Question
1 2 3 4 5 TIME REMAININ 58:04 The mean shoe size of the students in a math class is. 7.5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9 . What is the standard deviation of the shoe size data for the math class? 1.5 2.7 3.0 3.8
Ask by Deleon Hobbs. in the United States
Jan 22,2025
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Tutor-Verified Answer
Answer
The standard deviation of the shoe size data is 1.5.
Solution
To determine the **standard deviation** of the shoe size data for the math class, let's analyze the information provided:
- **Mean (μ)**: 7.5
- **Range within 1 standard deviation**: 6 to 9
In a normal distribution, approximately 68% of the data falls within **one standard deviation** from the mean. This range is represented as:
\[ \mu - \sigma \quad \text{to} \quad \mu + \sigma \]
Given:
\[ \mu - \sigma = 6 \]
\[ \mu + \sigma = 9 \]
Substitute the mean (7.5) into the equations:
1. **Lower Bound**:
\[ 7.5 - \sigma = 6 \]
\[ \sigma = 7.5 - 6 \]
\[ \sigma = 1.5 \]
2. **Upper Bound**:
\[ 7.5 + \sigma = 9 \]
\[ \sigma = 9 - 7.5 \]
\[ \sigma = 1.5 \]
Both calculations confirm that the **standard deviation (σ)** is **1.5**.
**Answer:**
**1.5**
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Simplify this solution Extra Insights
To find the standard deviation, we can look at the range of shoe sizes that falls within one standard deviation from the mean. Given that the mean is 7.5 and most shoe sizes fall between 6 and 9, we can calculate the standard deviation as follows: The distance from the mean (7.5) to the lower boundary (6) is 1.5, and the distance to the upper boundary (9) is also 1.5. This tells us that 1 standard deviation equals 1.5. Therefore, the standard deviation of the shoe size data for the math class is **1.5**.
