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Question

Find the mean marks of students from the following cumulative frequency distribution:
MarksNumber of students
o and above80
10 and above77
20 and above72
30 and above65
40 and above55
50 and above43
60 and above28
70 and above16
80 and above10
90 and above8
100 and above 0

Solution
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Here we have, the cumulative frequency distribution. So, first we convert it into an ordinary frequency distribution. we observe that are 80 students getting marks greater than or equal to 0 and 77 students have secured 10 and more marks. Therefore, the number of students getting marks between 0 and 10 is 80-77= 3.
Similarly, the number of students getting marks between 10 and 20 is 77-72= 5 and so on. Thus, we obtain the following frequency distribution.
Marks Number of students
0-103
10-205
20-307
30-4010
40-5012
50-6015
60-70 12
70-806
80-902
90-1008
Now, we compute mean arithmetic mean by taking 55 as the assumed mean.
Computative of Mean
Marks
(xi)
Mid-value (fi)Frequency uixi5510fiui
0-1053-5-15
10-20155-4-20
20-30257-3-21
30-403510-2-20
40-504512-1-20
50-60551500
60-706512112
70-80756212
80-9085236
90-100958432
Total
fi=80
fiui= -26
We have,
N= sumfi=80,fiui=26, A= 55 and h= 10
¯¯¯¯¯X=A+h[1Nfiui]
¯¯¯¯¯X=A+h[1Nfiui]
¯¯¯¯¯X=55+10×2680=553.25=51.75Marks.

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Q1
Find the mean marks of students from the following cumulative frequency distribution:
MarksNumber of students
o and above80
10 and above77
20 and above72
30 and above65
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50 and above43
60 and above28
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Q5
The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.

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From the prepared table, answer the following questions :
(i) How many students obtained marks 40 or above 40 ?
(ii) How many students obtained marks 90 or above 90 ?
(iii) How many students obtained marks 60 or above 60 ?
(iv) What is the cumulative frequency of equal to or more than type of the class 0-10?
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