Cumulative frequency (Higher Tier)

Cumulative frequency (Higher Tier)

Cumulative Frequency

  • Cumulative frequency is defined as the running total of frequencies. It shows the accumulation of data as the variable increases.

  • Cumulative frequencies are often used to create cumulative frequency graphs which can help us understand the distribution of data.

  • In cumulative frequency tables, each frequency is added to the sum of the frequencies of all the data values before it in the data set.

  • Cumulative frequencies are useful for determining the number of observations that lie above (or below) a particular value in a data set.

Cumulative Frequency Graphs

  • A cumulative frequency graph (or ogive) is a curve graph used to determine the number of observations within a given interval.

  • Cumulative frequency graphs are drawn by plotting the upper class boundary on the x-axis against the cumulative frequency on the y-axis.

  • The points in a cumulative frequency graph are joined by a line and never by bars.

  • Cumulative frequency graphs can help us easily identify the median, quartiles and interquartile range of a dataset.

Median and Quartiles

  • The median is the middle value of a data set. It is found by drawing a line at 50% height on the cumulative frequency graph and reading the corresponding value on the x-axis.

  • The lower quartile (Q1) is the value below which 25% of the data fall. It is represented by the 25% mark on the vertical axis.

  • The upper quartile (Q3) is the value below which 75% of the data fall. It is represented by the 75% mark on the vertical axis.

  • The interquartile range (IQR) is the range within which the middle 50% of a data set lies. It is calculated by subtracting the value of the lower quartile from the value of the upper quartile.

Box-and-Whisker Plots

  • A box-and-whisker plot (or box plot) is a way of summarizing a data set graphically based on its quartiles.

  • A box-and-whisker plot is constructed from five values: the minimum, the lower quartile (Q1), the median (Q2), the upper quartile (Q3), and the maximum.

  • Box-and-whisker plots can be used to easily visualize the spread and skewness of a data set, as well as to spot any outliers.

Remember, understanding cumulative frequency and how to construct and interpret cumulative frequency graphs, quartiles and box-and-whisker plots is key to making sense of statistical data. However, always be aware of the limitations of these methods and that outliers or missing data can affect your results.