Quartiles & Percentiles
Quartiles and percentiles are measures used to understand the position of data within a data set. Key points to remember:
- Quartiles divide the data into four equal parts, while percentiles divide the data into one hundred equal parts.
- The horizontal axis represents the data values or measurements.
- The vertical axis represents the frequency, or the number of data points.
Related Lessons:
How Cumulative Freq Graph Is Plotted
In this video, we will learn how to plot a cumulative frequency graph from a table of data. When drawing the graph, keep these key points in mind:
- Arrange the data values in ascending order.
- Create a new column called cumulative frequency by adding up the frequencies step by step.
- Label the horizontal axis with the data values.
- Label the vertical axis with the cumulative frequency.
- Plot each cumulative frequency against its corresponding value.
- Join the points with a smooth curve.
Mean & IQR & Stem-&-Leaf Diagram
In this video, we will learn how to use a cumulative frequency graph to find the median and interquartile range (IQR) & how the stem-and-leaf diagram is derived. Keep these key points in mind:
- Divide the cumulative frequency scale on the vertical axis into four equal parts: 25%, 50%, 75%, and 100%.
- The value at 50% gives the median.
- The values at 25% and 75% give the lower quartile and upper quartile. The interquartile range (IQR) is found by subtracting the lower quartile from the upper quartile.
- The range is the difference of the maximum and minimum value
- Always read the corresponding values from the horizontal axis when finding the median and IQR.
Reading Values In Cumulative Freq Graph
When reading values from a cumulative frequency graph, remember that it is always a less than graph:
- If the question asks for the number of values less than a given value, you can read the answer directly from the graph.
- If the question asks for the number of values more than a given value, first find the cumulative frequency up to that value, then subtract it from the total frequency.
This is because a cumulative frequency graph shows the total number of data points that are less than or equal to each value.
Example 1 - Continuous Data
- Use the graph to find (i) the median mark (ii) the upper quartile (iii) the interquartile range (iv) the 35th percentile mark.
- Given that 72% of the students passed the paper, use the graph to find the pass mark.
- The box and whisker diagram below illustrates the marks obtained when the same 300 students took an English Examination. The total mark for the English Paper is 60. Cindy said the English Paper was easier than the Mathematics Paper. Do you agree with Cindy? State your reason.
Example 2 - Discrete Data
The marks scored by 10 students in a Math test are shown below.
44 , 28 , 32 , 83 , 45 , 55 , 54 , 58 , 60 , 84
Find the
- range
- median
- upper and lower quartiles