To properly represent the given data by a pie diagram, we need to follow a series of steps that will help us display the relative proportions of infant mortality rates (IMR) among the regions listed. Here's a step-by-step solution:
### Step 1: Understand the Data
We have the following data:
- Andhra Pradesh: IMR = 29
- D & N Haveli: IMR = 11
- Goa: IMR = 08
- Karnataka: IMR = 21
- Kerala: IMR = 06
- Tamil Nadu: IMR = 15
### Step 2: Sum of IMR Values
Calculate the total IMR value for all regions:
[tex]\[ \text{Total IMR} = 29 + 11 + 8 + 21 + 6 + 15 = 90 \][/tex]
### Step 3: Calculate the Angle for Each Segment
Since a pie chart is a circle divided into 360 degrees, each region's angle can be calculated as follows:
[tex]\[ \text{Angle} = \left(\frac{\text{IMR}}{\text{Total IMR}}\right) \times 360 \][/tex]
Let's calculate the angles for each region:
- Andhra Pradesh:
[tex]\[ \left(\frac{29}{90}\right) \times 360 \approx 116^\circ \][/tex]
- D & N Haveli:
[tex]\[ \left(\frac{11}{90}\right) \times 360 \approx 44^\circ \][/tex]
- Goa:
[tex]\[ \left(\frac{8}{90}\right) \times 360 \approx 32^\circ \][/tex]
- Karnataka:
[tex]\[ \left(\frac{21}{90}\right) \times 360 \approx 84^\circ \][/tex]
- Kerala:
[tex]\[ \left(\frac{6}{90}\right) \times 360 \approx 24^\circ \][/tex]
- Tamil Nadu:
[tex]\[ \left(\frac{15}{90}\right) \times 360 \approx 60^\circ \][/tex]
### Step 4: Create a Pie Chart
Now we can visualize this into a pie diagram.
1. Draw a circle.
2. Divide the circle into segments based on the angles calculated:
- Andhra Pradesh: 116 degrees
- D & N Haveli: 44 degrees
- Goa: 32 degrees
- Karnataka: 84 degrees
- Kerala: 24 degrees
- Tamil Nadu: 60 degrees
3. Label each segment with the respective region's name and its percentage of the total IMR.
### Step 5: Label Percentages
Convert the angle into percentages for better visualization:
[tex]\[ \text{Percentage} = \left(\frac{\text{IMR}}{\text{Total IMR}}\right) \times 100 \][/tex]
Percentage for each region:
- Andhra Pradesh:
[tex]\[ \left(\frac{29}{90}\right) \times 100 \approx 32.2\% \][/tex]
- D & N Haveli:
[tex]\[ \left(\frac{11}{90}\right) \times 100 \approx 12.2\% \][/tex]
- Goa:
[tex]\[ \left(\frac{8}{90}\right) \times 100 \approx 8.9\% \][/tex]
- Karnataka:
[tex]\[ \left(\frac{21}{90}\right) \times 100 \approx 23.3\% \][/tex]
- Kerala:
[tex]\[ \left(\frac{6}{90}\right) \times 100 \approx 6.7\% \][/tex]
- Tamil Nadu:
[tex]\[ \left(\frac{15}{90}\right) \times 100 \approx 16.7\% \][/tex]
By following these steps, you should have a clear and accurate pie diagram representing the infant mortality rates in the given regions for 2019. Ensure each segment is color-coded and labeled appropriately with the region name and percentage value for clarity.
