Statistical Diagrams Flashcards

All 32 cards in this deck

What is a tally chart used for?

Recording how often each category or value occurs as data is collected.

How is the fifth item recorded in a tally?

As a diagonal stroke across the previous four, making a group of five.

What are the steps to complete a frequency table from a list of raw data?
e.g. red, blue, red, red, blue

1. Go through the list once, putting a tally mark by each item: red $|||$, blue $||$
2. Count each row's tally marks to get the frequency: red 3, blue 2
3. Add the frequencies to check the total matches the amount of data: $3+2=5$

What does the total of the frequency column tell you?

The total number of items (observations) in the data set.

What is a two-way table?

A table showing two variables at once — one down the rows, one across the columns — usually with row, column and overall totals.

True or false? The classes in a grouped frequency table may overlap.

False.
Classes must not overlap, so every value fits in exactly one class.

What are the steps to draw a bar chart from a frequency table?
e.g. May 20, June 35

1. Choose an even scale on the vertical (frequency) axis: 0 to 40 in 5s
2. Draw a bar of equal width for each category at its frequency: May to 20, June to 35
3. Label both axes and leave gaps between the bars

What does the key on a pictogram tell you?

How many items each whole symbol represents.
e.g. one symbol represents 2 hours of sunshine

How do you show a frequency that is not a whole number of symbols on a pictogram?
e.g. show 11 where one symbol represents 4

Draw part of a symbol for the remainder.
2 full symbols and 3 quarter symbols

What is a dual bar chart?

A bar chart with two bars drawn side by side for each category, with a key saying what each colour stands for.

What is a composite (stacked) bar chart?

A bar chart where one bar per category is split into sections, so the whole bar shows the total.

What is a vertical line chart and what data is it used for?

A chart of single vertical lines instead of bars, used for ungrouped discrete numerical data.

True or false? On a bar chart for categorical data the bars should touch each other.

False.
The bars are equal width with gaps between them.

What is the formula for the angle of a sector in a pie chart?

$\text{angle} = \dfrac{\text{frequency}}{\text{total frequency}} \times 360^\circ$

What are the steps to draw an accurate pie chart from a frequency table?
e.g. Tea 50, Coffee 30, Hot chocolate 10

1. Add the frequencies to get the total: $50+30+10=90$
2. Work out each angle as $\frac{\text{frequency}}{\text{total}}\times 360^\circ$: $200^\circ$, $120^\circ$, $40^\circ$
3. Draw the sectors with a protractor and label each with its category: Tea, Coffee, Hot chocolate

What quick method gives the angle per item in a pie chart?
e.g. a total frequency of 60

Divide $360^\circ$ by the total frequency, then multiply by each frequency.
$360\div 60 = 6^\circ$ for each item

What must be shown on a finished pie chart to gain the labelling mark?

Each sector labelled with its category name from the table, not just the angle size.

How do you find what fraction of the data a sector of a pie chart represents?
e.g. a sector of $90^\circ$

$\dfrac{\text{sector angle}}{360}$, simplified.
$\frac{90}{360}=\frac14$

True or false? The angles in a pie chart must add up to $360^\circ$.

True.
The whole circle represents the whole data set.

What is a time series graph?

A line graph showing how a quantity changes over time, with time on the horizontal axis.

Which axis is used for time on a time series graph?

The horizontal axis.

How are the plotted points joined on a time series graph?

With straight line segments, in time order.

What does 'describe the trend' mean for a time series graph?

State the general direction of the values over time, e.g. the trend is upwards (increasing) or downwards (decreasing).

True or false? Values read from between two plotted points on a time series graph are only estimates.

True.
No data was collected between the points; the joining line is only a guide.

What makes a bar chart's vertical scale misleading?

A scale that does not start at 0, or that has unequal gaps — differences between bars look bigger than they are.

In 'write down one thing wrong with this bar chart', what kind of answer earns the mark?

A genuine error in the diagram, e.g. a bar drawn at the wrong height so it does not match the table, or a missing axis label/scale.

Can you compare the actual numbers in two pie charts drawn from different data sets?

Not unless you know the total frequency for each — pie charts show proportions only.

True or false? If a sector for French is bigger in one pie chart than in another, more people chose French in that group.

False.
The sector only shows a larger proportion; without both totals you cannot compare the actual numbers.

What extra information do you need to compare frequencies from two pie charts?

The total frequency each pie chart is based on.

Which diagram is appropriate for showing data collected over time?

A line graph (time series graph).

Which diagrams are appropriate for categorical data?

Bar charts, pictograms and pie charts.

What is a pie chart best for showing?

The proportion each category makes of the whole.