In: Math
Classes (Percentage) | No of Students |
0 < 10 | 10 |
10 < 20 | 20 |
20 < 30 | 25 |
30 < 40 | 15 |
40 < 50 | 20 |
50 < 60 | 35 |
60 < 70 | 45 |
70 < 80 | 10 |
80 < 90 | 15 |
90 < 100 | 5 |
2.1 Determine the:
2.1.1 Mean number of marks (1 mark)
2.1.2 Median number of marks
2.1.3 Modal number of marks
2.2 Calculate the standard deviation
The following table shows the necessary calculations:
Class Interval | x | f | fx | fx2 | Cumulative Frequency |
0-10 | 5 | 10 | 50 | 250 | 10 |
10-20 | 15 | 20 | 300 | 4500 | 30 |
20-30 | 25 | 25 | 625 | 15625 | 55 |
30-40 | 35 | 15 | 525 | 18375 | 70 |
40-50 | 45 | 20 | 900 | 40500 | 90 |
50-60 | 55 | 35 | 1925 | 105875 | 125 |
60-70 | 65 | 45 | 2925 | 190125 | 170 |
70-80 | 75 | 10 | 750 | 56250 | 180 |
80-90 | 85 | 15 | 1275 | 108375 | 195 |
90-100 | 95 | 5 | 475 | 45125 | 200 |
200 | 9750 | 585000 |
2.1.1
2.1.2
Since the cumulative frequency of the class 50-60 is 125, therefore, this is the median class.
where,
is the lower limit of the median class
is the total frequency
is the cumulative frequency of the class preceeding the median class
is the frequency of median class
is the size of the class interval.
2.1.3
The class with the hisghest frequency is called the modal class. In the given data, the frequency corresponding to class 60-70 is the highest. Thus, this is the modal class.
where,
is the lower limit of the median class
is the frequency of class preceeding modal class
is the frequency of modal class
is the frequency of class succeeding modal class
is the size of the class interval.
2.2
RESULT: