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

Good average, Examine properties of good average with reference to AM, GM, ...

Examine properties of good average with reference to AM, GM, HM, MEAN MEDIAN MODE

Use of calculators in statistics, In recent years a number of calculators a...

In recent years a number of calculators are available for doing statistical calculations over and above the usual addition, subtraction, multiplication and division. The fx-82 mode

Data project, Choose any published database from the internet or Bethel lib...

Choose any published database from the internet or Bethel library (such as those from the Census Bureau or any financial sites). You may opt to use one of the data files provided b

Help!, in a normal distribution with a mean of 85 and a STD of 5, what is t...

in a normal distribution with a mean of 85 and a STD of 5, what is the percentage of scores between 75 and 90?

Implement a simple k-means method, There exists an unclassified data set wi...

There exists an unclassified data set with hidden data structures in it. The task in this assignment is to perform comprehensive Cluster Analysis in order to reveal the structures

What are the null and alternative hypotheses, Test the following claim. Id...

Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that

Box plot of income, The box plot displays the diversity of data for the inc...

The box plot displays the diversity of data for the income; the data ranges from 20 being the minimum value and 1110 being the maximum value. The box plot is positively skewed at 4

Importance and application of probability, Importance and Application of pr...

Importance and Application of probability: Importance of probability theory  is in all those areas where event are not  certain to take place as same  as starting with games of

Angle count method, Angle Count method The method for estimating the pr...

Angle Count method The method for estimating the proportion of the area of a forest which is in fact covered by the bases of trees. An observer goes to each of the number of po

Correlation coefficients, What type of correlation coefficient would you us...

What type of correlation coefficient would you use to examine the relationship between the following variables? Explain why you have selected the correlation coefficients. A. Re

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