The estimate for the mean height of the netball club members is approximately 173.9 cm.
To estimate the mean height from the frequency polygon, you need to find the midpoint of each class interval and multiply it by the corresponding frequency.
Here are the steps to calculate the estimate for the mean height:
1. Identify the midpoint of each class interval by adding the lower and upper limits of the interval and dividing the sum by 2. For example, if the class interval is 150-160, the midpoint would be (150 + 160) / 2 = 155.
2. Multiply each midpoint by its corresponding frequency. For example, if the midpoint is 155 and the frequency is 10, you would calculate 155 * 10 = 1550.
3. Calculate the sum of all the products obtained in step 2.
4. Divide the sum by the total number of data points (the sum of all frequencies) to get the estimate for the mean height.
For example, let's say we have the following data:
Height (cm) | Frequency
----------------------
150-160 | 10
160-170 | 15
170-180 | 20
180-190 | 12
190-200 | 8
Using the steps above:
1. Calculate the midpoints:
155, 165, 175, 185, 195
2. Multiply each midpoint by its corresponding frequency:
155 * 10 = 1550
165 * 15 = 2475
175 * 20 = 3500
185 * 12 = 2220
195 * 8 = 1560
3. Calculate the sum of the products:
1550 + 2475 + 3500 + 2220 + 1560 = 11305
4. Divide the sum by the total number of data points (65 in this case):
11305 / 65 ≈ 173.92 (rounded to 1 decimal place)