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

Package design ratings, Consider the sample of 60 package design ratings gi...

Consider the sample of 60 package design ratings given in the table below.                                    A Sample of Package Design Ratings                 (Composite S

Standard erro, practical application of standard error

practical application of standard error

Level process control lab, Based on the following graphs (next page) you sh...

Based on the following graphs (next page) you should write a discussion report (2 pages) on: 1. Determination of whether the open-loop system response is consistent with a 1st o

Advantages of sampling, Advantages of Sampling Why should we settle on ...

Advantages of Sampling Why should we settle on a sample instead of studying the entire population?  Sampling has the following advantages over a census (study of the entire pop

Median, The median, as the name suggests, is the middle value of a series a...

The median, as the name suggests, is the middle value of a series arranged in any of the orders of magnitude i.e. ascending or descending order. As distinct from the arithmetic

Coefficient of variation, Coefficient of Variation The standard dev...

Coefficient of Variation The standard deviation discussed above is an absolute measure of dispersion. The corresponding relative measure is known as the coefficient of vari

Problem set for logistic regression, (1) What values can the response varia...

(1) What values can the response variable Y take in logistic regression, and hence what statistical distribution does Y follow? The response variable can take the value of either

Uses of arthematic mean, give me question on mean is the aimplest average t...

give me question on mean is the aimplest average to understand and easy to compute

Age at first marrage, get a questionnaire that captured age at first marria...

get a questionnaire that captured age at first marriage

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