Statistical Diagrams Flashcards

All 36 cards in this deck

What is the purpose of the key on a stem and leaf diagram?

e.g. $2\mid 5$

It tells you how to read a stem and a leaf as a data value — here $2\mid 5$ means $25$.

What are the steps to draw an ordered stem and leaf diagram?

e.g. data $23, 31, 25$

1. Choose stems (tens digits): $2$ and $3$
2. Write the units as leaves in each row, in size order: $2\mid 3\ 5$ and $3\mid 1$
3. Add a key: $2\mid 3$ means $23$

True or false? In an ordered stem and leaf diagram the leaves in each row must be written in size order.

True. Each row is written smallest to largest, reading away from the stem.

True or false? A stem and leaf diagram loses the individual data values.

False. Every original value can be read back from the stems and leaves.

In a bar chart for categorical data, what must be true of the bars?

They must all be the same width, with equal gaps between them.

What is a dual bar chart used for?

Comparing two sets of data across the same categories, using side-by-side bars and a key.

In a composite (stacked) bar chart, how do you find the frequency of the top section of a bar?

Subtract the value where the section starts from the total height of the bar.

In a pictogram, what does half a symbol represent?

e.g. key: one circle $= 10$ people

Half the value in the key — here $5$ people.

What are the steps to draw a bar chart from a frequency table?

e.g. Red $4$, Blue $7$, Green $3$

1. Label the axes: categories along the bottom, frequency up the side
2. Choose a scale that fits the largest frequency: up to $7$
3. Draw equal-width bars with gaps, at heights $4$, $7$, $3$

What kind of data is a vertical line chart used for?

Ungrouped discrete numerical data, e.g. number of pets per household.

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

e.g. frequency $5$ out of a total of $40$

$\frac{\text{frequency}}{\text{total}}\times 360^\circ$; here $\frac{5}{40}\times 360^\circ = 45^\circ$.

How do you find the frequency represented by a sector of a pie chart?

e.g. a $90^\circ$ sector when the total is $60$ people

$\frac{\text{angle}}{360}\times \text{total}$; here $\frac{90}{360}\times 60 = 15$ people.

What are the steps to draw a pie chart from a frequency table?

e.g. Bus $5$, Walk $15$

1. Find the total frequency: $5 + 15 = 20$
2. Angles $= \frac{\text{frequency}}{\text{total}}\times 360^\circ$: $90^\circ$ and $270^\circ$
3. Draw a circle and measure the angles with a protractor, then label each sector

What do the angles of all the sectors in a pie chart add up to?

$360^\circ$.

True or false? If the 'walk' sector is larger in school A's pie chart than in school B's, then more pupils walk at school A.

False. Sectors show proportions, so you need both totals before comparing frequencies.

What do you plot for each class when drawing a frequency polygon?

The midpoint of the class against its frequency.

How do you find the midpoint of a class interval?

e.g. $10 < s \leq 20$

Add the two class boundaries and halve: $\frac{10+20}{2} = 15$.

What are the steps to draw a frequency polygon from a grouped frequency table?

e.g. $0<s\leq 10$: $14$, $10<s\leq 20$: $18$

1. Find each class midpoint: $5$, $15$
2. Plot midpoint against frequency: $(5,14)$, $(15,18)$
3. Join consecutive points with straight line segments

How should the plotted points on a frequency polygon be joined?

With straight line segments, not a smooth curve.

True or false? The first and last points of a frequency polygon should be joined up to close the shape.

False. The line stops at the last plotted point; it is not closed.

What type of data is a frequency polygon suitable for?

Grouped data, usually continuous, given in class intervals.

What is a time series graph?

A line graph of values recorded at successive points in time, with the plotted points joined by straight lines.

On a time series graph, which variable goes on the horizontal axis?

Time.

What does the trend of a time series mean?

The general direction the values move in over time (upward, downward or steady), ignoring short-term ups and downs.

What are seasonal variations in a time series?

A pattern of ups and downs that repeats at regular time intervals, e.g. every winter.

True or false? Continuing a time series graph beyond the last plotted point gives a reliable prediction.

False. It assumes the trend continues, so predictions become less reliable the further ahead you go.

What is a two-way table?

A table showing frequencies for two different categories at the same time, usually with row and column totals.

How do you work out the percentage of the total in one row of a frequency table?

e.g. frequency $2$ out of $40$ students

$\frac{\text{frequency}}{\text{total}}\times 100$; here $\frac{2}{40}\times 100 = 5\%$.

In a two-way table, what must the row totals and the column totals each add up to?

The grand total in the bottom-right cell.

Name two features that can make a statistical diagram misleading.

A vertical axis that does not start at zero or has an uneven scale; missing labels, scale or key.

True or false? Starting the vertical axis of a bar chart at a value other than zero can exaggerate the differences between the bars.

True. The bar heights no longer compare fairly.

True or false? Exact frequencies can be read from a pictogram that has no key.

False. Without a key you do not know what one symbol represents.

Which statistical diagram should you use for data recorded over a period of time?

A time series graph (line graph), with time on the horizontal axis.

Which diagram is most appropriate for showing what proportion of a whole each category makes up?

A pie chart.

When comparing two data sets shown in statistical diagrams, what two things should your comparison mention?

An average (e.g. median or modal class) and the spread — with at least one comparison in context.

True or false? A dual bar chart is better than two separate pie charts for comparing the actual frequencies of two data sets.

True. Pie charts only show proportions, so frequencies cannot be compared without the totals.