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

Effect in frequency domain, A) The three images shown below were blurred us...

A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le_ lower part of (a) and (c) are blurred, but a c

Express the null hypothesis, Examine the given statement, then express the ...

Examine the given statement, then express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. The mean weight of women who won a beauty pageant is equal t

What are the hypotheses, Assume that a simple random sample has been select...

Assume that a simple random sample has been selected from a normally distribute population and test the given claim. Identify the null and alternative hypotheses, test statistic,

Stream flow gauging, (a) At a stream gauging station, the following dischar...

(a) At a stream gauging station, the following discharges and stage measurements were taken for the purpose of the rating curve at that section: Stage (m) 1

Circul;atory ststistics Lab, What statistics can be obtained from a circula...

What statistics can be obtained from a circulatory lab?

Trying to find test statistic and P value, Ask question #Minimum The data i...

Ask question #Minimum The data in the accompanying table give the weights? (in g) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a med

Calculation of degrees of freedom, Calculation of Degrees of Freedom Fi...

Calculation of Degrees of Freedom First we look at how to calculate the number of DOF for the numerator. In the numerator since we calculate the variance from the sample means,

Eco203, Waht is the product of £ x

Waht is the product of £ x

Simple random sampling, Simple Random Sampling In Simple Random Sampli...

Simple Random Sampling In Simple Random Sampling each possible sample has an equal chance of being selected. Further, each item in the entire population also has an equal chan

Active control equivalence studies (aces), Active Control Equivalence Studi...

Active Control Equivalence Studies (ACES) Clinical trials the field in which the object is easy to show that the new treatment is  as good as the existing treatment. Such type

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