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

Mode, Mode The mode is the value which occurs most frequ...

Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste

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

Perform clustering of the unlabeled data set, Perform clustering of the unl...

Perform clustering of the unlabeled data set. You could use provided initial centroids set or generate your own. Also there could be considered next stopping criteria : - maxim

Professional Counselor, A researcher hypothesized that the pulse rates of ...

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a ra

Simulation, Simulation When decisions are to be taken under conditions ...

Simulation When decisions are to be taken under conditions of uncertainty, simulation can be used. Simulation as a quantitative method requires the setting up of a mathematical

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

Skewness, Skewness Meaning and Definition  Literal meaning of skew...

Skewness Meaning and Definition  Literal meaning of skewness is lack of symmetry; it is a numerical measure which reveals asymmetry of a statistical series. According t

Range, Range Official Exports Target 2000-2001 ...

Range Official Exports Target 2000-2001 Product ($ million) Plantation 500 Agriculture and Alli

Draw a network diagram for this problem, The project of building a backyard...

The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the follow

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 )

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