Today we are taking a look at Frequency and Two-way tables. Frequency tables are created from raw data that have categorised, tallied and then totalled. We can use frequency tables to calculate relative frequencies which can be useful to describe proportions. If the sample is large enough, it can enable us to interpret them as probabilities. Two-way tables provide information about the frequency of two variables and the key to solving problems of this type is to pay attention to the totals column. This will enable you to complete a two-way table accurately and then use the information to calculate probabilities based on the data within the table.
On day 23, our focus is on Histograms which is a special 'Bar' chart for grouped data and will often have different widths. Beware the trap that the y axis is NOT frequency but should be labelled frequency density. The formula for calculating frequency density is covered in this snapshot and you may need to create extra columns in order to calculate this.
By rearranging the formula, you can calculate the frequency of each bar by multiplying frequency density by the bar width. This will help to fill in an incomplete data table.
On day 21 we move on and have a look at Cumulative frequency tables and graphs. This is essentially a running total where we add up the frequencies as we go along. It is important to check to see if your final value of the cumulative frequency matches the total frequency (normally given in the question).
When constructing a cumulative frequency graph, it is important to plot each point at the end of each group and join the points up with a nice smooth curve ('s' shaped). The graph is used to estimate numbers above and below certain values.
The focus for today's snapshot is Representing data. Once data has been collected, diagrams are used to represent the data so that it is easier to extract the key points from the data without having to look at all the numbers etc. The most common diagrams that are used are Pie charts, Bar charts, Line graphs and Pictograms. It is important that you follow the rules regarding the construction of the diagrams.
On day 19 we extend our understanding of averages by looking at Grouped frequency tables. Here you will find that your data has been grouped into categories. It is important to note a change in the vocabulary for the questions. Because the data is grouped, you will be unable to use specific values as you don't know what they are hence you will be asked to find an estimate for the mean or an estimate for the median.
You will often have to create two extra columns, one for the midpoints of each group and one for your fx column.
On day 18, we focus on calculating averages from a simple frequency table. There will be times where you will need to create the fx column so that the total amount can be worked out. Remember the formula for the median shows you where the median is located.
It will be important to look and check your answers to see if they are reasonable answers and fit within the data set.