Answer to Question #257388 in Economics of Enterprise for Vinay

Question

The distribution of marks scored by college students is shown below: Marks No. of students 45 0-20 20-30 30-50 50-60 21 15 10 60-90 90-100 2 i. Draw a histogram and comment on it's shape Calculate the mean and median ii. What proportion of students score less than 60 marks and what proportion scores between 50 to 80 marks. 1

Answer 1

Let's present the response data in Excel.

To do this, we will form a data table.

Using the data analysis-histogram option, we will post a histogram

This is a histogram with a non-metric distribution.

Find the average and median. If the intervals of the interval dynamic series are unequal, then the value of the average level is found by the weighted arithmetic mean formula, in which the length of time periods corresponding to the levels of the dynamics series is used as weights.

$mean=\frac{45\times20+21\times10+45\times20+21\times10+15\times20+10\times10+2\times30+2\times10}{20+10+20+10+30+10}=\frac{1680}{100}=16.8$

The median corresponds to the variant standing in the middle of the ranked row. The median is the interval 0-20, because in this interval the accumulated frequency S is greater than the median number (the median is the first interval, the accumulated frequency S of which exceeds half of the total sum of frequencies).

$median=20+\frac{10}{21}(\frac{98}{2}-45)=21.905$

Calculate the shares

less than 60 marks:

$d=\frac{45+21+15+10}{45+21+15+10+5+2}=0.9286$ or 92.86%

between 50 to 80:

$d=\frac{10+5}{45+21+15+10+5+2}=0.1531$ or 15.31%