In a class of 32 students

the mean height of the 14 boys is 1.56 metres

the mean height of all 32 students is 1.515 metres.

Work out the mean height of the girls.

To find the mean height of the girls, we can use the given data and apply the formula for the mean:

1. **Given data**:
   - Number of boys = 14
   - Number of girls = 32 - 14 = 18
   - Mean height of boys = 1.56 meters
   - Mean height of all students = 1.515 meters

2. **Calculate the total height of boys**:
   \[
   \text{Total height of boys} = \text{Number of boys} \times \text{Mean height of boys}
   \]
   \[
   \text{Total height of boys} = 14 \times 1.56 = 21.84 \text{ meters}
   \]

3. **Calculate the total height of all students**:
   \[
   \text{Total height of all students} = \text{Number of students} \times \text{Mean height of all students}
   \]
   \[
   \text{Total height of all students} = 32 \times 1.515 = 48.48 \text{ meters}
   \]

4. **Calculate the total height of the girls**:
   \[
   \text{Total height of girls} = \text{Total height of all students} - \text{Total height of boys}
   \]
   \[
   \text{Total height of girls} = 48.48 - 21.84 = 26.64 \text{ meters}
   \]

5. **Calculate the mean height of the girls**:
   \[
   \text{Mean height of girls} = \frac{\text{Total height of girls}}{\text{Number of girls}}
   \]
   \[
   \text{Mean height of girls} = \frac{26.64}{18} = 1.48 \text{ meters}
   \]

So, the mean height of the girls is **1.48 meters**.

Would you like to know more details or have any questions?

Here are some related questions you might find interesting:
1. How do you find the mean height if only the heights of a few individuals are given?
2. How does adding or removing individuals affect the mean?
3. What if the heights were given in centimeters instead of meters?
4. How would the mean change if one student was significantly taller than the others?
5. What is the relationship between mean, median, and mode in a dataset?

**Tip:** When working with averages, it's often useful to use the total sum, as it can make it easier to manipulate and solve problems involving groups.

In a class of 32 students, the mean height of the 14 boys is 1.56 metres, and the mean height of all 32 students is 1.515 metres. Work out the mean height of the girls.

Learn how to calculate the mean height of girls in a class of 32 students. The mean height of the boys is 1.56 metres, and the overall mean height is 1.515 metres. This problem demonstrates how to apply the arithmetic mean formula to find the answer, making it perfect for students in Grades 6-8.

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