Minimum = 18, Q₁ = 27.5, median = 39.5, Q₃ = 43, maximum = 49.
The five-number summary is a descriptive statistic that provides information on a series of observations. It consists of the following statistics:
1. Minimum: the smallest observation
2. First quartile Q₁: the average of the values below the median.
3. Medium M: the average term.
4. third quartile Q₃: the average of values above the median.
5. Maximum: The largest observation.
The data represents the numbers of runs allowed by 8 college pitchers.
{18, 49, 38, 41, 33, 44, 42, 22}
The five-number summary is:
First, we have to sort the data from least to greatest.
{18, 22, 33, 38, 41, 42, 44, 49}
From the ordered data we can see that the minimum value is 18 and the maximum is 49.
The median is the middle term of the data set. In this case of an even number of terms, the median is the average of the terms located in the middle. So, the terms located in the middle if the data are in bold:
{18, 22, 33, 38, 41, 42, 44, 49}
Median= (38 + 41)/2 = 79/2 = 39.5
To calculate the first quartile Q₁, the values below the median are {18, 22, 33, 38}. So, the median of this values is the first quartile Q₁:
{18, 22, 33, 38}
Q₁ = (22 + 33)/2 = 55/2 = 27.5
To calculate the third quartile Q₃, the values above the median are {41, 42, 44, 49}. So, the median of this values is the third quartile Q₃:
{41, 42, 44, 49}
Q₃ = (42 + 44)/2 = 86/2 = 43
