Answer to Question #312670 in Statistics and Probability for Nunda

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.