You want to compare the distributions of two sets of raw, ungrouped data. Which diagram is the best choice, and why?

A box plot for each set of data. A box plot shows the shape of a distribution at a glance, so two of them make the patterns quick to compare. It also suits raw, ungrouped data, unlike a histogram or a cumulative frequency graph, which both need the data to be grouped.

Which diagram is used to display data collected for two variables, and what does it show?

A scatter diagram , used with ungrouped data for two variables. It shows the pattern of the relationship between the two variables.

A graph's vertical scale is labelled Population (millions) . What does the value 60 on that scale represent?

60 000 000 people. Numbers on a scale are often abbreviated so that they fit on the axis, so always read the axis label and its units before taking a value off a graph.

True or False? A graph cannot be misleading if every value on it has been plotted correctly.

False. The scales , the units and the way the data is represented can all be chosen to make a graph look more or less convincing, even when every value is plotted accurately. Check the scales on both axes before drawing any conclusion from a graph.

Which values can be read from a box plot, and which cannot?

You can read the minimum , the lower quartile , the median , the upper quartile and the maximum , together with any outliers . No other individual data value can be read from a box plot: it shows the shape of the distribution, not the data itself.

What proportion of the data lies inside the box of a box plot, and what proportion lies along each whisker?

The box holds the middle 50% of the data, between the lower and upper quartiles. Each whisker holds 25% : the lowest quarter of the data on one side and the highest quarter on the other.

True or False? A box plot drawn with a deeper box represents a larger set of data.

False. The box can be drawn to any depth, and the depth carries no information at all. Only positions along the scale mean anything on a box plot.

How is an outlier shown on a box plot, and where does the whisker end when there is one?

The outlier is marked with a cross beyond the end of the whisker. The whisker then stops at the most extreme value that is not an outlier, so it no longer reaches the smallest or largest value in the data set.

Two sets of data are to be compared using box plots. How should the two box plots be presented?

One above the other, drawn against the same scale on the horizontal axis, with each one clearly labelled. Reading across from one plot to the other is only valid if both use the same scale.

Define cumulative frequency .

The running total of the frequencies: the frequency of a class added to the frequencies of all the classes below it.

When a cumulative frequency graph is plotted, which value of each class is the cumulative frequency plotted against, and why?

The upper boundary of the class. The cumulative frequency counts every value in that class as well as every value in the classes below it, so that total is only reached at the top of the class.

A question asks how many data values are greater than a particular value. How is that found from a cumulative frequency graph?

Read up from that value on the horizontal axis to the curve, then across to the cumulative frequency axis. That gives the number of values less than it, so subtract the result from the total frequency to get the number greater than it.

True or False? The median read from a cumulative frequency graph is the exact median of the data.

False. The data has been grouped , so the individual values are no longer known. The median, the quartiles and any percentile read from the graph are all estimates .

What is plotted on the vertical axis of a histogram, and why is it not the frequency?

Frequency density . The classes of a histogram may have different widths , so it is the area of each bar that represents the frequency, not its height. Plotting frequency density is what makes the areas come out in proportion to the frequencies.

True or False? In a histogram the bars for adjacent classes always touch.

True. A histogram displays grouped continuous data, so each class ends where the next begins and there is no gap between the bars. A bar chart, which displays discrete or qualitative data, does have gaps between its bars.

A grouped frequency table gives the classes as 1 to 5, 6 to 10 and 11 to 15. What must you do before you can find the class widths for a histogram?

Close the gaps between the classes first, so that the upper boundary of one class is the lower boundary of the next. Check whether the values were rounded or truncated before deciding where the boundaries lie. For data rounded to the nearest whole number the boundaries become 0.5 to 5.5, 5.5 to 10.5 and 10.5 to 15.5, each of class width 5 .

A histogram question tells you that the area of each bar is proportional to the frequency rather than equal to it. How do you find the frequencies?

Use a class whose frequency you are given to find the scale factor : work out the area of that bar and compare it with the frequency it represents. That tells you how many data values one unit of area stands for, and every other bar can then be converted in the same way. A question of this kind will always give you enough information to find the scale factor.

True or False? The two ends of a frequency polygon are joined down to the horizontal axis.

False. The polygon is left open, unless a frequency at the end happens to be zero. The first and last points are not joined to the axis, and the last point is not joined back to the first. The points themselves are plotted at the midpoint of each class and joined with straight lines.

A LevelMathsEdexcelStatisticsFlashcardsData Presentation & InterpretationData Presentation

Data Presentation (Edexcel A Level Maths: Statistics): Flashcards

Exam code: 9MA0

1/21

0Still learning

Know0

FrontData Presentation
You want to compare the distributions of two sets of raw, ungrouped data. Which diagram is the best choice, and why?

Was this flashcard helpful?

Cards in this collection (21)

You want to compare the distributions of two sets of raw, ungrouped data. Which diagram is the best choice, and why?
A box plot for each set of data.
A box plot shows the shape of a distribution at a glance, so two of them make the patterns quick to compare.
It also suits raw, ungrouped data, unlike a histogram or a cumulative frequency graph, which both need the data to be grouped.
Which diagram is used to display data collected for two variables, and what does it show?
A scatter diagram, used with ungrouped data for two variables.
It shows the pattern of the relationship between the two variables.
A graph's vertical scale is labelled Population (millions). What does the value 60 on that scale represent?
60 000 000 people.
Numbers on a scale are often abbreviated so that they fit on the axis, so always read the axis label and its units before taking a value off a graph.
True or False?
A graph cannot be misleading if every value on it has been plotted correctly.
False.
The scales, the units and the way the data is represented can all be chosen to make a graph look more or less convincing, even when every value is plotted accurately.
Check the scales on both axes before drawing any conclusion from a graph.
Which values can be read from a box plot, and which cannot?
You can read the minimum, the lower quartile, the median, the upper quartile and the maximum, together with any outliers.
No other individual data value can be read from a box plot: it shows the shape of the distribution, not the data itself.
What proportion of the data lies inside the box of a box plot, and what proportion lies along each whisker?
The box holds the middle 50% of the data, between the lower and upper quartiles.
Each whisker holds 25%: the lowest quarter of the data on one side and the highest quarter on the other.
True or False?
A box plot drawn with a deeper box represents a larger set of data.
False.
The box can be drawn to any depth, and the depth carries no information at all.
Only positions along the scale mean anything on a box plot.
How is an outlier shown on a box plot, and where does the whisker end when there is one?
The outlier is marked with a cross beyond the end of the whisker.
The whisker then stops at the most extreme value that is not an outlier, so it no longer reaches the smallest or largest value in the data set.
Two sets of data are to be compared using box plots. How should the two box plots be presented?
One above the other, drawn against the same scale on the horizontal axis, with each one clearly labelled.
Reading across from one plot to the other is only valid if both use the same scale.
Define cumulative frequency.
The running total of the frequencies: the frequency of a class added to the frequencies of all the classes below it.
When a cumulative frequency graph is plotted, which value of each class is the cumulative frequency plotted against, and why?
The upper boundary of the class.
The cumulative frequency counts every value in that class as well as every value in the classes below it, so that total is only reached at the top of the class.
Complete the positions used to estimate the quartiles of $n$ data values from a cumulative frequency graph:
$Q_{1} = \frac{n}{______} th value, Q_{2} = \frac{n}{______} th value, Q_{3} = \frac{______n}{4} th value$
The completed positions are:
$Q_{1} = \frac{n}{4} th value, Q_{2} = \frac{n}{2} th value, Q_{3} = \frac{3 n}{4} th value$
Find each position on the cumulative frequency axis, read across to the curve, then down to the horizontal axis to get the data value.
A question asks how many data values are greater than a particular value. How is that found from a cumulative frequency graph?
Read up from that value on the horizontal axis to the curve, then across to the cumulative frequency axis.
That gives the number of values less than it, so subtract the result from the total frequency to get the number greater than it.
True or False?
The median read from a cumulative frequency graph is the exact median of the data.
False.
The data has been grouped, so the individual values are no longer known.
The median, the quartiles and any percentile read from the graph are all estimates.
What is plotted on the vertical axis of a histogram, and why is it not the frequency?
Frequency density.
The classes of a histogram may have different widths, so it is the area of each bar that represents the frequency, not its height. Plotting frequency density is what makes the areas come out in proportion to the frequencies.
Complete the formula used to find the height of each bar of a histogram:
$frequency density = \frac{______}{______}$
The completed formula is:
$frequency density = \frac{frequency}{class width}$
In some questions the area of a bar is only proportional to the frequency, and a scale factor has to be found first.
True or False?
In a histogram the bars for adjacent classes always touch.
True.
A histogram displays grouped continuous data, so each class ends where the next begins and there is no gap between the bars.
A bar chart, which displays discrete or qualitative data, does have gaps between its bars.
A grouped frequency table gives the classes as 1 to 5, 6 to 10 and 11 to 15. What must you do before you can find the class widths for a histogram?
Close the gaps between the classes first, so that the upper boundary of one class is the lower boundary of the next.
Check whether the values were rounded or truncated before deciding where the boundaries lie.
For data rounded to the nearest whole number the boundaries become 0.5 to 5.5, 5.5 to 10.5 and 10.5 to 15.5, each of class width 5.
A histogram question tells you that the area of each bar is proportional to the frequency rather than equal to it. How do you find the frequencies?
Use a class whose frequency you are given to find the scale factor: work out the area of that bar and compare it with the frequency it represents.
That tells you how many data values one unit of area stands for, and every other bar can then be converted in the same way.
A question of this kind will always give you enough information to find the scale factor.
How do you estimate the frequency for part of a class from a histogram, for example the values above 13 in the class $12 \leq m < 15$ ?
Find the area of that part of the bar, from 13 to 15, and convert it to a frequency exactly as you would for a whole bar.
This assumes the values are spread evenly across the class, so the answer is an estimate.
True or False?
The two ends of a frequency polygon are joined down to the horizontal axis.
False.
The polygon is left open, unless a frequency at the end happens to be zero. The first and last points are not joined to the axis, and the last point is not joined back to the first.
The points themselves are plotted at the midpoint of each class and joined with straight lines.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Statistical MeasuresNext:Working with Data