Question

There are 150 students in a class. The distribution if their marks in a mathematics test are as follows

Class                                                   frequency

0-9                                                      3

10-19                                                  10

20-29                                                  17

30-39                                                  x

40-49                                                  35

50-59                                                  y

60-69                                                  18

70-79                                                  10

80-89                                                  5

90-99                                                  2

Required

i)       The value of x given that the median mark is 44.357            (2marks)

ii)     The value of y given that the modal is 43.0                          (2marks)

iii)   Draw an ogive of the data in (a) above                                 (3 marks)

Answer 1

i. median $=44.357=L+(\frac{(\frac{N}{2}-pcf)}{f})i$

$=40+(\frac{(75-(30-x)}{35})10$

$=39.5+(\frac{(45-x)}{35})10$

$4.357=(\frac{(45-x)}{35})10$

$0.4357=\frac{(45-x)}{35}$

$15.2495=45-x$

$x=29.75$

ii. Mode $=43.0=40+(\frac{7}{(7+35-y)})10$

$40+(\frac{7}{(42-y)})10$

$3=(\frac{7}{(42-y)})10$

$0.3=\frac{7}{(42-y)}$

$42-y=\frac{7}{0.3}=23.33$

$y=42-2.33=18.67$

iii.