Question
A sample data set has a mean of 61.1 and a standard deviation of 7.8. Fine the minimum and maximum "usual" values of the data set
1)51.3 and 70.9
2)45.5 and 76.7
3)53.3 and 68.9
4)37.7 and 84.5
1)51.3 and 70.9
2)45.5 and 76.7
3)53.3 and 68.9
4)37.7 and 84.5
Answers
GPT-4o mini
In statistics, "usual" values are often defined as those that fall within ±2 standard deviations from the mean.
Given:
- Mean (\( \mu \)) = 61.1
- Standard deviation (\( \sigma \)) = 7.8
To find the minimum and maximum usual values:
1. Calculate \( \mu - 2\sigma \) for the minimum usual value:
\[
61.1 - 2(7.8) = 61.1 - 15.6 = 45.5
\]
2. Calculate \( \mu + 2\sigma \) for the maximum usual value:
\[
61.1 + 2(7.8) = 61.1 + 15.6 = 76.7
\]
Thus, the minimum and maximum usual values are 45.5 and 76.7, respectively.
The correct answer is:
**2) 45.5 and 76.7**.
Given:
- Mean (\( \mu \)) = 61.1
- Standard deviation (\( \sigma \)) = 7.8
To find the minimum and maximum usual values:
1. Calculate \( \mu - 2\sigma \) for the minimum usual value:
\[
61.1 - 2(7.8) = 61.1 - 15.6 = 45.5
\]
2. Calculate \( \mu + 2\sigma \) for the maximum usual value:
\[
61.1 + 2(7.8) = 61.1 + 15.6 = 76.7
\]
Thus, the minimum and maximum usual values are 45.5 and 76.7, respectively.
The correct answer is:
**2) 45.5 and 76.7**.