Name the different statistical diagrams ?
- Cumulative frequency graphs
- Histograms
- Box-and-whisker plot
- Stem-and-leaf diagrams
- Frequency polygons
- Scatter diagrams
How do you draw a cumulative frequency graph ?
- Calculate the cumulative frequency of each data range
- Plot the points, at the top of each range on the x axis
- X axis is a variable , y axis is cumulative frequency
- Draw a curve joining the points smoothly
How do you find the median, LQ and UQ using a cumulative frequency graph ?
- Median : Halve the cumulative frequency and find the corresponding x value
- LQ : Divide the cumulative frequency by 4 and find corresponding x value
- UQ : Multiple the cumulative frequency by 3/4, find the corresponding x value
How do you find a y percentile using a cumulative frequency graph ?
- eg. 90th percentile = 0.9 x cumulative frequency, and then find the corresponding x value
- eg. 45th percentile = 0.45 x cumulative frequency
How to find the IQR using a cumulative frequency graph ?
- Find the corresponding UQ and LQ values
- UQ - LQ = IQR
What is the equation for histograms ?
How do you draw a histogram diagram ?
- Calculate the frequency density form the data provided
- The x axis is the x variable groups, the y axis is the frequency density
- Draw columns corresponding to the width of the groups and the frequency density
What is the assumption you make when calculating the mean and standard deviation from a histogram ?
The data is at the centre of each group
How do you draw a box-and-whisker plot ?
- Find the median, LQ, UQ, maximum and minimum
- Plot the values using lines
- The y axis is non existent, the x axis is the variable x groups
- Connect the lines to makes a box shape
What does each section of a box-and-whisker plot represent ?
25 % of data
If a box-and-whisker plot showed the scores students got when doing different tests, what piece of information is required to determine which test was easier ?
To determine this you would need to make a direct comparison with the same cohort of students taking both exams
What piece of information does a box-and-whisker plot not show ?
- It does not show how many individual values are found in the data
- Eg. If it shows the scores obtained by students on an exam, it does not show the number of students taking the exam
How do you compare two data sets presented on a box-and-whisker plot ?
- Comment on average : The median of A is greater than median of B meaning on average X is greater in A than b
- Comment on spread : The range/ IQR of A is greater than B, meaning A has a greater spread of X
What is one piece of information missing from a box-and-whisker plot ?
The number of individual pieces of data in each section
Eg. When showing scores attained on an exam, it doesn’t show the number of students taking the exam
How do you draw a stem-and-leaf diagram ?
- Make a key
- Organise the data in terms of size order
- Plot the values on the diagram
How do you compare tow data sets on a stem-and-leaf diagram ?
- Comment on the average : A is greater on average
- Comment on the spread : The spread is similar for A and B/ A has a greater spread than B
- comment on the shape of the distribution : The distribution of A is more symmetrical
What are the advantages of a stem-and-leaf diagram over a box-and-whisker plot ?
- Shows individual data values
- Shows the shape of the distribution
- Allows you to easily determine the mean and the mode
What are the advantages of a box-and-whisker plot over a leaf-and-stem diagram ?
- Easier to find the median, UQ, LQ
- Easier to calculate the IQR range
- Allows outliers to be easily identified
- Allows distribution to be compared between multiple groups / more than two
What is the equation for the standard deviation ?
How do you comment on the mean and standard deviation of two data sets ?
- A has a greater mean than B so on average X is greater in A
- A has a greater standard deviation than B so has a greater spread of X than B/ B has a smaller standard deviation so has more consistent X values than A
If there is one extreme, comment on the validity in the comparison between the means of the two data sets ?
- This is not an accurate comparison
- The mean for data set A is affected / skewed by one extreme or outlier resulting in a low/high mean
What may be another reason the standard deviation between two data sets may not be compared ?
Without a scale the stands deviation cannot be compared between two data sets on a test/ cannot be points scored compared to SD of percentage )
What is the equation for the standard deviation using frequency tables ?
What is the equation for the mean using frequency tables ?
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1) Proof and mathematical communication11
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2) Indices and Surds11
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3) Quadratic functions0
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4) Polynomials0
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5) Using Graphs11
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6) Coordinate Geometry0
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7) Logarithms0
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8) Exponential models11
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9) Binomial Expansion7
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10) Trigonometric functions21
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11) Triangle Geometry6
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12) Vectors15
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13) Differentiation9
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14) Applications of differentiation0
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15) Integration0
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16) Working with data35
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17) Probability14
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18) Statistical hypothesis testing13
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19) Introduction to Kinematics14
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20) Motion with constant acceleration4
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21) Force and motion8
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22) Objects in Contact10
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2.1 ) Proof20
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2.2 ) Functions21
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3.2 ) Further transformations of graphs9
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4.2 ) Sequences and Series0
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5.2 ) Rational functions and partial fractions8
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6.2 ) General Binomial Expansion2
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7.2 ) Radian measure16
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8.2 ) Further Trigonometry12
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9.2 ) Calculus of exponential and trigonometric functions12
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10.2 ) Further differentiation13
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11.2 ) Further integration techniques9
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12.2 ) Further applications of calculus18
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13.2 ) Differenital Equations0
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14.2 ) Numerical solutions of equations0
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15.2 ) Numerical integration0
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16.2 ) Conditional probability10
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17.2 ) The normal distribution14
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18.2 ) Further hypothesis testing14
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19.2 ) Applications of vectors0
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20.2 ) Projectiles0
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21.1 ) Forces in context0
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22.2 ) Moments0
