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

Agreement, Agreement The degree to which different observers, raters or ...

Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu

Iterative convergence of the method, You are given the differential equatio...

You are given the differential equation dy/dx = y' = f(x, y) with initial condition y(0 ) 1 = . The following numerical method is also given: where  f n = f( x n , y n )

Random sampling method, Random Sampling Method In this method the units...

Random Sampling Method In this method the units are selected in such a way that every item in the whole universe has an equal chance of being included. In the words of croxton

Make a decision about the claim, Make a decision about the given claim. Do...

Make a decision about the given claim. Do not use any formal procedures and exact calculation. Use only the rare event rule. Claim: A coin favors head when tossed, and there

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

Types of business forecasting , Types  of business forecasting  are genera...

Types  of business forecasting  are generally as follows: 1.      Sales  and Demand  forecasts 2.      Porduction  forecasts. 3.       Cost  Forecasts 4.       Financi

Find the backward induction equilibrium, A rightist incumbent (player I) an...

A rightist incumbent (player I) and a leftist challenger (player C) run for senate. Each candidate chooses among two possible political platforms: Left or Right. The rules of the g

Markov Chain, Each weekend, Derek either reads a book (B), goes to the cine...

Each weekend, Derek either reads a book (B), goes to the cinema (C), visits his local museum (M), or plays squash (S). If he reads a book one weekend, then he will take part in one

Accident proneness, Accident proneness  A personal psychological issue w...

Accident proneness  A personal psychological issue which affects the individual's probability of suffering the accident. The concept has been studied statistically under the num

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