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

Universe or population, Universe or Population The word universe as use...

Universe or Population The word universe as used in statistics denotes the aggregate from which a sample is to be taken. According to Simpson and Kafka, a universe or populatio

Genmod procedure, The following dataset is from a study of the effects of s...

The following dataset is from a study of the effects of second hand smoking in Baltimore, MD, and Washington, DC. For the 25 children involved in this study the outcome variable is

Standard deviation and variance, Explanation of standard deviation and vari...

Explanation of standard deviation and variance Describe the importance of standard deviation and variance, what they calculate and why they are required. Importance of char

Ryan-joiner - normal probability plot, The Null Hypothesis - H0:  The rando...

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

Time series, Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 ...

Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 2012 14 2013 16 Determine the trend from data given above?

What are the coefficients of the linear combination, For the following ques...

For the following questions we are interested in a comparison of the 16 years education vs. > 16 years. (Recall we did the analysis on the log scale, so these are actual means on t

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

get a questionnaire that captured age at first marriage

Half of market share, Your company has developed a new product .Your compan...

Your company has developed a new product .Your company is a reputed company with 50% market share of same range of products. Your competitors also come with their new products equa

HLT 362, What is an interaction? Describe an example and identify the varia...

What is an interaction? Describe an example and identify the variables within your population (work, social, academic, etc.) for which you might expect interactions?

Standard deviation for grouped data, Grouped data  For ...

Grouped data  For grouped data, the formula applied is  σ = Where f = frequency of the variable, μ= population mea

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