Final answer:
The arithmetic mean is calculated by finding the midpoints of each class, multiplying them by their corresponding frequencies, summing these products, and then dividing by the total frequency. The mean for the provided frequency distribution is approximately 110.67, so answer choice d. 113 is the closest.
Step-by-step explanation:
To calculate the arithmetic mean of the frequency distribution, we need to find the midpoint (also known as the class mark) of each class and then multiply it by the frequency of that class. Once we have done this for all classes, we'll sum these products and divide by the total number of frequencies to get the mean.
Step-by-Step Calculation
- Find the midpoints of each class: (0+40)/2 = 20, (40+80)/2 = 60, (80+120)/2 = 100, (120+160)/2 = 140, (160+200)/2 = 180.
- Multiply each midpoint by its frequency: 20*12 = 240, 60*20 = 1200, 100*35 = 3500, 140*30 = 4200, 180*23 = 4140.
- Sum these products: 240 + 1200 + 3500 + 4200 + 4140 = 13280.
- Divide by the total frequency: 13280 / (12+20+35+30+23) = 13280 / 120 = 110.67.
Therefore, the arithmetic mean of the given frequency distribution is approximately 110.67, and the closest answer option is 113.