Statistics flashcards
14 cards on Statistics: the key points, worked examples and the slips to watch. Swipe through them, or print them.
Card 1 of 14
Statistics
Bar charts and pictograms
How do you draw and read a bar chart and a pictogram?
Answer it in your head, then turn the card over.
Bar charts and pictograms
Key points
- Bar chart: bars of equal width, the height showing the frequency, both axes labelled.
- Separate categories, like favourite sports, get gaps between their bars.
- A pictogram needs a key saying what one symbol stands for.
- Part of a symbol stands for that part of its value.
Key: one symbol = 4 people
3½ symbols = 3.5 × 4 = 14 people
A quarter of a symbol = 1 person
Watch out
Always read the key: if one symbol is 4 people, half a symbol is 2 people, not 1.
Statistics
Pie charts
How do you work out the angles for a pie chart, and how do you read one?
Answer it in your head, then turn the card over.
Pie charts
Key points
- Each item gets 360° ÷ the total, so a group's angle is its frequency × that.
- The angles add up to 360°: check this before you draw.
- A pie chart shows proportions, not counts: a group's share is its angle ÷ 360°.
60 students, 15 of whom walk
Each student gets 360 ÷ 60 = 6°
The walkers get 15 × 6 = 90°, a quarter of the circle.
Watch out
Equal angles on two pie charts mean equal shares, not equal numbers, unless the totals match.
Statistics
Mean, median, mode and range
How do you find the mean, median, mode and range of a set of data?
Answer it in your head, then turn the card over.
Mean, median, mode and range
Key points
- Mean: add up all the values, then divide by how many there are.
- Median: put the values in order and take the middle one; with two in the middle, go half-way between.
- Mode: the most common value. There can be more than one, or none.
- Range: largest − smallest. It measures spread, not a typical value.
8, 3, 5, 3, 11
In order: 3, 3, 5, 8, 11
Mean = 30 ÷ 5 = 6, median = 5, mode = 3
Range = 11 − 3 = 8
Watch out
Order the data before finding the median: for 7, 2, 9, 4, 5 it is 5, not the 9 in the middle of the list.
Statistics
Choosing the best average
How do you decide whether the mean, median or mode is the best average to use?
Answer it in your head, then turn the card over.
Choosing the best average
Key points
- Mean: uses every value, but one extreme value drags it towards it.
- Median: hardly moved by extreme values, so best for data like house prices or pay.
- Mode: the only average for non-number data, such as favourite colours, and gives the most common value.
Five salaries, in £1000s
20, 22, 23, 25, 160
Mean = 250 ÷ 5 = 50, but the median is 23.
The median fits better: the 160 drags the mean far above four of the five.
Watch out
The range is never an average: it says how spread out the data is, not what is typical.
Statistics
Averages from a frequency table
How do you find the mean and the mode from a frequency table?
Answer it in your head, then turn the card over.
Averages from a frequency table
Key points
- Multiply each value by its frequency (an fx column), then add the column up.
- Divide that total by the total frequency, the number of items.
- The mode is the value with the highest frequency, not the frequency itself.
Goals scored per match
Goals 0, 1, 2, 3 with frequencies 4, 6, 7, 3
Total frequency: 4 + 6 + 7 + 3 = 20
fx: 0 + 6 + 14 + 9 = 29 goals
Mean = 29 ÷ 20 = 1.45 goals; mode = 2 goals
Watch out
Divide by the total frequency, not the number of rows: here by 20, not 4.
Statistics
Estimating the mean of grouped data
How do you estimate the mean from grouped data, and why is it only an estimate?
Answer it in your head, then turn the card over.
Estimating the mean of grouped data
Key points
- Use each group's midpoint to stand for every value in it.
- Multiply each midpoint by its frequency, add, then divide by the total frequency.
- It is an estimate because the exact values are not known, only their groups.
- The modal class is the group with the highest frequency.
Times, in minutes
0 < t ≤ 10: 5 people; 10 < t ≤ 20: 12; 20 < t ≤ 30: 3
Midpoints: 5, 15, 25. Total frequency: 20
5 × 5 + 15 × 12 + 25 × 3 = 25 + 180 + 75 = 280
Estimated mean = 280 ÷ 20 = 14 minutes
Watch out
Use the midpoint, never the class width or one end: the group 10 < t ≤ 20 stands for 15.
Statistics
Discrete and continuous data
What is the difference between discrete and continuous data?
Answer it in your head, then turn the card over.
Discrete and continuous data
Key points
- Discrete data can only take certain values, and is usually counted: goals, people, shoe sizes.
- Continuous data can take any value in a range, and is measured: height, mass, time.
- Continuous data is grouped with inequalities, like 10 < t ≤ 20, so no value fits two groups.
Watch out
Shoe sizes are discrete even though some end in a half: there is no size 7.3.
Statistics
Scatter graphs and correlation
What do positive, negative and no correlation look like, and what does correlation tell you?
Answer it in your head, then turn the card over.
Scatter graphs and correlation
Key points
- Each point is one individual with two measurements, such as height and shoe size.
- Positive: the points go uphill, so as one increases, so does the other.
- Negative: the points go downhill, so as one increases, the other decreases.
- No correlation: no pattern. The closer the points are to a line, the stronger it is.
Watch out
Correlation does not prove one thing causes the other: ice cream sales and sunburn both rise with sunny weather.
Statistics
Lines of best fit
How do you draw a line of best fit, and when is a prediction from it reliable?
Answer it in your head, then turn the card over.
Lines of best fit
Key points
- Draw one straight line along the trend, with about as many points on each side.
- It need not pass through any point, or through the origin. Ignore an outlier.
- A value read off the line is an estimate.
- Inside the data (interpolation) it is fairly reliable; beyond it (extrapolation) it is not.
Watch out
Do not stretch the line beyond the data: the pattern may not carry on there.
Statistics
Comparing two sets of data
How do you write a full comparison of two sets of data?
Answer it in your head, then turn the card over.
Comparing two sets of data
Key points
- Compare one average (the median or the mean) and one measure of spread (the range or IQR).
- Say what each means in context, one sentence for each.
- A higher average: they typically did more. A smaller spread: they were more consistent.
Class A and Class B
A: median 62, range 15. B: median 55, range 30.
Class A's median is 7 marks higher, so Class A typically scored more.
Class A's range is smaller, so their scores were more consistent.
Watch out
The spread is about consistency, never about who did better: the averages answer that.
Statistics
HigherCumulative frequency graphs
How do you draw a cumulative frequency graph and read the median and quartiles from it?
Answer it in your head, then turn the card over.
Cumulative frequency graphs
Key points
- Cumulative frequency is a running total of the frequencies.
- Plot each running total at its group's upper boundary, and join with a smooth curve.
- Read across at half the total for the median, a quarter and three quarters for the quartiles.
- Interquartile range (IQR) = upper quartile − lower quartile.
80 values
Median: read across from 80 ÷ 2 = 40
Quartiles: from 20 and 60
If they read 23 and 41, the IQR is 41 − 23 = 18
Watch out
Plot at the upper boundary of each group, not the midpoint: only by its end is the whole group counted.
Statistics
HigherBox plots
What does a box plot show, and how do you use box plots to compare data?
Answer it in your head, then turn the card over.
Box plots
Key points
- Five values: the lowest, the lower quartile, the median, the upper quartile and the highest.
- The box runs from quartile to quartile, with a line at the median; whiskers reach the extremes.
- Compare the medians for average and the IQRs for spread, each in context.
- The IQR is the middle half's spread, so one extreme value cannot stretch it.
12, 18, 24, 30, 41
IQR = 30 − 18 = 12, the width of the box
Range = 41 − 12 = 29
Watch out
The width of the box is the IQR, not the range: the range runs from whisker end to whisker end.
Statistics
HigherDrawing histograms
How do you draw a histogram when the classes have different widths?
Answer it in your head, then turn the card over.
Drawing histograms
Key points
- The area of each bar, not its height, shows the frequency.
- The height is the frequency density: frequency ÷ class width.
- The bars touch, with no gaps, because the data is continuous.
Formula
frequency density = frequency ÷ class width
Example
0 < h ≤ 10, frequency 30: height 30 ÷ 10 = 3
10 < h ≤ 30, frequency 50: height 50 ÷ 20 = 2.5
Watch out
Plotting the frequency itself makes the wider classes look far bigger than they are.
Statistics
HigherReading histograms
How do you find a frequency from a histogram with unequal class widths?
Answer it in your head, then turn the card over.
Reading histograms
Key points
- Reverse the drawing: frequency = frequency density × class width, the bar's area.
- For part of a class, use the width of just that part.
- The total frequency is the total area of all the bars.
Formula
frequency = frequency density × class width
A bar from 20 to 50, height 1.6
Width 50 − 20 = 30, so the frequency is 1.6 × 30 = 48
From 20 to 30 only: 1.6 × 10 = 16
Watch out
Multiply by the class width, not the boundary: the frequency is 1.6 × 30, not 1.6 × 50.
Print these cards
Four cards to an A4 sheet, each the size of a standard A6 revision card.
One-sided
Each card prints on one face: the question at the top, the notes under it.
Two-sided
Questions on the front, notes on the back. Print double-sided and flip on the long edge, then cut along the lines.
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