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

Descriptive Statistics, To determine the proportion of people in your town ...

To determine the proportion of people in your town who are smokers, it has been decided to poll people at one of the following local spots: (a) the pool hall; (b) the bowling alley

Regression model, Using a random sample of 670 individuals for the populati...

Using a random sample of 670 individuals for the population of people in the workforce in 1976, we want to estimate the impact of education on wages. Let wage denote hourly wage in

#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

LPP, b. A paper mill produces two grades of paper viz., X and Y. Because of...

b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y

Null and alternative hypothesis, 1) Suppose you want to test a hypothesis t...

1) Suppose you want to test a hypothesis that two treatments, A and B, are equivalent against the alternative that the response for A tend to be larger than those of B. You plan to

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

Simple linear regression, We are interested in assessing the effects of tem...

We are interested in assessing the effects of temperature (low, medium, and high) and technical configuration on the amount of waste output for a manufacturing plant. Suppose that

Determine the matrix of the transformation, Consider the linear transformat...

Consider the linear transformation (a) Find the image of (3 , -2 , 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transf

Statistical generalisations, From the information given, what seems to be t...

From the information given, what seems to be the main flaw in each of the following statistical generalisations? (i) Banking industry employees are facing a crisis, if their

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