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LearnAQA7357First teaching 2017Paper 3 · Pure and StatisticsData presentation and interpretation

Paper 3 · Module

Data presentation and interpretation

6 subtopics≈ 195 min in total

Start the module: Stem-and-leaf diagrams and box plots Open graphing calculator

Stem-and-leaf diagrams and box plots
Two ways to see a whole data set at a glance. A stem-and-leaf diagram keeps every value; a box plot squeezes the data into five numbers that show its centre, its spread and its shape.
≈ 30 min
Histograms and cumulative frequency
In a histogram, area (not height) shows frequency, which is what makes unequal class widths fair. A cumulative frequency graph turns the same table into a curve from which the median and quartiles can be read.
≈ 35 min
Mean and standard deviation
The mean is the balance point of the data; the standard deviation is a typical distance from it. One formula, "mean of the squares minus the square of the mean", gives the variance from almost any form of data.
≈ 35 min
Coded and combined data
Shifting every value moves the mean but leaves the spread alone; scaling every value scales both. Knowing this, you can work with simpler "coded" numbers and translate back, and you can merge two groups using their totals.
≈ 30 min
Summary statistics and the PMCC
The summary statistics $S_{xx}$ , $S_{yy}$ and $S_{xy}$ measure spread and how $x$ and $y$ vary together. The product moment correlation coefficient $r=\dfrac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}$ lies between $-1$ and $1$ and measures how close the points are to a straight line.
≈ 30 min
The least squares regression line
The regression line of $y$ on $x$ , $y=a+bx$ , is the straight line that makes the squared vertical distances from the points as small as possible. Its gradient is $b=\dfrac{S_{xy}}{S_{xx}}$ and it always passes through $(\bar x,\bar y)$ , so $a=\bar y-b\bar x$ .
≈ 35 min