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# Presenting Data (Higher Level): Cumulative Frequency Graphs, Boxplots, and Histograms - GCSE Maths

Watch this video to learn the key concepts of presenting data (higher level) in the context of the statistics and probability topic of GCSE Maths.

In the video below our GCSE Maths tutor explains how to create a cumulative frequency graph, estimate median and quartiles, and create box plots and histograms for data with variable class intervals.

Watch step-by-step instructions on how to calculate the cumulative frequency, plot the graph, and estimate median and quartiles. The video then shows how to use the cumulative frequency graph to create box plots, and how to compare two sets of data using box plots.

Finally, the video explains how histograms are used to represent data with variable class intervals, and how to calculate frequency density.

Key learning outcomes for this video:

1. To be able to calculate cumulative frequency and draw a cumulative frequency graph.

2. To be able to estimate the median and quartiles from a cumulative frequency graph and calculate the interquartile range.

3. To be able to draw and interpret a boxplot from a set of data.

4. To be able to compare boxplots.

5. To be able to calculate frequency density to create a histogram.

When we talk about presenting data, we mean displaying information in a way that makes it easier to understand and interpret. This is important in statistics because it allows us to make sense of the information we have collected and draw meaningful conclusions from it.

One way we can present data is through the use of graphs. There are different types of graphs that we can use depending on the type of data we have.

## Cumulative Frequency Graphs

One type of graph that we use frequently in statistics is the cumulative frequency graph.A cumulative frequency graph shows the cumulative frequency of a set of data, which is the total frequency up to a certain point. To draw a cumulative frequency graph, we first need to calculate the cumulative frequency for each value in our data set. We can then plot these cumulative frequencies against the corresponding values on a graph. The resulting graph will show us how many values are less than or equal to a certain value.

From a cumulative frequency graph, we can estimate the median and quartiles, which are measures of central tendency and spread respectively. The median is the middle value of a set of data, and the quartiles divide the data into four equal parts. To estimate the median and quartiles from a cumulative frequency graph, we can read the values off the graph and use interpolation if necessary.

## BoxPlot Graphs

Another way we can present data is through the use of boxplots. A boxplot is a diagram that shows the distribution of a set of data by displaying the median, quartiles, and extreme values. To draw a boxplot, we first need to calculate the median and quartiles of our data set. We can then draw a box that spans from the lower to upper quartile, with a line at the median. We also draw "whiskers" from the box to the minimum and maximum values of the data set. Boxplots are useful for comparing the distribution of different data sets.

## Histogram

Finally, we can create a histogram by calculating the frequency density of our data and plotting it on a graph. Frequency density is calculated by dividing the frequency of each interval by the width of the interval. Histograms are useful for showing the distribution of data and identifying any patterns or trends.

## Exam Application

In the GCSE maths exam, students at the higher level will be expected to demonstrate their understanding and application of the topics related to presenting data in the statistics and probability topic.

Here are some typical types of questions that may be asked in the assessment:

1. Cumulative frequency graphs: Students may be asked to interpret a given cumulative frequency graph by estimating the median, quartiles, and interquartile range, or by making comparisons between different data sets. They may also be asked to draw a cumulative frequency graph from a given set of data and use it to answer questions about the data set.

2. Boxplots: Students may be asked to draw a boxplot from a given set of data, or to interpret a given boxplot by identifying the median, quartiles, and outliers. They may also be asked to compare two or more boxplots and make inferences about the data sets.

3. Histograms: Students may be asked to draw a histogram from a given set of data, or to calculate the frequency density and use it to draw a histogram. They may also be asked to interpret a given histogram by identifying the shape, center, and spread of the data set.

4. Interpreting data: Students may be asked to interpret a given data set by calculating measures of central tendency (e.g. mean, median, mode) and measures of spread (e.g. range, interquartile range, standard deviation), or by making comparisons between different data sets. They may also be asked to draw conclusions from the data set and explain their reasoning.

5. Statistical analysis: Students may be asked to carry out a statistical analysis of a given data set, which could involve calculating measures of central tendency and spread, drawing graphs and diagrams to represent the data, and making inferences about the data set.

In addition to these types of questions, students may also be asked to solve problems or answer open-ended questions that require them to apply their knowledge of presenting data in the statistics and probability topic. These questions may involve real-life scenarios or data sets, and may require students to use their problem-solving and critical-thinking skills to arrive at a solution.