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

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

Find probability of remaining paint free - ball duel, In a three-cornered p...

In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. Once hit, a player is out of the game and gets no

CERTIFICATE OF AIRWORTHINESS FOR EXPORT, CERTIFICATE OF AIRWORTHINESS FOR E...

CERTIFICATE OF AIRWORTHINESS FOR EXPORT When aircraft manufacturers go into series production of a new type of aircraft, then obviously they are hopeful of world wide sales. Sim

Normal distribution, Normal Distribution Meaning: According  to ya Lu...

Normal Distribution Meaning: According  to ya Lun Chou  There perfectly smooth and symmetrical  curve, resulting  from the expansion of the binomial (p+q) n    when n approac

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

Calculate total surplus, When the number of farmers growing wheat in Russia...

When the number of farmers growing wheat in Russia increases, the increase in world supply lowers the world price of wheat. Draw an appropriate diagram to analyze how this chang

Semiaverages and least square, how can we graph a trend line by semiaverage...

how can we graph a trend line by semiaverages and least square method?

Test for equality of two means, Let X 1  and X 2  be two independent po...

Let X 1  and X 2  be two independent populations with population means μ 1  and  μ 2  respectively. Two samples are taken, one from each population, of sizes n 1  and n 2  re

Frailty in multi state models, how can i use continuous frailty in multi st...

how can i use continuous frailty in multi state models?

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