Question
5. The weights (in kg ) of 8 children are \( 13.4,10.6,12.7,17.2,14.3,15,16.5,9.8 \). Find the median weight.
Ask by Norton Wilson. in India
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The median weight is 13.85 kg.
Solution
To find the median weight of the 8 children, follow these steps:
1. **List the Weights:**
\[
13.4,\ 10.6,\ 12.7,\ 17.2,\ 14.3,\ 15,\ 16.5,\ 9.8 \text{ kg}
\]
2. **Arrange the Weights in Ascending Order:**
\[
9.8,\ 10.6,\ 12.7,\ 13.4,\ 14.3,\ 15,\ 16.5,\ 17.2 \text{ kg}
\]
3. **Determine the Median:**
- Since there are **8** data points (an even number), the median is the average of the 4th and 5th values.
- **4th value:** 13.4 kg
- **5th value:** 14.3 kg
4. **Calculate the Median:**
\[
\text{Median} = \frac{13.4\ \text{kg} + 14.3\ \text{kg}}{2} = \frac{27.7\ \text{kg}}{2} = 13.85\ \text{kg}
\]
**Answer:** The median weight is 13.85 kg.
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Simplify this solution The Deep Dive
To find the median weight, first, you need to arrange the weights in ascending order: \( 9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2 \). Since there are 8 values (an even number), the median will be the average of the two middle values. The two middle values are \( 13.4 \) and \( 14.3 \). Calculating the median: \[ \text{Median} = \frac{13.4 + 14.3}{2} = \frac{27.7}{2} = 13.85 \text{ kg} \] So, the median weight of the children is \( 13.85 \) kg.
