Question

Analyze Data Shape and Context Practice

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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

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To calculate the mean of a dataset, you add up all the values and then divide by the number of values.

Original dataset: 24, 15, 18, 30, 32, 40, 22, 27, 33, 35

Step 1: Calculate the mean of the original dataset.
Sum of original dataset = 24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 35 = 296
Number of values = 10
Mean of original dataset = Sum of original dataset / Number of values = 296 / 10 = 29.6

Step 2: Form the new dataset by replacing the maximum age with 50.
New dataset: 24, 15, 18, 30, 32, 40, 22, 27, 33, 50

Step 3: Calculate the mean of the new dataset.
Sum of new dataset = 24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 50 = 291
Number of values = 10
Mean of new dataset = Sum of new dataset / Number of values = 291 / 10 = 29.1

Step 4: Calculate the difference in means.
Difference in means = Mean of new dataset - Mean of original dataset = 29.1 - 29.6 = -0.5

The mean of the new dataset is 0.5 lower than the mean of the original dataset. Therefore, the mean of the new dataset is -0.5 years higher than the mean of the original dataset.