Question

a class teacher has the following absentee records of 40 students of a class for the whole term
no of days /0-6/6-10/10-14/14-20/20-28/28-38/38-40/
no of students 11 / 10/ 7 / 4 / 4 / 3 / 1 /
write the above distribution as less than type cumulative frequency distribution

Answer 1

a class teacher has the following absentee records of 40 students of a class for the whole term no of days /0-6/6-10/10-14/14-20/20-28/28-38/38-40/

no of students 11 / 10/ 7 / 4 / 4 / 3 / 1 /

Given,

No. of days   No. of students (fi)   Class mark (xi)       fi ×  xi

0-6                        11                        0+6/2 = 3               11 × 3 = 33

6-10                       10                       6+10/2 = 8             10 × 8 = 88            

10-14                     7                         10+14/2 = 12           7 × 12 = 84

14-20                    4                         14+20/2 = 17          4 × 17 = 68

20-28                   4                         20+28/2 = 24        4 × 24 = 96

28-38                   3                         28+38/2 = 33         3 × 33 = 99

38-40                   1                          38+40/2 = 39         1 × 39 = 39

∑ fi = 40

∑ fi × xi = 499

$Mean (\bar {x}) = \dfrac{\sum f_i \times x_i} {\sum f_i }\\\\= \dfrac{499}{40}\\\\\bar{x} = 12.48$

Answer 2

less than type cumulative frequency distribution is drawn.

no. of no. of less Cumula-

days students than type tive

frequency

0-6 11 6 11

6-10 10 10 21

10-14 7 14 28

14-20 4 20 32

20-28 4 28 36

28-38 3 38 39

38-40 1 40 40

•For making less than cumulative frequency distribution we have to draw a table with the columns as drawn above.

•cumulative frequency corresponding to particular observation is sum of all the previous frequency in less than type

•cumulative frequency distribution is useful for finding median and for making ogive .