Q1 of 33 Page 14

The following table shows marks secured by 140 students in an examination:


Marks 0-10 10-20 20-30 30-40 40-50
    Number of      students 20 24 40 36 20


Calculate mean marks by using all the three methods, i.e., direct method, assumed mean method and step-deviation method.

 Direct Method 


MarksNumber of Students (fi)Mid-point (xi)fixi
0 - 10205100
10 - 202415360
20 - 3040251000
30 - 4036351260
40 - 502045900
Total140 3620

Hence mean = = = 25.86 marks
Assumed Mean Method

MarksNumber of Students(fi)Mid-point (xi)Deviation
di= xi - 25		fidi
0 - 10205-20-400
10 - 202415-10-240
20 - 3040a = 2500
30 - 40363510360
40 - 50204520400
Total140  120

 Hence mean = a + = 25 + = 25.86 marks
Step-Deviation Method

MarksNumber of Students (fi)Mid-point (xi)Deviation
ui= (xi - 25)/10		fiui
0-10205-2-40
10 - 202415-1-24
20 - 3040a=2500
30 - 403635136
40 - 502045240
Total140  12


Hence mean = a + h × [where h = 10]                         = 25 + 10 × = 25.86 marks

More from this chapter

All 33 →
2 New Page 2 Find the mean marks from the following data:

Marks Number of Students
Below 10
Below 20
Below 30
Below 40
Below 50
Below 60
Below 70
Below 80
Below 90
Below 100		 5
9
17
29
45
60
70
78
83
85 
3  New Page 2 Find the mean age of 100 residents of a colony from the following data:



Age in years (Greater than or equal to) Number of Persons
0 10 20 30 40 50 60 70 100 90 75 50 25 15 5 0 

4 If the mean of the following data is 21.5, find the value of k:
          
xi 5 15 25 35 45
fi 6 4 3 k 2
5 Find the values of f1 and f2 of the frequency, if the mean of the following frequency distribution is 21.4 and the total frequency is 40.
Class-interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 6 f1 10 f2 9