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

Business forecasting, Meaning and Definitions of Business Forecasting T...

Meaning and Definitions of Business Forecasting The problem of business  forecasting  refers to the  analysis  of the past and  present economic  conditions. With  the objectiv

Calculation for discrete series or ungrouped data , Calculation for Discre...

Calculation for Discrete Series or Ungrouped Data The formula for computing mean is = where,          f  = fr

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,

Statistical inquiry, Main stages of Statistical Inquiry The following a...

Main stages of Statistical Inquiry The following are the various stages of a statistical inquiry (1)   Planning the Inquiry: First of all we have to assess the problem und

Choose the correct null hypotheses, For the following claim, find the null ...

For the following claim, find the null and alternative hypotheses, test statistic, P-value, critical value and draw a conclusion. Assume that a simple random sample has been selec

Geometric mean, Geometric Mean The geometric mean   of numbers is defin...

Geometric Mean The geometric mean   of numbers is defined as the th root of the product of numbers .It is obtained by multiplying all the values of a variable and then extracti

Rank correlation, Rank Correlation Sometimes the characteristics whose ...

Rank Correlation Sometimes the characteristics whose possible correlation is being investigated, cannot be measured but individuals can only be ranked on the basis of the chara

Evaluate gross reproduction rate, Evaluate Gross Reproduction Rate: Fr...

Evaluate Gross Reproduction Rate: From the data given below compute : i)   General  Fertility  Rate ii)  Specific  Fertility  Rate iii)  Total  Fertility  Rate iv)

Chi-square test, Consider the following linear regression model:      a)...

Consider the following linear regression model:      a) What does y and x 1 , x 2 , . . . . x k represent?      b) What does β o , β 1 , β 2 , . . . . β k represent?

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