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Y10A Data Representation & Interpretation (Standard Deviation…
Y10A Data Representation & Interpretation
Standard Deviation
Introduction to the Standard Deviation
What is the standard deviation? measure of spread, similar to the range/IQR
Guessing which data set (looking at graphs) has the bigger/smaller standard deviation
Interpreting the standard deviation - long answer questions that ask the student to interpret information based on a graph and the given standard deviation
Calculating the Standard Deviation
Formula for the standard deviation
practise calculating by hand
explain why the standard deviation is calculated by using the squares of (x - xi)
Calculating the Standard Deviation Using Technology
Investigate the effect of: adding data values equivalent to the mean, greater than or less than the mean; altering ALL the values, e.g. doubling all values, or adding a constant to all values
Using the Standard Deviation to Compare Two Sets of Data
give students two graphs (make sure to give a variety of graph types - stem and leaf, histogram, etc.), either with given SD or they have to calculate, and ask students to make interpretations based on the information given.
give questions that have the same mean and different means
Comparing Measures of Spread
comparing the range, interquartile range and standard deviation
NSW Curriculum
Use information technologies to investigate bivariate numerical data sets; where appropriate, students use a straight line to describe the relationship, allowing for variation
use digital technologies, such as a spreadsheet, to construct a line of best fit for bivariate numerical data
investigate different methods of constructing a line of best fit using digital technologies (Problem Solving)
use lines of best fit to predict what might happen between known data values (interpolation) and predict what might happen beyond known data values (extrapolation)
compare predictions obtained from different lines of best fit (Problem Solving, Reasoning)
Calculate and interpret the mean and standard deviation of data and use these to compare data sets
find the standard deviation of a set of data using digital technologies
investigate and describe the effect, if any, on the standard deviation of adding a data value to the set of data, eg adding a data value equivalent to the mean, or adding a data value more or less than one standard deviation from the mean (Problem Solving, Reasoning) ICTCCT
investigate and describe the effect, if any, on the standard deviation of altering all of the data values in the set of data by operations such as doubling all data values or adding a constant to all data values (Problem Solving, Reasoning)
use the mean and standard deviation to compare two sets of data
compare and describe the spread of sets of data with the same mean but different standard deviations (Communicating, Reasoning) CCT
told same mean, asked to describe spread or consistency of data sets
give them data sets and ask them to calculate mean - then compare
compare and describe the spread of sets of data with different means by referring to standard deviation (Communicating, Reasoning)
for q types: same standard deviation and also different standard deviations
investigate the meaning and calculation of standard deviation using a small set of data
explain why the standard deviation is calculated using the squares of (x−x¯) for all data values in a set of data (Communicating, Reasoning)
compare the relative merits of the range, interquartile range and standard deviation as measures of spread
Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278 - Scootle )
using the standard deviation to describe the spread of a set of data
using the mean and standard deviation to compare numerical data sets
Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation (ACMSP279 - Scootle )
investigating different techniques for finding a ‘line of best fit’
Line of Best Fit
Constructing Lines of Best Fit using Technology
Least Squares Regression Line
Median-Median Line
Define linear regression
Introduction to Lines of Best Fit
Explain what a LOBF is.
drawing by hand
talk about when you can use a line of best fit / when a LOBF is useful (this is kinda the same thing) - i.e. not when there is no relationship between the data.
positive/negative / strong correlation (good line of best fit)
Using LOBF to Make Predictions
both interpolation and extrapolation
Finding Equations of Lines of Best Fit
Get students to choose the line of best fit on a given graph (this is only if I think it's necessary
finding equations of lines of best fit
Review
Shape and Spread in Data
Bivariate Data
displaying data
Interquartile range?
Core Concepts
Problem Solving - context based problem solving lesson. Give them a study to analyse.
Pre-learning
Extension
Deriving the Standard Deviation Formula
Understanding Least Squares Regression (calculating by hand)
the red lines here are points in the NSW curriculum that I still need to build lessons for