To find the average height of children based on the given data, we will follow these steps:
1. Identify the heights and the number of children associated with each height category.
Given the data:
- Heights (in Inches): [10, 20, 30, 40, 50, 60]
- Number of children: [8, 11, 15, 22, 25, 30]
2. Calculate the total number of children:
The total number of children is the sum of the number of children in all height categories:
[tex]\[
\text{Total Number of Children} = 8 + 11 + 15 + 22 + 25 + 30 = 111
\][/tex]
3. Calculate the weighted sum of heights:
Each height category will be multiplied by the number of children in that category to get the weighted sum of heights:
[tex]\[
\text{Weighted Sum of Heights} = (10 \times 8) + (20 \times 11) + (30 \times 15) + (40 \times 22) + (50 \times 25) + (60 \times 30)
\][/tex]
Simplifying each term:
[tex]\[
= 80 + 220 + 450 + 880 + 1250 + 1800
\][/tex]
Now, sum these products to get the total weighted sum of heights:
[tex]\[
\text{Weighted Sum of Heights} = 80 + 220 + 450 + 880 + 1250 + 1800 = 4680
\][/tex]
4. Calculate the average height:
The average height can be found by dividing the weighted sum of heights by the total number of children:
[tex]\[
\text{Average Height} = \frac{\text{Weighted Sum of Heights}}{\text{Total Number of Children}}
\][/tex]
Using the values calculated:
[tex]\[
\text{Average Height} = \frac{4680}{111} \approx 42.16216216216216
\][/tex]
So, the average height of the children based on the given data is approximately 42.16 inches.
