1A TYPES OF DATA
Name the type of categorical data where values have no inherent order.
Nominal.
What does the height of a bar represent in a bar chart of categorical data?
The frequency (or count) of that category.
What does each dot represent in a dot plot?
One individual data value (or one observation).
On a log scale, does each step represent equal increases or equal multiplication?
Equal multiplication (e.g., ×10 each step).
What does Q1 represent?
The value that separates the lowest 25% of the data from the rest (the first quartile).
Is “temperature in °C” discrete or continuous data, and why?
Continuous — because it can take any value within a range.
In a pie chart showing the favourite sport of students, what does the size of each slice represent?
The proportion or percentage of students selecting that category.
A stem-and-leaf plot has the stem “3” and leaves “2 4 7.” What three data values are represented?
32, 34, 37.
Why are log scales often used to display very large ranges of data?
They allow large values to be displayed in a compact and readable way.
A boxplot has a long whisker on the left side.
What does this suggest about the distribution?
The data is left-skewed (negatively skewed).
A set of data records the number of cars passing a point each minute. Explain why this is numerical data, and also identify whether it is discrete or continuous.
Numerical, because the data are counts of a measurable amount.
Discrete, because the number of cars must be whole numbers.
A bar chart shows three sports played at lunchtime: Soccer, Basketball, and Netball. Soccer has the tallest bar. What conclusion can you make?
Soccer is the most popular lunchtime sport of the three.
What is the key difference between a histogram and a bar chart?
A histogram displays numerical data in continuous intervals with touching bars. A bar chart displays categorical data with bars separated.
You are looking at a logarithmic axis where ticks are labelled: 1, 10, 100, 1000. What pattern do these numbers follow?
Each value is 10 times the previous one (powers of 10).
A dataset has: min = 12, Q1 = 16, median = 19, Q3 = 25, max = 30. Calculate the IQR.
25 − 16 = 9.
A data set records ATAR bands as:
<60, 60–69, 70–79, 80–89, 90+
Categorical ordinal data.
Even though the values relate to numbers, the data are grouped into ordered categories rather than individual measured numbers, so calculations like mean cannot be performed directly.
Explain one advantage and one limitation of using a pie chart to display categorical data.
Advantage: Shows proportions of categories clearly as parts of a whole.
Limitation: Hard to compare categories accurately, especially when slices are similar in size.
A dot plot has most data values clustered to the left with a long tail to the right.
What is the shape of this distribution, and what does that mean?
Right-skewed (positively skewed).
Most values are low, with a few unusually high values.
When the vertical axis of a graph is logarithmic, what does a straight line on the graph tell you about the data?
The data is increasing (or decreasing) at a constant percentage rate — exponential growth or decay appears as a straight line on a log scale.
Explain how to identify an outlier using the 1.5 × IQR rule.
Calculate IQR
Multiply IQR by 1.5
Any data point below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier.