To draw a histogram to represent the given data, we need to complete the table by calculating the frequency density for each weight class. Here are the detailed steps:
1. Weight Classes and Frequencies:
- 30-40 kg: Frequency = 5
- 40-45 kg: Frequency = 7
- 45-50 kg: Frequency = 10
- 50-55 kg: Frequency = 5
- 55-70 kg: Frequency = 3
2. Determine the Class Width for Each Weight Class:
- 30-40 kg: Class width = 40 - 30 = 10
- 40-45 kg: Class width = 45 - 40 = 5
- 45-50 kg: Class width = 50 - 45 = 5
- 50-55 kg: Class width = 55 - 50 = 5
- 55-70 kg: Class width = 70 - 55 = 15
3. Calculate the Frequency Density:
- Frequency Density is given by the formula:
[tex]\[
\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}
\][/tex]
Applying this formula to each class:
- For 30-40 kg: Frequency Density = [tex]\(\frac{5}{10} = 0.5\)[/tex]
- For 40-45 kg: Frequency Density = [tex]\(\frac{7}{5} = 1.4\)[/tex]
- For 45-50 kg: Frequency Density = [tex]\(\frac{10}{5} = 2.0\)[/tex]
- For 50-55 kg: Frequency Density = [tex]\(\frac{5}{5} = 1.0\)[/tex]
- For 55-70 kg: Frequency Density = [tex]\(\frac{3}{15} = 0.2\)[/tex]
4. Complete the Table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Weight (kg)} & \text{Frequency} & \text{Frequency Density} \\
\hline
30-40 & 5 & 0.5 \\
\hline
40-45 & 7 & 1.4 \\
\hline
45-50 & 10 & 2.0 \\
\hline
50-55 & 5 & 1.0 \\
\hline
55-70 & 3 & 0.2 \\
\hline
\end{array}
\][/tex]
5. Draw the Histogram:
- On the horizontal axis (x-axis), mark the weight ranges: 30-40, 40-45, 45-50, 50-55, 55-70.
- On the vertical axis (y-axis), mark the frequency density. Use an appropriate scale to represent values up to 2.0.
- For each weight range, draw a bar whose height corresponds to the frequency density:
- 30-40 kg: Bar height = 0.5
- 40-45 kg: Bar height = 1.4
- 45-50 kg: Bar height = 2.0
- 50-55 kg: Bar height = 1.0
- 55-70 kg: Bar height = 0.2
Your histogram should visually represent the data and show the differences in frequency density for each given weight range.
