)
year(s)

Answer 1

To find the mean of the original dataset, we add all the ages together and divide by the total number of individuals:

Mean of original dataset = (24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 35) / 10
= 296 / 10
= 29.6 years

Now, to find the mean of the new dataset, we replace the maximum age (40) with 50 and find the mean using the same method:

Mean of new dataset = (24 + 15 + 18 + 30 + 32 + 50 + 22 + 27 + 33 + 35) / 10
= 286 / 10
= 28.6 years

The mean of the new dataset is 28.6 years.

The difference between the mean of the new dataset and the mean of the original dataset is:

29.6 - 28.6 = 1 year

Therefore, the mean of the new dataset is 1 year higher than the mean of the original dataset.