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1 General

General Mathematics (Preliminary Course) | Statistics and Society, Data Collection & Sampling (DS1)

Data & Statistics (DS1)

Statistics and Society,

Data Collection & Sampling

Name ..............................................................................

G. Georgiou

2 General


• Investigate the Process of Statistical Inquiry and Describe the Following Steps: Posing Questions, Collecting Data, Organising Data, Summarising and Displaying Data, Analysing Data and Drawing Conclusions, and Writing a Report

Posing Questions: Determining what information is needed and then constructing relevant questions accordingly. Good questions use simple language, are clear and unambiguous, respect personal privacy, are free from bias and do not force an answer or opinion. Collecting Data: Generally occurs by asking questions via interviews or questionnaires. Interviews can occur either by phone, face-‐to-‐face or through teleconferencing. Questionnaires are generally distributed on paper or online. Organising Data: Grouping and sorting the data so it is easy to manage, usually with tables. Large organisations and investigative institutions organise data in complex computer programs but most people can just use spreadsheets. Summarising and Displaying Data: Data is generally displayed in graphs. This makes it easy for patterns and popular characteristics to be determined. Analysing Data and Drawing Conclusions: Involves applying statistical formulae and processes to the collected data in order to draw conclusions, summarise findings and make predictions. Writing a Report: A report generally occurs at the end of the data collection process. This report summarises the statistical inquiry process that was undertaken and puts an argument forward based on the findings. The Australian Bureau of Statistics, United Nations and World Health Organisation regularly publish reports.

HSC Question (1)

3 General


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HSC Question (2)

4 General


• Identification of the Target Population to be Investigated When conducting a survey, it is important to ensure that the data being obtained is not overrepresented from one type of person or group of people. It is also vital that you ask the right group of people so that the data you are collecting is valid. For example, if you wanted to know which football team the residents of Liverpool favoured, you would not ask residents from Parramatta. Determine the target population for these statistical inquiries. (a) Determining whether a new swimming pool complex should be built. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... (b) Evaluating the comfort of a new school uniform. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... (c) Asking about the affordability of houses. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...............................................................................................................................................

Example 3

5 General


• Determining whether Data for the Whole Population is Available (Eg: the Results of a Round of a Sporting Competition), or whether Sampling is Necessary

Census ........................................................................................................................................ .................................................................................................................................................... Sample ........................................................................................................................................ .................................................................................................................................................... The purpose of a sample (while not as accurate as a census) is to provide an estimate for a particular population characteristic when a census is not feasible (due to cost, time etc.) or when the entire population cannot be accessed. State whether a census or a sample would be more appropriate to determine: (a) The number of goals scored by a netball team in 10 games ……………………………………… (b) The heights of members of a football team ……………………………………… (c) The most popular radio station in Australia ……………………………………… (d) The number of children in an Australian family ……………………………………… (e) The amount of milk bought per week by an Australian family ………………………………………

(f) The pets owned by a class of students ……………………………………… (g) The number of leaves on stems of plants ……………………………………… (h) The gender of school principals in NSW catholic schools ……………………………………… (i) The reasons people use taxis in Australia ……………………………………… (j) The items sold at a school canteen ……………………………………… (k) The sports played by students in all high schools in NSW ……………………………………… (l) The time spent on homework by all students in Australia ………………………………………

Example 4

6 General


Activity Ex 1.04 Q 4, 5, 9 Ex 1.05 Q 1

Mr Hines suspected that Maths was the favourite subject of students in Year 11. To prove this, he asked students in his class to conduct a survey.

• Demetri decided just to ask five of his friends. Since three of them liked Maths the best, he reported that 3 out of 5 or 60% of students liked Maths best.

• Ahmed decided just to survey his class of 30. Since 20 students liked Maths best, he

reported that ⅔ of the year were Maths lovers.

• Alexander thought the only way to be really sure was to ask each student in the year.

• Caroline decided to ask 10 students from each home room class their opinion. From this she concluded that 70% of students liked Maths best.

(a) Which student actually carried out a census? .................................................................................................................................................... .................................................................................................................................................... (b) Three students surveyed a sample of the year. Which sample is most likely to have been the most accurate? Explain your answer clearly. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... (c) What is one problem with conducting a census rather than a sample? .................................................................................................................................................... ....................................................................................................................................................

Example 5

7 General


• Distinguishing between the Following Sample types: Random, Stratified, Systematic

• Describe a Random Sample as a Sample in which Every Member of the Population has an Equal Chance of being Included in the Sample

• Relating Sample Selection to Population Characteristics (Eg: if 20% of the Australian Population is Aged under 20, your Sample should include 20% of under 20s)

• Identify Possible Sources of Bias in the Collection of a Sample

There are 3 different ways which samples can be taken. Random ..................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... One method of conducting a random sample is: .................................................................................................................................................... .................................................................................................................................................... Systematic .................................................................................................................................. .................................................................................................................................................... .................................................................................................................................................... One method of conducting a systematic sample is: .................................................................................................................................................... .................................................................................................................................................... Stratified ..................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... Eg: There are 100 people in a population, 80 of which are males and 20 of which are female. If a survey of 5 people were to be conducted, 4 people would need to be male and 1 female such that the ratio is kept the same.

8 General


In a school, the amount of students in each year group is as follows: Year 7 – 120 Year 8 – 150 Year 9 – 130 Year 10 – 170 Year 11 – 130 Year 12 – 100 The principal wants to survey 100 people. Calculate how many students he should choose from each year if a stratified sample based on year groups were to be conducted. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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Example 6

HSC Question (7)

9 General


.................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... Determine which sample type is appropriate for each given situation. (a) The running time of a light globe .................................................................................................................................................... (b) Finding the most popular restaurant in Sydney. .................................................................................................................................................... (c) Surveying students in your school for their favourite sport. .................................................................................................................................................... (d) The shelf life of bread. ....................................................................................................................................................

A sample of 30 students is to be taken from a school of 850 students. Explain how this could be done for each of the following sample techniques. You may wish to incorporate the following information into your response for some of the sampling techniques. Use calculations where appropriate.

Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 110 150 140 180 120 150

(a) Random Sample .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Example 8

Example 9

10 General Mathematics (Preliminary Course) | Statistics and Society, Data Collection & Sampling (DS1)

(b) Systematic Sample .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... (c) Stratified Sample .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... The first 50 people to leave the screening of a specific movie are surveyed as to what type of movies they like. Identify the potential bias in the way the sample has been conducted. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... In 1936 in the US, 10 million questionnaires were mailed to households listed in telephone directories or state car registrations. This was an attempt to find out who would win the next Federal election. There were two main contenders: Alf Landon, a Republican and Franklin D. Roosevelt, a Democrat. Wealthy and well-‐educated people were more likely to vote Republican, while poorer people and the working class were likely to vote Democrat.

Example 10

Example 11


Activity Ex 1.05 Q 3 -‐ 8

About 2.4 million questionnaires were returned. The questionnaires showed that Landon would win comfortably. When the election was held, Roosevelt won by a landslide. The survey had got it terribly wrong! (a) Were all the questionnaires returned completed? Why or why not? .................................................................................................................................................... .................................................................................................................................................... (b) Do you think people who voted Democrats vs. people who voted Republican would have returned questionnaires equally? Explain. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... (c) This survey was done on a sample. Why was a census not done? .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... (d) Do you think the sample was randomly chosen? Why do you think the investigators got it so wrong? .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................


• Classify Data as Quantitative (either Discrete or Continuous) or Categorical (either Nominal or Ordinal)

Categorical Data ......................................................................................................................... .................................................................................................................................................... Ø Nominal ................................................................................................................................

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.................................................................................................................................................... Ø Ordinal ..................................................................................................................................

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.................................................................................................................................................... Quantitative Data ....................................................................................................................... .................................................................................................................................................... Ø Continuous ...........................................................................................................................

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.................................................................................................................................................... Ø Discrete ................................................................................................................................

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Classify the following data as quantitative discrete, quantitative continuous, categorical nominal or categorical ordinal. (a) Number of cars per household ................................................................................ (b) Temperature of the ocean ................................................................................ (c) Height of Yr 11 students ................................................................................ (d) Favourite food of a person ................................................................................. (e) People per household ................................................................................. (f) Gender ................................................................................. (g) Teaching position at school …………………………………………………………………………….. e.g. principal, coordinator etc (g) Phone calls received in a day ................................................................................. (h) A business’ profit ................................................................................ (i) Distance travelled by a car ............................................................................... (j) Month of birth .............................................................................. (k) Position in a race ……………………………………………………………………………

Example 12


Activity Ex 1.03 ALL

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HSC Question (13)

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