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

Non-sampling errors, Statistics Can Lead to Errors The use of st...

Statistics Can Lead to Errors The use of statistics can often lead to wrong conclusions or wrong estimates. For example, we may want to find out the average savings by i

Determine how the ordinary least squares, Question Following the general...

Question Following the general methodology used by econometricians as explained in the session for week 1 (eight steps), explain how you would proceed to determine if a good com

Business staitistices- soltion to :, A file on DocDepot in the assignments ...

A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies

Confidence interval, a) List down several measures of central tendency and ...

a) List down several measures of central tendency and define the difference among them? b) What do you mean by confidence interval, and why it is useful? What is a confidence lev

Harmonic mean, The Harmonic Mean is based on the reciprocals of numbers ave...

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th

E-mail messages should be answered quickly, Do people of different age grou...

Do people of different age groups differ in their response to e-mail messages? A survey by the Cent of the Digital Future of the University of Southern California reported that 70.

Pattie-lynns utility function, Pattie-Lynn's utility function for total as...

Pattie-Lynn's utility function for total assets is, in which A represents total assets in thousands of dollars. (a) Graph Pattie-Lynn's utility function. How would y

Pneumatic actuator design matrix, Pneumatic Actuator Design Matrix: The ra...

Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

Frequency distribution, Frequency distribution A frequency distribution...

Frequency distribution A frequency distribution is a series where a number of items with similar values are put in separate groups or bunches. In other words a frequency distri

Probability, There are 15 types of ice cream: A,B,C,D,E,F,G,H,I,J,K,L,M,N, ...

There are 15 types of ice cream: A,B,C,D,E,F,G,H,I,J,K,L,M,N, and O. How many combinations are there to sample 5 flavors if you sample 1 flavor 4 times? How many combinations are t

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