Standard deviation for grouped data, Applied Statistics

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%.

Posted Date: 9/14/2012 3:15:32 AM | Location : United States







Related Discussions:- Standard deviation for grouped data, Assignment Help, Ask Question on Standard deviation for grouped data, Get Answer, Expert's Help, Standard deviation for grouped data Discussions

Write discussion on Standard deviation for grouped data
Your posts are moderated
Related Questions
Modify your formulas from (1) to compute the price at time 0 of an American put option with the same contract speci cations in the binomial model. Report the price of the American

Waht is the product of £ x

Accelerated Failure Time Model A basic model for the data comprising of survival times, in which the explanatory variables measured on an individual are supposed to act multipli

Define sampling unit and population for selecting a random sample in every case. a) 100 voters from a constituency b) 20 stocks of National Stock Exchange c) 50 account ho

If the test is two-tailed, H1:  μ ≠  μ 0  then the test is called two-tailed test and in such a case the critical region lies in both the right and left tails of the sampling distr

Arithmetic Mean   The process of computing Arithmetic Mean in the case of individual observations is to take the sum of the values of the variable and then divide by the number

PCA is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinat

Use the given information to find the P-value. The test statistic in a two-tailed test is z = 1.49 P-value = (round to four decimal places as needed)

Examples of grouped, simple and frequency distribution data