## Abstract

Mathematics finds its application in census activities. Census activities require mathematical skills and concepts to be integrated for its success. Thus census data preparation, data collection, data analysis, representation and analysis all require mathematical knowledge and skills. Therefore, graphical data representation, tabulation, mathematical operations (subtraction, addition, divisions and multiplication) and interpretation is necessary to understand the meaning in census data. However, mathematical understanding and skills acquisition can be enhanced through the use of census data in mathematical instruction. This makes learning of mathematic interesting with learners using real census data. Moreover, students use data that they find meaningful in their daily life. The paper focuses on the interrelation between mathematics and census.

## Introduction

One can consider mathematic as a scientific study of hypotheses which are framed and followed to their effect. Mathematics can be split into two broad categories which include the applied and the pure mathematics. In applied mathematics, hypotheses are treated in a manner in which they were brought by experience. It involves procedural deductions that may result to some features with less meaning. However, pure mathematics serves to eliminate these features through careful thought (Moore and Charles, 2010). The interest of a mathematician would lie on the desire to analyze the hypotheses for purposes of inferences. In this regard, mathematics can be viewed as the study of mental creations aimed at drawing necessary conclusions. Several disciplines in mathematics can be identified such as algebra, analysis, statistics, geometry, and arithmetic etc. all mathematical disciplines can be grouped in to theory and practice part. Mathematics provides tools that are used in collection, organization and analysis of census data. In addition, Statistical mathematics is broadly used in this field (Moore and Charles, 2010).

Census can be defined as a process through which data regarding the population of a particular subject is collected and upon which every member is included in the study. Where population refers to any total collection of plants, persons, animals or any basic object under which the study is based. Moreover, census is made to provide a statistical data, such as population size, gender, employment levels and education levels among others. In a census, data is obtained for the entire population. A good example of a census is the national population census carried out after a specific number of years depending on different nationalities (Moore and Charles, 2010). Anderson (1990) shows that “population counts were reported in ancient Japan and taken by Egyptians, Greeks, Hebrews, Persians, and Romans”. When data is collected in a portion of the population, the study is referred as a sample survey.

## Discussion

Mathematics is related to the process of census preparation, data collection, recording, representation and presentation, analysis and data interpretation. This makes the census process to run without much difficulty. This has been discussed in depth with relevant examples outlined.

## Census preparation

Knowledge is essential in estimating the number of questionnaires to be used. One must use the previous census results, and then try to project the expected number of households to determine the required questionnaires. A certain percentage of error is including to the projected values making sure that those on the field will not experience shortage of resources. A prior training of the census enumerators require mathematical knowledge on vectors to ensure that they do not skip households and also to carry out the exercise within the shortest time possible. The ability to estimate innumerate’s birthday with certain historical events is critical for the census exercise in case it is a human population census. This is useful in events where dates required regarding enumerates is not well known. Enumerators require understanding simple mathematical calculations to ensure consistency of information provided by enumerates. For example in a human population total number of births should be given by the sum of the total children a life and total number of those who passed away. The census statistician job requires one to have done courses in numerical analysis, mathematical modeling, regression analysis, sampling theory and mathematical statistics among others (U.S census bureau, 2011).

## Data collection

The persons collecting the data or the questionnaire uses mathematical guided questions such as “how many…?” Moreover, most of the information collected in the census is represented using numbers. This presents case where mathematics is useful at the preliminary stage of the census process. The study of numbers ranges from discrete to decimal numbers. Mathematical skills of representing the numbers is also useful more so when dealing with decimals. Basic mathematical operation skills are essential in the census exercise such as additions, subtractions, multiplications and divisions. They spearhead the process of data collection. Moreover, most data collection techniques require coding information provided. This process requires high accuracy and mathematics improves accuracy skills (Townsend, 2005).

## Data representations

Data collected is later represented in tables, charts, and graphs. Mathematical skills are essential for representing data using different tools such as pie charts, graphs and simulations. To represent the census data one must be acquainted with the mathematical knowledge of how the data can be represented effectively using the right tools. This is a real life application of mathematical knowledge. For comparisons, data is represented using pie charts, compound graphs, bar graphs as well as other mathematical tools of representation. To show the distribution of the population it is necessary to represent data collected using histograms, bar charts, scatter diagrams. This helps in establishing the shape of the population distribution. In addition, it gives an early indication of the expected variation or skewness from the normal distribution. Moreover, one will be able to determine whether the data is positively or negatively skewed.

## Data analysis

Statistical mathematics is essential in analyzing census data. Population parameters such as the total population, average age, growth rate, mortality rate, literacy rate are determined using mathematical formulae. Moreover, statistical inference is used to draw conclusions about the populations.

## Use of census data in mathematics instructions

Instruction upon which real data is used promotes learning and achievement of learning and curriculum objectives. Census data from various bureaus of statistics such as US and the Australian bureaus of statistics is very useful in teaching various parts of the curriculum. These sources provide data regarding the population and the economy. Census data provides a ready resource and tools for educators. Extension of the census activities through census programs at schools has been undertaken by statistics Canada with its project “census at school project” (Townsend, 2005). With emphasis on mathematical literacy, the project aims at enabling pupils to apply knowledge acquired directly into the practical world. Mathematical literacy involves the development interpretation, numerical reasoning, graphical representation, estimation, and problem solving skills a major area of study in mathematics. The New Zealand school curriculum for mathematics, statistics and social studies includes the use of census collected data and census activities in the study (Statistics New Zealand, 2011).

Students can involve in real life census data collection from the internet. This gives them a practical approach to learning of statistics and probability. A study showed that Canadian students had a better performance in mathematics in comparison with students from other thirty ones nations (Townsend, 2005). This is attributed to data driven instruction techniques and learning, and development of literacy skills at earlier age while in kindergarten. For example the curriculum for grade one includes collection, organization and analysis of first hand data.

Using real census data promotes sampling and modeling techniques in statistics as learners are able to collect and model data that has a real life meaning. Moreover, they are able to use the statistical tools of analysis to daily issues. In this way, they learn data management techniques essential for managing census data.

Technology based data sourcing and use of census data promotes the development of an interesting student teacher community. This is because students enjoy learning things that they find a meaning in life. Graphs like the one shown below are available from the internet

## Source: U.S census bureau, population division

Census data can be used to teach various mathematic topics such as ranking, percentages and subtractions. For example a learning instruction could be framed as follows “use the census data to complete the table shown below”. This table could be testing many or particular area of study.

## Conclusion

Mathematics is essential in carrying out a census activity. It is highly required in the training of the census personnel, in data collection, presentation and analysis. Mathematical skills of representing tabulating, drawings and interpretation of data are very essential. In addition statistical tools of analysis are required to derive meaning of the census data. Statistical parameters such as the mean, the standard deviation, the mode, and the median among others are used to estimate population characteristics such as the average population age, literacy rates and population distribution. However, the census data finds its application in the learning of mathematics. This makes learning more interesting and more realistic as the learners use meaning data. Census charts, tables and graphs are useful in teaching mathematical skills such as data interpretation, percentages and subtractions among other mathematical operations.

## References

Anderson Margo J (1990). The American history: A social history. Yale university press

Moore M E & Charles SP (2010). Philosophy of mathematics. Bloomington: Indian University

Press

Statistics New Zealand (2011). School corner: 2011 census activities. Retrieved from < http://www.stats.govt.nz/tools_and_services/services/schools_corner/Census/2011-census-activities.aspx> accessed [2011 June 20th]

Townsend Mary (2005). Supporting data driven instruction in Canadian schools: Statistics

Canada and census at school. Ottawa: International statistical institute

U.S census bureau (2011). Resident population. Retrieved from accessed

[2011 June 20th].