Answer to Question #214459 in Statistics and Probability for Leila

Question

A sample of quarterly amounts invested in Ethan-Jaden Company by its employees is depicted in the table below;

Amount Invested

|30<35| 35<40 |40<45| 45<50| 50<55| 55<60| 60<65| 65<70|

Number of employees 

|4| 8| 24| 44| 20| 10| 2| 6|

NB: Use two decimal places

i. How many employees invest in the company? 

ii. Estimate the mean amount invested. 

iii. Calculate the modal amount invested. 

iv. Estimate the median amount invested.

v. Estimate the sample standard deviation and interpret it.

Answer 1

i) 118 employees invest in the company

ii)$\bar x=\frac{\sum f(x)}{f(x)}$ =$\frac{5695}{118}$ =48.26

iii) The mode is the number that appears frequently or the class interval with high frequency in grouped data. The modal amount was between 45 and 50

iv)$median=l+h(\frac{\frac n 2-cf}{fm})$

$=45+5(\frac{\frac {118}{2}-36}{44})$

=47.6136

v) sd

$sd=\sqrt{\sum fx^2 - \frac{(\sum fx)^2}{n}}$

$=\sqrt{281437.5 - \frac{5695^2}{118}}$

=81.1255