Find the mean of the following frequency distribution:
Class | 0-50 | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |
Frequency | 10 | 15 | 30 | 20 | 15 | 8 | 2 |
Since, this is a grouped frequency distribution, this is solved by creating a table and using certain formulae. To find mean, we need to create a table showing class intervals, midpoints, frequencies and product of those midpoints and frequencies.
CLASS INTERVAL | MIDPOINT (xi) | FREQUENCY (fi) | MIDPOINT × FREQUENCY (xifi) |
0 – 50 | 25 | 10 | 25 × 10 = 250 |
50 – 100 | 75 | 15 | 75 × 15 = 1125 |
100 – 150 | 125 | 30 | 125 × 30 = 3750 |
150 – 200 | 175 | 20 | 175 × 20 = 3500 |
200 – 250 | 225 | 15 | 225 × 15 = 3375 |
250 – 300 | 275 | 8 | 275 × 8 = 2200 |
300 – 350 | 325 | 2 | 325 × 2 = 650 |
TOTAL | ∑fi = 100 | ∑xifi = 14850 |
Now, we have
∑fi = 100 and ∑xifi = 14850
The formula of mean by direct method is given by,
⇒ 
[from the given information]
⇒ Mean = 148.5
Thus, mean is 148.5.
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