Consider the following partially completed frequency table:
Class xi fi
[87; 97) 92 3
[97; 107) 102 5
[107; 117) 112 9
[117; 127) 122 11
[127; 137) 132 2
Determine the arithmetic mean.
133.3333
120
113.3333
138.3333
To determine the arithmetic mean, we need to first calculate the midpoint of each class interval, which is given by the formula xi = (lower bound + upper bound) / 2. Then we find the product of xi and fi for each class, sum them up, and divide by the total frequency.
The calculations are as follows:
(92*3) + (102*5) + (112*9) + (122*11) + (132*2) = 276 + 510 + 1008 + 1342 + 264 = 3400
Total frequency = 3 + 5 + 9 + 11 + 2 = 30
Arithmetic Mean = 3400 / 30 = 113.3333
Therefore, the arithmetic mean is 113.3333.
The correct answer is:
113.3333