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

Sampling error , Sampling Error  It is the difference between the value...

Sampling Error  It is the difference between the value of the actual population parameter and the sample statistic. Samples are used to arrive at conclusions regarding the p

Correlation coefficient test, 1. If you are calculating a correlation coeff...

1. If you are calculating a correlation coefficient testing the relationship between height and weight, state the null and alternative hypotheses. 2. What kind of relationship d

Inverse cumulative distribution function, The Null Hypothesis - H0: β0 = ...

The Null Hypothesis - H0: β0 = 0, H0: β 1 = 0, H0: β 2 = 0, Β i = 0 The Alternative Hypothesis - H1: β0 ≠ 0, H0: β 1 ≠ 0, H0: β 2 ≠ 0, Β i ≠ 0      i =0, 1, 2, 3

Show the hypothesis test, The file Midterm Data.xls has a tab labeled "Inc...

The file Midterm Data.xls has a tab labeled "Income Data 2009". This data is collected income data from a sample of 400 people in 2009. Use a hypothesis test to see whether the av

Median, introduction of median

introduction of median

Perform a one-way anova, The Tastee Bakery Company supplies a bakery produc...

The Tastee Bakery Company supplies a bakery product to many supermarkets in a metropolitan area. The company wishes to study the effect of shelf display height employed by the supe

Choose the correct null hypotheses, For the following claim, find the null ...

For the following claim, find the null and alternative hypotheses, test statistic, P-value, critical value and draw a conclusion. Assume that a simple random sample has been selec

Find a nash equilibrium, 2 bidders have identical valuations of an object f...

2 bidders have identical valuations of an object for sale. The value of the object is either 0; 50 or 100, with equal probabilities. The object is allocated to one of the bidders i

Determine the optimal order size, The Truly Canadian Restaurant stocks a pr...

The Truly Canadian Restaurant stocks a private red table wine that it purchases from a local winery in the Niagara Falls region. The daily demand for the wine at the restaurant is

Calculate the one year interest rate, A.The coupon rate of Erie-Chicago Rai...

A.The coupon rate of Erie-Chicago Rail is 7%. The interest rate of Florida municipal bond with equal risk is 6%.  At what tax rate the two bonds are as good as each other B.Supp

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