Elementary Statistcs - Math 105

Project Title

Determination of Age of Books in the Library

Objective

Objective of this project was to determine average age of the books in the library and also obtain the other relevant statistical values data pertaining to the books in the library

Introduction

The library has a large collection of books . It contains about 25000 books . A statistical project was undertaken to determine average age of the books in the library . Besides , other relevant statistics on the books in the library were also determined and the results were presented

using histograms and Box plot

Methodology

Sample Size , standard deviation of sample (S ) and allowed error (e ) in percentage terms is required . Because , we do not have any of these values , therefore , a sample of 500 books was selected to generate these values , so that appropriate sample size can be determined , based on these values and if required sample size may be increased

Randomness

To generate random sample of size 500 , a random number between 1 and 10 was generated using simple lottery . For this numbers 1 , 2 , 3 , 10 were written on identical small chits and it was thrown in air , a friend was called and asked to pick one of the chits . The number on the chit was the random number . This number turned out to be 7 . Therefore , 7th book was picked up from the top layer of the last row in the farthermost corner of the library . Subsequently books at location numbers 57 , 107 157 , 207 , 257 , 307 , 25007 were selected . Thus a random sample of 500 books was selected

Age of Books in the Sample

Age of the books in the sample was taken from the date of purchase of the books in the library . This date was written on the books . The age of the books was rounded to the nearest years . Processing of the Sample

1 . The sample was grouped into six equidistant or equalized classes and frequency distribution table was prepared for the data

2 . Average age of the books and standard deviation was calculated from the frequency distribution table

3 . Appropriate sample size was determined using the sample mean standard deviation of the sample , allowed error of one year and 90 confidence interval

4 . The frequency table was graphically presented as histogram

5 . From the raw data a 5-number summary was and a box plot was made

Results

Results of the statistical project carried out for determination of age of books in the library are presented below

1 . Frequency table for the age of the books is presented in table 1 below

Table 1 : Frequency table for age of books in the library

years

Therefore , mean age of the books in the sample is 20 .6 years

Standard deviation of the sample (S ) is 13 .4 years

Therefore , standard deviation of population ) will be

year

3 . Appropriate Sample Size

Sample mean 20 .6 years

Assuming tolerable error to be 1 year , error e 1 /20 .6 0 .05

For 90 confidence interval...