Sets of data which have two modes are known as bimodal data.

The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values.

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

The mode is the most frequent value in a dataset.

Changing a data point

Maths

Checking understanding of the mean

Calculating the mean

Understanding the median

Calculating the median

Understanding the mode

Calculating the mode

Understanding and calculating the range

Summarising data

Evaluating the range

Comparing statistical representations

Comparing summaries of data

Analysing different statistical representations

Correlation

Statistical problems - data collection

Statistical problems - statistical summaries

Statistical problems - data presentations

Statistical problems - drawing conclusions

Problem solving with numerical summaries of data

In this unit, pupils consider the mean, median and mode and evaluate their usefulness in a variety of contexts. In the sampling unit, pupils are given the opportunity to consider where the data came from and how it was collected and can therefore start to evaluate how good a representation the sample is of the whole population.

In this unit, pupils learnt how to calculate the mean and began to use the mean to make comparisons between two sets of data. Pupils also considered whether the mean was an appropriate way of representing the data 

In this unit pupils explore the concept of measures of central tendancy, developing understanding of different types of average and their relative benefits and drawbacks. We then investigate other summaries of data such as the range and data comparison techniques.

Numerical summaries of data

One data point on this dot plot was incorrectly typed in. After the data point is modified and corrected, Andeep notices the mode has changed. Which of these statements must be true?

The mean of this dot plot is currently 15.75. A new data point is collected and added to the data set. Laura re-calculates the mean and notices it has decreased. What could the new data point be?

The mean of this dot plot is 15.75. A data point is no longer relevant and removed from the data set. Sam re-calculates the mean and notices it has decreased. What could the new data point be?

The mode of the data set may stay the same.

The mode of the data set may change to a different value.

A data point is removed from this dataset, as it is no longer relevant to an investigation. Which of the following are possible outcomes after the data point is removed?

Match each possible change to the data set to the correct description of its impact on the median.

Match each possible change to the data set to the correct description of its impact on the mean.

The most frequent value when the data are put into numerical order.

The distance on a number line between the smallest and largest data point.

The sum of values divided by the number of values in a data set.

The middle piece of data when the data are put into numerical order.

Which of these statements defines the median?

Match the summary statistic to its value.

The mode does not appear to be the most representative summary.

Because the mode is not representative, it is not a useful summary.

Even though the mode isn't representative, this information can still be useful.

Which of these statements is true for this dot plot?

The mean is representative because many data points share the same value.

The mean isn't very representative because not many data point are close to it.

The mean isn't very representative because the range is bigger.

First calculate the mean for this dot plot, then select the correct statements.

The median is close to the two peaks of high frequency values in the data set.

The median is in the dip of low or no frequency values in the data set.

Without carrying out any calculations select which of these statements are likely to be true for this dot plot.

Changing a data point

Lesson outcome