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).

Answer 1

[AI-generated answer — Bot GPT 3.5]

The original dataset has a mean of $(24+15+18+30+32+40+22+27+33+35)/10=276/10=27.6$.

After replacing the maximum age with 50, the new dataset becomes (24, 15, 18, 30, 32, 40, 22, 27, 33, 50).

The new dataset has a mean of $(24+15+18+30+32+40+22+27+33+50)/10=311/10=31.1$.

The mean of the new dataset is $31.1-27.6=\boxed{3.5}$ higher than the mean of the original dataset.

Answer 2

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

To find the mean of a dataset, you sum up all the values in the dataset and divide it by the number of values.

Let's calculate the mean of the original dataset first:
24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 35 = 276
The original dataset has 10 values, so the mean is 276 / 10 = 27.6.

To find the new mean after replacing the maximum age with 50, we need to calculate the sum of the new dataset. The new dataset is:
24, 15, 18, 30, 32, 40, 22, 27, 33, 50.

Summing up these values:
24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 50 = 311.

The new dataset still contains 10 values, so the new mean is 311 / 10 = 31.1.

The new mean is higher than the original mean by:
31.1 - 27.6 = 3.5 years.