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

Riemannian integral approximations, Investigate the use of fixed and perce...

Investigate the use of fixed and percentile meshes when applying chi squared goodness-of- t hypothesis tests. Apply the oversmoothing procedure to the LRL data. Compare the res

Classification of universe, Classification of Universe The universe may...

Classification of Universe The universe may be classified either on the basis of number of units and on the basis   of existence of units as is clear from the following chart :

#vital statistics, # I have to make assignment on vital statistics so kindl...

# I have to make assignment on vital statistics so kindly guide me how to make and get good marks

Calculate the length of the rope, The tension, T, in the tow rope pulling t...

The tension, T, in the tow rope pulling the car in Newtons is given in P8.  Determine the minimum length of the rope l, between A and B, so that the tension in either AB or AC equa

Recitilinear motion, velocity of a particle which moves along the s-axis is...

velocity of a particle which moves along the s-axis is given by v=2-4t+5t then find position velocity,acceleration

Utility index , If the economy does well, the investor's wealth is 2 and if...

If the economy does well, the investor's wealth is 2 and if the economy does poorly the investor's wealth is 1. Both outcomes are equally likely. The investor is offered to invest

Stratified sampling, Stratified Sampling Stratified Sampling is ...

Stratified Sampling Stratified Sampling is generally used when the population is heterogeneous. In this case, the population is first subdivided into several parts (or s

Calculation for discrete series or ungrouped data , Calculation for Discre...

Calculation for Discrete Series or Ungrouped Data The formula for computing mean is = where,          f  = fr

Expected average time, Question: A car was machine washes each car in 5 min...

Question: A car was machine washes each car in 5 minutes exactly. It has been estimated that customers will arrive according to a Poisson distribution at an average of 8 per hour.

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