Question

In: Math

Classes (Percentage) No of Students 0 < 10 10 10 < 20 20 20 < 30...

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

Solutions

Expert Solution

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:


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