Answer :
Given: Following data- 6, 4, 5, 8, 3, 7, 1, 4
Required: To determine the mean, median, mode, and range.
Explanation: The mean of the data is calculated by taking the sum of the observations and dividing it by the total no of observations.
Hence,
[tex]\begin{gathered} Mean=\frac{6+4+5+8+3+7+1+4}{8} \\ =\frac{38}{8} \\ =4.75 \end{gathered}[/tex]The Median for an even number of observations is the mean of the (n/2)th term and (n/2+1)th term when the data is arranged in ascending or descending form.
The given data in ascending form is-
[tex]1,3,4,4,5,6,7,8[/tex]The two middle terms are 4 and 5.
Hence, the Median is
[tex]\begin{gathered} Median=\frac{4+5}{2} \\ =\frac{9}{2} \\ =4.5 \end{gathered}[/tex]The observation repeating a maximum number of times is called the Mode of the data.
Here observation 4 repeats twice, and every other observation only occurs once.
Hence,
[tex]Mode=4[/tex]The range is the spread of data. It is calculated by taking the difference between the maximum and minimum values of the data.
Here the maximum value is 8 and the minimum value is 1.
Hence,
[tex]\begin{gathered} Range=8-1 \\ =7 \end{gathered}[/tex]Final Answer:
Mean=4.75
Median=4.5
Mode=4
Range=7
