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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

The Statistical Cycle

1.10 Multivariate Home | Assessment Criteria | The Statistical Cycle | Form a Question | Collecting Data | Cleaning Data | Stem & Leaf Plots | Dot Plots | Central Tendency | Measures of Spread | Box Plots | Comparing Boxplots | Describing Features | Sampling from a Population | Population Inference | Revision



The Statistical Cycle

1) A PROBLEM to investigate: Define the Problem, Define the Population, Define the Variables.

2) PLAN what variables and subgroups to compare and how to collect relevant statistics

3) DATA Collection: Organise the research, Decide on a sampling method, Collect the data.

4) ANALYSIS: Summarise data into tables, calculate measures of Central Tendency (averages: mean, median, mode) and measures of Spread (range, inter quartile range)
Data Display: Draw appropriate graphs, especially Box-and-Whisker

5) CONCLUSION: Comment on graphs, Comment on analysis, Draw conclusions, Suggest possible sources of error, Suggest improvements.


Achievement Standard | Overview |

pg 276

pg 262

pg 76, 77


"I wonder if there are differences between..."

What information will you need to answer the question?

Identify two or more sub-groups of the population to compare.

What variables are likely to show differences?



Remember that you are analysing and comparing data from a SAMPLE from a population

Is there a difference between the subgroups?

Comparisons made from a Box-and-Whisker graph

Comparisons bases on measures of central tendency

Comparisons made from measures of spread


If collecting data you will need to plan a survey of questionnaire.

Using available data sets is recommended

If using a data set decide what sub-groups of data are needed and choose from the available variables (choose carefully so you can answer the problem


Analyse the data to find similarities and differences.

You will need measures of central tendency (mean, median, mode) AND measures of spread (range, inter quartile range, standard deviation)

Use technology to calculate the statistics: calculator, or EXCEL (using excel)

Data displays

Remember you are trying to compare your sub-groups
Use suitable technology to produce appropriate graphs such as EXCEL

Essential: Box-and-Whisker Plot
Recommended: Dot Plot, Stem and Leaf plot,
Possible: Histogram, Pictograph, Bar graph, Comparative bar graph, Pie graph


Collect data by making a survey or questionnaire, OR take a sample from large data set. (at least 30 values)

eg Census at School or Gamma Maths Data Set

Clean the data set before continuing











Statistics is about the collection and summarising of data from the world around us.

Government & council planning
Business profits – market research, product design, pricing, advertising
Media articles & reports, Trade and travel
Sport & recreation, Health & medicine

A ‘population’ is all the members of a group  (eg all Y11 students in NZ)

A ‘sample’ is a small group of a population (eg Y11 students in this class)

We collect data from a sample because a population is too large to handle
The sample data is analysed and used to gain an insight about the population 

We need a sample of at least 30 to have some accuracy

A sample is a ‘snapshot’ of the population.
A different sample will give different results

Words & Concepts

Measure of central tendency
Individual data
Grouped data
Continuous data
Class interval
Stem & leaf plot
Bar graph
Univariate data
Double column bar graph
Two-variable data
Independent variable
Dependent variable
Short term features
Long term features





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