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

Frequency distribution, mark number of student 0-10 4 10-20 8 ...

mark number of student 0-10 4 10-20 8 20-30 11 30-40 15 40-50 12 50-60 6 calculate frequency distribution

Measures of dispersion, calculate variance and standard deviation of the f...

calculate variance and standard deviation of the following sample 12,22,32,13,12,23,34,52,56,23,44,32,11,11

Standard deviation , Standard Deviation  The concept of standard deviat...

Standard Deviation  The concept of standard deviation was first introduced by Karl Pearson in 1893. The standard deviation is the most important and the popular measure of disp

Decision making ., it is said that management is equivalent to decision mak...

it is said that management is equivalent to decision making? do you agree? explain

Regression Analysis, Question 3 25 marks Your employer, Quick Hit Agency ...

Question 3 25 marks Your employer, Quick Hit Agency (QHA), is a debt collections agency. The company specializes in collecting small accounts. QHA does not deal in large accounts

Probability theory, Origin and Development of probability Theory: The c...

Origin and Development of probability Theory: The credit for origin and development of probability goes to the European gamblers of 17 th century. They  used to gamble  on gam

Estimation, what do we mean by critical region

what do we mean by critical region

Descriptive statistics for every stock, Simple Linear Regression One ca...

Simple Linear Regression One calculate of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over

Dispersion.., discuss the advantages and disadvantages of measures of dispe...

discuss the advantages and disadvantages of measures of dispersions

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