Locating Median and Quartiles from Ogive The ogive, also known as the box plot, is a graphical representation of quantitative data that helps visualize cent...
Locating Median and Quartiles from Ogive
The ogive, also known as the box plot, is a graphical representation of quantitative data that helps visualize central tendency and dispersion. It consists of three lines: the median, first quartile (Q1), and third quartile (Q3).
Median:
The median is the middle value in the data set when arranged in order from smallest to largest.
For an odd number of values, the median is the average of the two middle values.
For an even number of values, the median is the average of the two middle values.
First Quartile (Q1):
The first quartile is the value that is 25% lower than the median.
It corresponds to the point at which 25% of the data is below.
For an odd number of values, Q1 is the middle value.
For an even number of values, Q1 is the average of the two middle values.
Third Quartile (Q3):
The third quartile is the value that is 75% lower than the median.
It corresponds to the point at which 75% of the data is below.
For an odd number of values, Q3 is the middle value.
For an even number of values, Q3 is the average of the two middle values.
Example:
Consider the following set of data: 10, 15, 20, 25, 30, 35.
The median is 25, since there are an even number of values.
The first quartile (Q1) is 15, since 25% of the data is below 15.
The third quartile (Q3) is 30, since 75% of the data is below 30.
Summary:
The median is the middle value in the data set.
The first quartile (Q1) is the 25% mark below the median.
The third quartile (Q3) is the 75% mark below the median