Let's analyze the given information and the changes that occur to the dataset.
The original dataset is:
\[ 24, 15, 18, 30, 32, 40, 22, 27, 33, 35 \]
The new dataset is formed by replacing the maximum age (40) with 50:
\[ 24, 15, 18, 30, 32, 50, 22, 27, 33, 35 \]
### Mean Comparison
To compare the means, we first compute the mean of the original dataset:
\[ \text{Sum of original dataset} = 24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 35 = 276 \]
\[ \text{Mean of original dataset} = \frac{276}{10} = 27.6 \]
Now, let's compute the mean of the new dataset:
\[ \text{Sum of new dataset} = 24 + 15 + 18 + 30 + 32 + 50 + 22 + 27 + 33 + 35 = 286 \]
\[ \text{Mean of new dataset} = \frac{286}{10} = 28.6 \]
Clearly, the mean of the new dataset (28.6) is higher than the mean of the original dataset (27.6).
### Range Comparison
The range is calculated as the difference between the maximum and minimum values in the dataset.
For the original dataset:
\[ \text{Range of original dataset} = 40 - 15 = 25 \]
For the new dataset:
\[ \text{Range of new dataset} = 50 - 15 = 35 \]
Thus, the range of the new dataset is higher than the range of the original dataset.
### Dispersion Comparison
The dispersion or variability of a dataset can be assessed by various measures such as standard deviation or range.
Replacing 40 with 50 in the dataset likely increases the dispersion since the presence of a more extreme value (50 instead of 40) tends to increase the spread of the data points as reflected in the higher range.
From this analysis, we can determine that:
- The mean of the new dataset is higher than the mean of the original dataset.
- The range of the new dataset is higher than the range of the original dataset.
- The new dataset is more dispersed than the original dataset since the range increased.
Thus, the most accurate statement is:
\[ \boxed{\text{The mean of the new dataset is higher than the mean of the original dataset.}} \]
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. Which statement best compares the two datasets?(1 point) Responses The mean of the new dataset is lower than the mean of the original dataset. The mean of the new dataset is lower than the mean of the original dataset. The mean of the new dataset is higher than the mean of the original dataset. The mean of the new dataset is higher than the mean of the original dataset. The range of the original dataset is higher than the range of the new dataset. The range of the original dataset is higher than the range of the new dataset. The original dataset is more dispersed than the new dataset.
1 answer