Statistical Diagrams (Cambridge (CIE) IGCSE Maths)
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- FrontStem & Leaf Diagrams
True or False?
In a stem-and-leaf diagram, the stems are written horizontally and the leaves are written vertically (in order)
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True or False?
In a stem-and-leaf diagram, the stems are written horizontally and the leaves are written vertically (in order)
False.
In a stem-and-leaf diagram, the stems are written vertically and the leaves are written horizontally (in order).
How do you find the median value of a data set from a stem-and-leaf diagram?
To find the median value from a stem-and-leaf diagram, you can cross off a pair of values (one from each end, highest and lowest) at a time until the middle value is found.
True or False?
The highest value in a data set will be the first data item (leaf) in the last row (stem).
False.
The highest value in a data set will be the last data item (leaf) in the last row (stem).
In the stem-and-leaf diagram below, what would be an appropriate key?
Adult Height (cm)15
0 1 6 9
16
0 1 2 2 3 5 7 8 9
17
2 3 5 5 6
18
0 3
An appropriate key for the stem-and-leaf diagram would be to have two digits as the stem, representing the hundreds and tens columns, and a single digit as the leaf, representing the ones column.
E.g. Key: 15 | 0 represents 150 cm.
The image below shows what type of statistical diagram?
The diagram shown is a pictogram.
A pictogram is a visual representation of discrete data using repeated symbols or icons.
True or false?
Bar charts are used for continuous data.
False.
Bar charts are not used for continuous data.
Bar charts are used for discrete data.
How do you identify the mode from a bar chart?
To identify the mode from a bar chart, find the bar with the highest height or frequency.
What is a comparative bar chart?
A comparative bar chart is a bar chart that displays two or more data sets side by side for easy comparison.
True or false?
A key is optional when creating a pictogram.
False.
A key is not optional when creating a pictogram.
A pictogram requires a key that specifies the frequency represented by each symbol or icon.
True or false?
Bar charts should have gaps between the bars.
True.
Bar charts should have gaps between the bars.
True or false?
Pictogram symbols can be of different sizes.
False.
Pictogram symbols should be of the same size for easy comparison.
(Though a pictogram may use part of a symbol, to represent a frequency that is less than the value of the complete symbol.)
A pie chart is drawn for a set of data where the total frequency is 180.
What do you do to the frequency of each item to find its angle for the pie chart?
If a pie chart is drawn for a set of data where the total frequency is 180, you multiply the frequency of an item by 2 (i.e. 360 ÷ 180) to find the size of its angle on the pie chart.
In a pie chart, if you know that the angle 30° represents a frequency of 10, how would you find the total frequency?
In a pie chart, if an angle of 30° represents a frequency of 10, then you can find the total frequency by:
dividing 10 by 30 to find how much 1° represents,
then multiplying this by 360.
Alternatively, you can see how many times 30° goes into 360° and then multiply this by 10.
How do you calculate the angles needed for a pie chart?
To calculate the angles needed for a pie chart:
Divide each frequency by the total frequency.
Multiply each result by 360°.
Alternatively:
Divide 360° by the total frequency.
Multiply each frequency by this number.
If you are given the angles in a pie chart and the total frequency, how do you calculate the individual frequencies?
If you are given the angles in a pie chart and the total frequency, you can calculate the individual frequencies by doing the following:
Divide each angle by 360°.
Multiply by the total frequency.
Alternatively:
Divide the total frequency by 360.
Multiply each angle by this number.
What sorts of things should you look for when reading and interpreting statistical diagrams?
When reading and interpreting statistical diagrams, you should look for:
Keys
Shading
Axis labels
The word "frequency"
Any unusual or unexpected information mentioned
Define anomaly in the context of statistical diagrams.
An anomaly, otherwise known as an extreme value or outlier, is a data point that is significantly different from the rest of the data.
True or false?
You may be asked to comment on aspects of a statistical diagram that could be misleading or incorrect.
True.
You may be asked to comment on aspects of a statistical diagram that could be misleading or incorrect, such as uneven gaps in axis values or a missing key.
Define key in the context of statistical diagrams.
In the context of statistical diagrams, a key is a legend that explains the meaning of symbols, colours, or shading used in the diagram.
True or False?
The purpose of comparing statistical diagrams is to identify and comment on differences or similarities in averages, spread, and unusual data values for the data sets represented by the diagrams.
True.
The purpose of comparing statistical diagrams is to identify and comment on differences or similarities in averages, spread, and unusual data values for the data sets represented by the diagrams.
What should you consider when deciding which measures to compare in statistical diagrams?
When deciding which measures to compare in statistical diagrams, you should consider:
Whether the mean, median or mode is the appropriate average to use.
Whether the range or interquartile range is the appropriate measure of spread to use.
Whether any assumptions or potential issues with the data could affect the reliability of the results and comparisons.
True or false?
You should aim to make at least one pair of comments when comparing statistical diagrams.
False.
You should aim to make at least two pairs of comments when comparing statistical diagrams:
One pair should compare averages and comment on what this means in the context of the question.
The other pair should compare spread and comment on what this means in the context of the question.