Answer to Question #98085 in Statistics and Probability for denis

Question

In a study to analyse performance in a 2012 examination series the following scores in percentage were compiled for a sample of 100 candidates.

42,51,52,53,61,62,63,64,71,72,81,46,53,54,55,63,64,65,66,73,74,82,48,57,58,59,67,68,69,77,78,87,43,54,56,64,65,66,67,74,75,84,47,52,53,54,62,63,64,65,72,73,82,45,56,57,58,66,67,68,69,76,77,86,44,55,56,57,65,66,67,75,76,85,49,50,51,52,60,61,62,70,71,51,52,53,61,62,63,71,72,58,59,57,68,69,67,78,79,80

a) Arrange the data in equal classes of size 10 starting from 40 percent.

b) Using an ogive for the data, find:

i) The approximate percentage of the candidates who passed the examination if the pass mark was 62.5 percent.

ii) The pass mark if 90 percent of the candidate passed examination.

Answer 1

a)

$$\def\arraystretch{1.5} \begin{array}{c:c} \text{Class interval} & Frequency \\ \hline 40-50 & 8 \\\hline 50-60 & 29\\\hline 60-70 & 35 \\\hline 70-80 & 20 \\ \hline 80-90 & 8 \\ \hdashline Sum & 100 \end{array}$$

b)

i) In Class interval 60-70 there are 1 mark with value of 60, 3 marks with value of 61, and 5 marks with value of 62. We doesnot consider these marks/

The approximate percentage of the candidates who passed the examination if the pass mark was 62.5 percent is

$$(35-8)+20+8=55$$

ii)

If 90 percent of the candidate passed examination, then 10% did not pass examination. 8 such candidates are in Class-interval 40-50 and 2 candidates are in class interval 50-60: 1 mark with value of 50 and 3 marks vith value of 51.

The pass mark is 51.