A histogram displays the frequency distribution of continuous quantitative data, with no gaps between the bars. Unlike a bar chart, its class intervals may be unequal and its vertical axis shows frequency density rather than frequency.

On a cumulative frequency graph, which value of each class is plotted horizontally?

The upper boundary of each class is plotted, because everything up to and including that value has been counted. The points are then joined by hand with a smooth increasing curve .

True or False? On a histogram, the height of a bar tells you the frequency of that class.

False. The height is the frequency density , and it is the area of the bar that is proportional to the frequency. In most questions that area is equal to the frequency directly.

Why must a stem and leaf diagram always have a key?

The key shows how a stem and a leaf are combined into a data value, and it gives the units. Without it, a row reading 2 | 5 could mean 25 years, or 2.5 degrees, or 2005 people.

Define cumulative frequency .

Cumulative frequency is the running total of the frequencies, built up class by class as you work through the data in order. It can never decrease, so the final cumulative frequency is the total number of values.

True or False? The depth of the box on a box and whisker plot shows how many values lie inside it.

False. The box can be drawn to any depth, because only the horizontal positions of the lines carry any information. Whatever depth it is drawn to, the box always covers the middle 50% of the data.

On a back to back stem and leaf diagram, how do you read the leaves on the left-hand side?

Read them outwards from the stem , so the leaf nearest the stem is the smallest value on that row. The two sides show two different sets of data for the same variable, so the key has to be read carefully.

Where does a whisker end on a box plot when the data set contains an outlier?

The whisker stops at the last value that is not an outlier, rather than stretching out to the extreme value. The outlier itself is marked beyond the end of the whisker with a cross .

True or False? A stem and leaf diagram shows the shape of the distribution as well as the individual data values.

True. Every value is written out in full as a stem and a leaf, so nothing is lost, and the length of each row shows where the data is concentrated. That makes it both an ordered list of the data and a picture of its distribution.

A cumulative frequency graph covers 200 values. How do you estimate how many of them are greater than 50?

Read up from 50 on the horizontal axis to the curve, then across to the vertical axis, which gives the number that are less than or equal to 50. Subtract that result from 200, because the graph only ever counts upwards from the smallest value.

Why are two box plots drawn against the same axis when two data sets are being compared?

Sharing one axis puts both sets on the same scale , so their medians and their spreads can be compared directly by eye. A box plot needs only one axis, which must carry an even scale and be labelled with its units.

On a stem and leaf diagram with stems of tens, the median is the leaf 6 on the row with stem 2. What is the median value?

The median is 26 , because a data value is made from its stem and its leaf together. Quoting the leaf on its own, as 6, gives only the last digit of the value.

A histogram question asks how many values lie in part of a class interval. How do you estimate that?

Work out the area of just the part of the bar that covers the range you want. That area is then converted into a frequency in the same way as the area of a whole bar is.

How can a cumulative frequency graph be used to draw a box plot?

Read the median and both quartiles off the curve, which supplies three of the five values a box plot needs. That is how a box plot is produced for grouped data, where the individual values are not known.

Where are the largest and smallest values on a stem and leaf diagram?

The largest value is the leaf furthest from the stem on the final row , and the smallest is the leaf closest to the stem on the first row . Subtracting the smaller from the larger gives the range of the data.

Level 3MathsAQAMathematical Studies (Core Maths)Paper 1: Data, Finance, Estimation & ModellingFlashcardsAnalysis of DataRepresenting Data Diagrammatically

Representing Data Diagrammatically (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Flashcards

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Cards in this collection (19)

Define histogram.
A histogram displays the frequency distribution of continuous quantitative data, with no gaps between the bars.
Unlike a bar chart, its class intervals may be unequal and its vertical axis shows frequency density rather than frequency.
On a cumulative frequency graph, which value of each class is plotted horizontally?
The upper boundary of each class is plotted, because everything up to and including that value has been counted.
The points are then joined by hand with a smooth increasing curve.
True or False?
On a histogram, the height of a bar tells you the frequency of that class.
False.
The height is the frequency density, and it is the area of the bar that is proportional to the frequency.
In most questions that area is equal to the frequency directly.
Complete the description of what a box and whisker plot displays.
A box plot shows the minimum, the $______$ quartile, the $______$ quartile and the maximum, as well as the $______$ that lies between the quartiles.
The completed description is:
A box plot shows the minimum, the lower quartile, the upper quartile and the maximum, as well as the median that lies between the quartiles.
Any outliers are marked separately as crosses, and no other individual data values appear on the plot.
Why must a stem and leaf diagram always have a key?
The key shows how a stem and a leaf are combined into a data value, and it gives the units.
Without it, a row reading 2 | 5 could mean 25 years, or 2.5 degrees, or 2005 people.
Complete the formula for the quantity plotted on the vertical axis of a histogram.
$frequency density = \frac{______}{______}$
The completed formula is:
$frequency density = \frac{frequency}{class width}$
Dividing by the class width is what allows classes of unequal width to be compared fairly on the same diagram.
Define cumulative frequency.
Cumulative frequency is the running total of the frequencies, built up class by class as you work through the data in order.
It can never decrease, so the final cumulative frequency is the total number of values.
True or False?
The depth of the box on a box and whisker plot shows how many values lie inside it.
False.
The box can be drawn to any depth, because only the horizontal positions of the lines carry any information.
Whatever depth it is drawn to, the box always covers the middle 50% of the data.
How do you estimate the median, a quartile or a percentile from a cumulative frequency graph?
Draw a horizontal line from the right height on the vertical axis across to the curve, then a vertical line down to the horizontal axis and read off the value.
With $n$ values in total, the height is $\frac{n}{2}$ for the median, $\frac{n}{4}$ for the lower quartile and $\frac{3 n}{4}$ for the upper quartile.
For the $p$ th percentile the height is $p$ per cent of the total frequency.
On a back to back stem and leaf diagram, how do you read the leaves on the left-hand side?
Read them outwards from the stem, so the leaf nearest the stem is the smallest value on that row.
The two sides show two different sets of data for the same variable, so the key has to be read carefully.
Where does a whisker end on a box plot when the data set contains an outlier?
The whisker stops at the last value that is not an outlier, rather than stretching out to the extreme value.
The outlier itself is marked beyond the end of the whisker with a cross.
True or False?
A stem and leaf diagram shows the shape of the distribution as well as the individual data values.
True.
Every value is written out in full as a stem and a leaf, so nothing is lost, and the length of each row shows where the data is concentrated.
That makes it both an ordered list of the data and a picture of its distribution.
A cumulative frequency graph covers 200 values. How do you estimate how many of them are greater than 50?
Read up from 50 on the horizontal axis to the curve, then across to the vertical axis, which gives the number that are less than or equal to 50.
Subtract that result from 200, because the graph only ever counts upwards from the smallest value.
Why are two box plots drawn against the same axis when two data sets are being compared?
Sharing one axis puts both sets on the same scale, so their medians and their spreads can be compared directly by eye.
A box plot needs only one axis, which must carry an even scale and be labelled with its units.
On a stem and leaf diagram with stems of tens, the median is the leaf 6 on the row with stem 2. What is the median value?
The median is 26, because a data value is made from its stem and its leaf together.
Quoting the leaf on its own, as 6, gives only the last digit of the value.
A histogram question asks how many values lie in part of a class interval. How do you estimate that?
Work out the area of just the part of the bar that covers the range you want.
That area is then converted into a frequency in the same way as the area of a whole bar is.
On a histogram, when is the frequency not simply equal to the area of a bar?
The frequency is not equal to the area whenever it is only proportional to it, so that $frequency = k \times area$ for some constant $k$ .
The value of $k$ then has to be worked out from other information given in the question.
How can a cumulative frequency graph be used to draw a box plot?
Read the median and both quartiles off the curve, which supplies three of the five values a box plot needs.
That is how a box plot is produced for grouped data, where the individual values are not known.
Where are the largest and smallest values on a stem and leaf diagram?
The largest value is the leaf furthest from the stem on the final row, and the smallest is the leaf closest to the stem on the first row.
Subtracting the smaller from the larger gives the range of the data.

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