What do the box and the whiskers on a boxplot represent?

The box is the middle 50% of the data, stretching from the lower quartile to the upper quartile. Each whisker is one of the outer 25%, running from the box out to the lowest value at one end and the highest at the other.

True or False? The depth of the box on a boxplot tells you something about the data.

False. The box can be drawn to any depth at all, and two boxplots of the same data may look quite different in height. Only the horizontal positions of the five lines carry information.

How do you draw a boxplot once you have the five values?

Draw vertical lines at all five values, then turn the two quartile lines into a rectangle by joining their ends. Finally draw a horizontal line from each side of the box out to the lowest and to the highest value, which gives the two whiskers.

Why can you not work out the mean from a boxplot?

Because a boxplot shows only the five summary values and no other individual data items. A mean needs the total of every value in the set, and those values simply are not on the diagram.

Define scattergraph .

A scattergraph is a graph used to plot pairs of data, with one of the two quantities on each axis. It is also called a scatter diagram or scatter plot, and its purpose is to show whether the two quantities are related.

How do you plot a pair of values on a scattergraph?

Find the first value on the horizontal axis and the second on the vertical axis. Mark the single point that lines up with both of them, and repeat for every pair in the table.

True or False? The points on a scattergraph should be joined up.

False. Each point is a separate pair of measurements from a different individual, not one reading in a sequence. Joining them would suggest the data moves from one point to the next, which is not what a scattergraph is showing.

What is a line of best fit?

A single straight line drawn through the scatter to show the overall direction of the data. It represents the best estimate of the relationship between the two quantities, which is what makes it usable for predictions.

What makes a line of best fit a good one?

Three things together: it starts in line with the leftmost point and ends in line with the rightmost one it passes as close to as many points as possible there are points both above it and below it It does not have to start at, end at, or pass through any of the plotted points.

True or False? A line of best fit should be drawn so that it passes through the origin.

False. The line has to follow the data, and forcing it through the origin imposes a relationship the data may not support. Start it in line with the leftmost point instead, wherever on the grid that happens to be.

How do you use a line of best fit to estimate a value?

Draw a line from the value you are given on its own axis across or up to the line of best fit. From that meeting point, draw a second line to the other axis and read the value off, checking the scale as you do.

A pie chart is a circle divided into sectors, each one representing a category of the data. The size of each sector shows that category's share of the whole.

True or False? A pie chart shows the actual frequency of each category.

False. It shows only the proportions , so two pie charts can look identical while representing quite different numbers of people. You need to be told the total frequency before any actual frequency can be recovered from one.

How do you find the angle for a category in a pie chart?

Write that category's frequency as a fraction of the total frequency. Then find that fraction of 360 degrees, so 11 students out of 30 gives an angle of 132 degrees.

How can you work with a pie chart using proportion instead of a formula?

Use the fact that 360 degrees stands for the whole total frequency, and scale from there. If a sector of 30 degrees represents 15 people, then 1 degree represents 0.5 people, and multiplying by 360 gives a total of 180 people.

True or False? The angles in a pie chart always add up to 360 degrees.

True. Each angle is that category's share of the whole, and the shares together make up the entire circle. This is the check worth making at the end: a set of angles that does not total 360 contains a mistake somewhere.

National 5MathsSQAApplications of MathematicsFlashcardsGraphical Data, Probability & Statistics SkillsBoxplots, Scattergraphs & Pie Charts

Boxplots, Scattergraphs & Pie Charts (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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FrontBoxplots
Complete the five values shown on a boxplot:
A boxplot shows the lowest value, the $______$ quartile, the median, the $______$ quartile and the highest value.

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Cards in this collection (20)

Complete the five values shown on a boxplot:
A boxplot shows the lowest value, the $______$ quartile, the median, the $______$ quartile and the highest value.
The completed list is:
A boxplot shows the lowest value, the lower quartile, the median, the upper quartile and the highest value.
Those five are all it shows: no other individual data item appears on the diagram.
What do the box and the whiskers on a boxplot represent?
The box is the middle 50% of the data, stretching from the lower quartile to the upper quartile.
Each whisker is one of the outer 25%, running from the box out to the lowest value at one end and the highest at the other.
True or False?
The depth of the box on a boxplot tells you something about the data.
False.
The box can be drawn to any depth at all, and two boxplots of the same data may look quite different in height.
Only the horizontal positions of the five lines carry information.
How do you draw a boxplot once you have the five values?
Draw vertical lines at all five values, then turn the two quartile lines into a rectangle by joining their ends.
Finally draw a horizontal line from each side of the box out to the lowest and to the highest value, which gives the two whiskers.
A boxplot has whiskers ending at 8 and 58, and a box running from 14 to 30. What are the range and the interquartile range?
The range is 50 and the interquartile range is 16.
The whiskers give the lowest and highest values, so the range is $58 - 8 = 50$ .
The box gives the two quartiles, so the interquartile range is $30 - 14 = 16$ .
Why can you not work out the mean from a boxplot?
Because a boxplot shows only the five summary values and no other individual data items.
A mean needs the total of every value in the set, and those values simply are not on the diagram.
Define scattergraph.
A scattergraph is a graph used to plot pairs of data, with one of the two quantities on each axis.
It is also called a scatter diagram or scatter plot, and its purpose is to show whether the two quantities are related.
How do you plot a pair of values on a scattergraph?
Find the first value on the horizontal axis and the second on the vertical axis.
Mark the single point that lines up with both of them, and repeat for every pair in the table.
True or False?
The points on a scattergraph should be joined up.
False.
Each point is a separate pair of measurements from a different individual, not one reading in a sequence.
Joining them would suggest the data moves from one point to the next, which is not what a scattergraph is showing.
What is a line of best fit?
A single straight line drawn through the scatter to show the overall direction of the data.
It represents the best estimate of the relationship between the two quantities, which is what makes it usable for predictions.
What makes a line of best fit a good one?
Three things together:
- it starts in line with the leftmost point and ends in line with the rightmost one
- it passes as close to as many points as possible
- there are points both above it and below it
It does not have to start at, end at, or pass through any of the plotted points.
True or False?
A line of best fit should be drawn so that it passes through the origin.
False.
The line has to follow the data, and forcing it through the origin imposes a relationship the data may not support.
Start it in line with the leftmost point instead, wherever on the grid that happens to be.
How do you use a line of best fit to estimate a value?
Draw a line from the value you are given on its own axis across or up to the line of best fit.
From that meeting point, draw a second line to the other axis and read the value off, checking the scale as you do.
Define pie chart.
A pie chart is a circle divided into sectors, each one representing a category of the data.
The size of each sector shows that category's share of the whole.
True or False?
A pie chart shows the actual frequency of each category.
False.
It shows only the proportions, so two pie charts can look identical while representing quite different numbers of people.
You need to be told the total frequency before any actual frequency can be recovered from one.
How do you find the angle for a category in a pie chart?
Write that category's frequency as a fraction of the total frequency.
Then find that fraction of 360 degrees, so 11 students out of 30 gives an angle of 132 degrees.
480, 150 and 90 people chose three types of show. What angles represent them?
The angles are 240, 75 and 45 degrees.
The total is $480 + 150 + 90 = 720$ , and $720 \div 2 = 360$ , so every frequency is halved to give its angle.
Spotting a scale factor like this avoids three separate fraction calculations.
A sector has an angle of 84 degrees and the total frequency is 180. What frequency does it represent?
It represents 42.
Write the angle as a fraction of the whole turn, $\frac{84}{360}$ , and find that fraction of the total frequency.
That gives $\frac{84}{360} \times 180 = 42$ .
How can you work with a pie chart using proportion instead of a formula?
Use the fact that 360 degrees stands for the whole total frequency, and scale from there.
If a sector of 30 degrees represents 15 people, then 1 degree represents 0.5 people, and multiplying by 360 gives a total of 180 people.
True or False?
The angles in a pie chart always add up to 360 degrees.
True.
Each angle is that category's share of the whole, and the shares together make up the entire circle.
This is the check worth making at the end: a set of angles that does not total 360 contains a mistake somewhere.

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