Answer:
B) 16.47
Explanation:
In order to find the mean of grouped data with intervals, we use the formula
(∑f * m) / (∑f)
- where (∑f * m) is the sum of the product of each frequency (f) and the corresponding midpoint (m) for its interval and (∑f is the sum of each frequency
Step 1: First, we need to find the sum of the frequencies: ∑f = 2 + 3 + 8 + 4 = 17
Step 2: Next, we need to find the midpoint (m) of each interval. We do this by averaging the end points of each interval
m of first interval: (9.5 + 12.5) / 2 = 11
m of second interval: (12,5 + 15.5) / 2 = 14
m of third interval: (15.5 + 18.5) / 2 = 17
m of fourth interval: (18.5 + 21.5) / 2 = 20
Step 3: Now, we multiply the frequency for each interval by its corresponding midpoint and add them together to find the sum
f * m for first interval: (2 * 11) = 22
f * m for second interval: (3 * 14) = 42
f * m for third interval: (8 * 17) = 136
f * m for fourth interval: (4 * 20) = 80
Sum of f * m for each interval: 22 + 42 + 136 + 80 = 280
Step 4: Finally, we divide the sum of f * m for each interval by the sum of f to find the mean:
280 / 17 = 16.47058824 = 16.47