Answer to Question #204827 in Statistics and Probability for Teddora

Question

In a study to analyse performance of Advanced Negotiation course in a 2020 CIPS 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.

The pass marks 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.