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

Sdsad, Ask questionsadsadsadsadas#Minimum 100 words accepted#

Ask questionsadsadsadsadas#Minimum 100 words accepted#

Methods of forecasting, Methods of Forecasting  Various techniques whic...

Methods of Forecasting  Various techniques which are generally used in business forecasting are as under: 1.      Forecasting  through the opinion of heads  of department

Probability, Ask queFrom these studies, which of the following may be consi...

Ask queFrom these studies, which of the following may be considered a variable that can have a probability distribution? [I] Percentage of Sub-Saharan Africans that smoke [II] Perc

the six conditions are equally likely, A medical researcher has 100 bone c...

A medical researcher has 100 bone cancer patients in a study. Every patient's condition is one of six types, type \A" to type \F". The 100 patients split as follows: x There

Draw a network diagram for this problem, The project of building a backyard...

The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the follow

Eliminate all of the insignificant variables, The file Midterm Data.xls ha...

The file Midterm Data.xls has a tab labeled "Many vs. S&P" which presents historical price data for several assets, a volatility condition (VIDX = 1 if the NYSE volatility is grea

Find the unbiased estimators for mean and variance matrix, Is the random ve...

Is the random vector (Trunk Space, Length, Turning diameter) of US car normally distributed? Why? If yes, find the unbiased estimators for the mean and variance matrix of (Trunk Sp

Primary and secondary data, Primary and Secondary Data: Primary Data: ...

Primary and Secondary Data: Primary Data: These data are those are collected for the first time. Thus primary data are original in character and gathered   by actual observat

Utility index , If the economy does well, the investor's wealth is 2 and if...

If the economy does well, the investor's wealth is 2 and if the economy does poorly the investor's wealth is 1. Both outcomes are equally likely. The investor is offered to invest

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