To find the mean, median, and mode, we first need to calculate the class marks, which are the midpoints of each class interval.
Class Interval | Class Mark
20-30 | (20+30)/2 = 25
30-40 | (30+40)/2 = 35
40-50 | (40+50)/2 = 45
50-60 | (50+60)/2 = 55
60-70 | (60+70)/2 = 65
70-80 | (70+80)/2 = 75
80-90 | (80+90)/2 = 85
Next, we calculate the total number of students:
Total students = 8 + 15 + 100 + 150 + 140 + 61 + 20 = 494
Now, let's calculate the mean, median, and mode:
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Mean:
Mean = (Sum of (Class Mark * Number of Students)) / Total Students
Mean = (258 + 3515 + 45100 + 55150 + 65140 + 7561 + 85*20) / 494
Mean ≈ 59.55
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Median:
To find the median, we first need to arrange the class marks in ascending order:
25, 35, 45, 55, 65, 75, 85
Since there are an even number of class marks (7), the median will be the average of the middle two class marks. In this case, the middle two class marks are 55 and 65.
Median = (55 + 65) / 2
Median = 60
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Mode:
The mode is the class mark with the highest number of students. Looking at the given data, the class mark with the highest number of students is 65 (with 140 students).
Mode = 65
In summary:
Mean ≈ 59.55
Median = 60
Mode = 65
