Secondary School Statistics

1
Secondary School Statistics

• The effect of NCEA and technology

2
NCEA in 1 easy lesson

• Each years course split into non overlapping
  Achievement Standards
• Internal or external
• Standard can be passed at Achieved, Merit or
  Excellence
• Pass rates vary for each standard
• Year 11 Level 1 Year 12 Level 2
• Year 13 Level 3 Schol Level 4

3
Year 11 Level 1

• SC Prescription
• 7.1 Describe how an investigation would be
  carried out
• write question
• devise ways of obtaining representative sample
• 7.2 Use graphs and statistics to analyse data
• include grouped data
• comparing sets of data
• 7.3 Make and justify statements about the results
• 7.4 Identify features in time series data
  including seasonal factors
• 7.5 Suggest improvements
• 7.6 Communicate findings effectively

4
Year 11 Level 1

• Achievement Standard 1.5 (Internal)
• Achievement
• Use statistical methods to respond to a question
  or hypothesis
• Use statistical information to answer
  straightforward questions
• Merit
• Pose a question and use statistical methods to
  produce a justified response
• Interpret statistical information
• Excellence
• Evaluate the statistical process used to respond
  to the question

5
So Whats Different?

• Emphasis pose a question
• limitations
• Missing grouped data
• collecting own data (often)
• Added
• Advantages coherent whole process
• Disadvantages set procedure

6
Year 12 Level 2

• SFC Prescription
• 6.1 Plan a statistical investigation to make
  inferences
• 6.2 Design and justify sample collection methods
• 6.3 Collect data, graph and discuss prominent
  features
• 6.4 Calculate sample statistics including mean
  and standard deviation
• 6.5 Analyse and discuss inferences
• evaluate statistics in the media and reports
• 6.6 Highlight features of simple time series
  graphs
• using moving averages and seasonal adjustments to
  make predictions
• identifying possible causes of features
• Use of appropriate technology for 6.3 and 6.4

7
Year 12 Level 2

• Achievement Standard 2.5 (Internal)
• Achievement
• Select a sample to answer a question
• Calculate appropriate sample statistics
• Make an inference about a population
• Merit
• Describe and justify a sampling method and use
  it to select a sample
• Justify inferences made about a population
• Excellence
• Critically evaluate the sampling process

8
So Whats Different?

• Emphasis representative sampling
• make inference
• Missing grouped data
• graphing
• time series
• in depth investigation
• evaluate reports
• Added evaluate process, reliability
• Advantages coherent whole process
• Disadvantages set procedure

9
Year 13 Level 3

• Bursary Prescription
• 1.1 Plan investigation, analyse data, present and
  discuss findings
• 1.2 Analyse statistical reports
• 1.3 Calculate and interpret sample statistics
• Derive identity
• 1.4 Sampling distribution of the mean and
  proportion
• 1.5 Explain the difference between statistics and
  parameters
• Calculate the sample size required
• 1.6 Explain and use the Central Limit Theorem
• 1.7 Confidence intervals mean, proportion,
  difference between two means
• 2.1 Investigate a process which produces time
  series data
• Planning
• Graphing, smoothing
• Identifying patterns
• Features and predictions

10
Year 13 Level 3

• Achievement Standard 3.1 (Internal)
• Achievement
• Determine the trend for time series data
• Merit
• Use time series analysis to make forecasts
• Excellence
• Analysis time series data and prepare a report
  on the analysis

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Year 13 Level 3

• Achievement Standard 3.2 (External)
• Achievement
• Calculate confidence intervals for population
  parameters
• Merit
• Demonstrate an understanding of confidence
  intervals
• Excellence
• Analyse estimates of population parameters
• Achievement Standard 3.5 (Internal)
• Achievement
• Plan and carrry out an investigation involving
  bivariate continuous data, analyse the data and
  report the findings
• Merit
• Carry out an in depth analysis of bivariate data
  within an investigation
• Excellence
• Produce a comprehensive report on the
  investigation

12
So Whats Different?

• Emphasis use of technology
• regression correlation
• Missing grouped data
• derive formulae excellence only
• design sampling method
• Added regression
• more complex time series model
• Advantages lots of real data analysed
• coherent whole process
• Disadvantages access to technology essential
• CI divorced from real data

13
Technology

• Graphics Calculator
• Calculates all stats
• mean, median, mode, range, IQ range,
  quartiles, totals, st dev, regression coeff
• Draws graphs
• scatter, line, box whisker, histogram
• Fits all types of lines/curves, finds eqn
• Calculates confidence intervals
• Easy to analyse affect of outliers

14
Technology

• Excel
• Calculates all stats
• mean, median, mode, range, IQ range, quartiles,
  totals, st dev, regression coeff
• Draws graphs
• scatter, line, (box whisker, histogram)
• Fits all types of lines/curves, finds eqn
• Calculate confidence interval for mean
• Easy to analyse affect of outliers

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Pros and Cons of NCEA

• Pros
• Less repetitive - different focus at each level
• Focus shifted from number crunching to whole task
  approach
• Focus on purpose ie making inference about popn
• Forced more uniformity in standard of teaching
• Forced use of Excel etc
• Look at reasons behind data
• Plenty of time year 13 add more content?
• Easy 9 credits for owners of graphic calculator

• Cons
• Teaching to assessment
• Lack of experience with grouped data
• Accuracy of stats or graphs not important
• Set procedure
• More time assessing
• Other subjects use more statistical methods
• Verification of individual work
• Access to technology
• Loss underlying mathematics