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

Estimation error on apparent arbitrage, This question explores the effect o...

This question explores the effect of estimation error on apparent arbitrage opportunities in a controlled simulation setting. We simulate returns for N = 10 assets over T = 30 year

Calculate the mle estimate for mean, Each section of the SAT test is suppos...

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They r

Determine the probability, For a distribution of scores with = 82 and stand...

For a distribution of scores with = 82 and standard deviation = 2.5, find the following: (Don't forget to sketch the normal curve to help you visualize what you are trying to fi

Andrews ‘plots, Andrews ‘Plots A graphical display of multivariate da...

Andrews ‘Plots A graphical display of multivariate data in which an observation, x0 = [x1, x2, . . . , xq] is represented can be represented in the form of function A set

Evaluate the p - value, Use the given information to find the P-value. T...

Use the given information to find the P-value. The test statistic in a two-tailed test is z = 1.49 P-value = (round to four decimal places as needed)

Stk, The mean tax-return preparation fee H&R Block charged retail customers...

The mean tax-return preparation fee H&R Block charged retail customers in 2012 was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume t

Probability, 1 A penny is tossed 5 times. a. Find the chance that the 5th t...

1 A penny is tossed 5 times. a. Find the chance that the 5th toss is a head b. Find the chance that the 5th toss is a head, given the first 4 are tails.

Three types of food question?, #There were three types of food, and the res...

#There were three types of food, and the researcher recorded which foods were bought. Peanut Butter Banana Hamburger 15

Sdsad, Ask questionsadsadsadsadas#Minimum 100 words accepted#

Ask questionsadsadsadsadas#Minimum 100 words accepted#

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