Measures of dispersion describe how values in a set of data are scattered or spread out. When data values are clustered closely together, the dispersion is small, whereas values that are widely spread have a large dispersion.
See how data distribution, spread and comparison between two groups are structured and read on both plots.
A stem-and-leaf plot splits each value into a stem and a leaf. Leaves are arranged in ascending order and a key must be included.
Key: \(2 \mid 7\) means \(27\) marks.
A dot plot uses one dot for every observation on a uniform scale. A wider spread of dots indicates greater dispersion.
Dots concentrated towards the right indicate generally higher values.
Dispersion gives an idea of how the values of a set of data are scattered. Dispersion is small if the data set has a small range, and large if it has a large range.
Measures of dispersion include quantitative measures such as range, interquartile range, variance and standard deviation.
A large difference indicates that data is widely dispersed, while a small difference indicates that data is closely concentrated.
The scale used in data representations must be uniform and must start from 0 to avoid confusion. The data displayed must be accurate.
Read the question, answer it in your mind, then press “Check Answer”.
Boiling points of four chemicals are \(60^\circ\text{C}\), \(75^\circ\text{C}\), \(150^\circ\text{C}\), and \(45^\circ\text{C}\). What is the difference between the highest and lowest boiling points?
In a stem-and-leaf plot, what does the key \(4 \mid 2\) represent if the stem represents tens and the leaf represents units?
When comparing two dot plots of test scores, how do you determine which group achieved better results?
A data set with a higher maximum value always has a wider dispersion.
Dispersion depends on the difference between the largest and smallest values (the spread), not solely on the maximum value.
On the left side of a back-to-back stem-and-leaf plot, leaves are read left-to-right.
Leaves on both sides are ordered starting from the stem outwards, meaning left-side leaves increase from right to left.
Complete all parts first, then press the check answer button.
1 Which of the following indicates that a set of data has a small dispersion?
2 In a dot plot, what does each plotted dot represent?
3 In a stem-and-leaf plot, leaf digits must be arranged in order from the smallest value to the ______ value.
4 To understand the dispersion of a data set, we calculate the difference between the largest value and the ______ value.
Drag each term to the correct description. On a phone, tap the answer choice first, then tap the description box.
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