Final answer:
The arithmetic mean of the given frequency distribution data is obtained by adding the products of each class's midpoint and frequency, and then dividing by the total number of observations, resulting in a mean of 39.9.
Step-by-step explanation:
The question is asking us to calculate the arithmetic mean of data presented in a frequency table. To do this, we need to find the sum of the products of each class's midpoint and its frequency, and then divide by the total number of observations.
- For the class 20-29, the midpoint is 24.5, and with a frequency of 9, the product is 220.5.
- For the class 30-39, the midpoint is 34.5, and with a frequency of 20, the product is 690.
- For the class 40-49, the midpoint is 44.5, and with a frequency of 12, the product is 534.
- For the class 50-59, the midpoint is 54.5, and with a frequency of 5, the product is 272.5.
- For the class 60-69, the midpoint is 64.5, and with a frequency of 2, the product is 129.
- For the class 70-79, the midpoint is 74.5, and with a frequency of 2, the product is 149.
We then sum up all the products to get 1995. We also need to sum up all the frequencies, which gives us 50. The arithmetic mean is then calculated as 1995 divided by 50, which equals 39.9.
Therefore, the arithmetic mean of the data is 39.9.