A stem and leaf diagram is a systematic way to organise and represent numerical data, by splitting each value into a stem and a leaf.

The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.

The median is the central (middle) piece of data when the data are in numerical order.

Mode is the most frequent value. It is a measure of central tendency representing the average of the values.

The range is a measure of spread. It is found by finding the difference between the two extreme points; the lowest and highest values.

Calculating summary statistics from stem and leaf diagrams

Maths

Checking understanding of summary statistics from a list

Checking understanding of summary statistics from a frequency table

Calculating summary statistics from a grouped frequency table

Calculating the mean from a grouped frequency table

Constructing stem and leaf diagrams

Checking understanding of measures of central tendency

Comparing data sets in context

Checking understanding of bar charts and pictograms

Checking understanding composite and bar-line charts

Statistical summaries using technology

Checking understanding of pie charts

Comparing various representations of data sets

Problem solving with comparisons of numerical data

In this unit, pupils began to compare two different sets of data. In the future unit, pupils will consider cumulative frequency graphs and histograms and compare the data from these diagrams to other graphical representations.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils extend this learning to comparing two different data sets and comparing these measures of central tendency.

In this unit pupils will compare two different data sets and compare different measures of central tendancy when interpreting the data. Pupils will learn to interrogate frequency tables and stem and leaf diagrams both with and without technology.

Comparisons of numerical summaries of data

The modal group in this stem and leaf diagram is __________.

The range of the data shown on this stem and leaf diagram is {{ }} km.

The total of the first row of leaves is {{ }} kg.

Sam and Andeep draw a back-to-back stem and leaf diagram to compare their classes' scores in a quiz. Match the summary statistic for each class with its value.

Calculate the mean mass (to 2 decimal places) of the data represented in this stem and leaf diagram. The totals for each row have been calculated already.

A statistical summary sums up the features of a data set. It may contain an {{ }} which measures the central tendency. It may also contain the range which measures the spread.

This table represents the number of cars in 40 households. The mean number of cars per household is {{ }} cars.

Calculating summary statistics from stem and leaf diagrams

Lesson outcome