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

Empirical mode, Empirical Mode Where mode is ill-defined, its value may...

Empirical Mode Where mode is ill-defined, its value may be ascertained by the following formula based upon the empirical relationship between Mean, Median and Mode: Mode = 3

Confirmatory factor analysis, Confirmatory factor analysis (CFA) seeks to d...

Confirmatory factor analysis (CFA) seeks to determine whether the number of factors and the loadings of measured (indicator) variables on them conform to what is expected on the ba

Ogive graphs, how many types of ogive are there

how many types of ogive are there

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

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

Statistical quality control assinment, how to get statistical quality contr...

how to get statistical quality control assignment in brief?

Dispersion.., discuss the advantages and disadvantages of measures of dispe...

discuss the advantages and disadvantages of measures of dispersions

Analysis of covariance (ancova), Analysis of covariance (ANCOVA) It is ...

Analysis of covariance (ANCOVA) It is initially used for an expansion of the analysis of variance which permits to the possible effects of continuous concomitant variables (suc

Calculate the maximum charge current, For the circuit shown below; Wr...

For the circuit shown below; Write a KCL equation for Node A, Node B, Node C and Node D. Write a KVL equation for Loop 1, Loop 2 and Loop 3.   A simple circ

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