Question
University students were surveyed randomly in their opinion regarding a recent tuition increase. The minimum age recorded was 18 and the maximum age was 45. Use the range rule of thumb to estimate the standard deviation of the ages.
1)6.8
2)27.0
3)31.5
4)7.9
1)6.8
2)27.0
3)31.5
4)7.9
Answers
GPT-4o mini
The range rule of thumb provides a way to estimate the standard deviation (σ) using the range of a dataset. The formula for this is:
\[
\sigma \approx \frac{\text{Range}}{4}
\]
Where the range is calculated as the difference between the maximum and minimum values in the dataset.
In this case, the minimum age is 18 and the maximum age is 45.
First, we calculate the range:
\[
\text{Range} = \text{Maximum} - \text{Minimum} = 45 - 18 = 27
\]
Now, we can use the range to estimate the standard deviation:
\[
\sigma \approx \frac{27}{4} = 6.75
\]
Rounding this value gives us approximately 6.8.
Therefore, the estimated standard deviation of the ages is:
**1) 6.8**.
\[
\sigma \approx \frac{\text{Range}}{4}
\]
Where the range is calculated as the difference between the maximum and minimum values in the dataset.
In this case, the minimum age is 18 and the maximum age is 45.
First, we calculate the range:
\[
\text{Range} = \text{Maximum} - \text{Minimum} = 45 - 18 = 27
\]
Now, we can use the range to estimate the standard deviation:
\[
\sigma \approx \frac{27}{4} = 6.75
\]
Rounding this value gives us approximately 6.8.
Therefore, the estimated standard deviation of the ages is:
**1) 6.8**.