Standard deviation for grouped data, Applied Statistics

Assignment Help:

Grouped data 

For grouped data, the formula applied is  σ = 1926_standard dviation for grouped data.png

Where f = frequency of the variable, μ= population mean.

Example 17

 

A security analyst studied hundred companies and obtained the following Return on Investment (ROI) data for the year 20x3.

Returns %

0-10

10-20

20-30

30-40

No. of companies

19

32

41

8

We can find how the ROI of the company varies with the mean ROI by calculating the standard deviations for the above data.

The steps involved are:

  • Find mean for grouped data.

  • Find deviations from mean for grouped data.

  • Find squares of the above deviations.

  • Total the squared deviations taking frequency into account.

  •  Calculate square root.

Return on investment

Mid-point

No. of companies

Deviation

%

X

f

fX

   X - μ

 f(X -  μ  )2

0-10

5

19

95

      -13.8

3618.36

10-20

15

32

480

-3.8

462.08

20-30

25

41

1025

6.2

1576.04

30-40

35

8

280

16.2

2099.52

Total

 

100

1880

 

7756.00

Mean

2299_standard dviation for grouped data1.png

= 18.8%.
 

 


Standard Deviation 

=

775_standard dviation for grouped data2.png
  = 309_standard dviation for grouped data3.png =8.81%

Thus, the standard deviation for the return on investment is 8.8%.

In such a calculation, we always assume that all the observations in a class interval are located at the mid-point of the class. For example, the first class interval has mid-point 5 and frequency 19. Hence the assumption is that all the 19 companies have an ROI of exactly 5%.


Related Discussions:- Standard deviation for grouped data

Plot diagnostic quantities, The data in the data frame compensation are fro...

The data in the data frame compensation are from Myers (1990), Classical andModern Regression with Applications (Second Edition)," Duxbury. The response y here is executive compens

Population variance, Examining the Population Variance Business decisio...

Examining the Population Variance Business decision making does not limit itself to setting up the hypothesis to test for the equality of more than two means or proportions sim

Distribution of sample means, 1. Use the concepts of sampling error and z-s...

1. Use the concepts of sampling error and z-scores to explain the concept of distribution of sample means. 2. Describe the distribution of sample means shape for samples of n=36

Simple linear regression, We are interested in assessing the effects of tem...

We are interested in assessing the effects of temperature (low, medium, and high) and technical configuration on the amount of waste output for a manufacturing plant. Suppose that

Evaluation tracking system, BCBSRI was able to reduce MSD related Workers C...

BCBSRI was able to reduce MSD related Workers Compensation cases with lost workdays by implementing a New Ergonomic Program in March 2000 and increasing workstation evaluations. Ex

Diversity of data , The box plot displays the diversity of data for the tot...

The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.

Critique 2, prepare a critical analysis of a quantitative study focusing on...

prepare a critical analysis of a quantitative study focusing on protection of human participants data collection data management and analysis problem statement and interpretation o

Admixture in human populations, Admixture in human populations The inte...

Admixture in human populations The inter-breeding amongst the two or more populations which were previously isolated from each other for the geographical or the cultural reason

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd