Question

Find the mean,median, mode, and range for the following data: 6, 4, 5, 8, 3,7,1,4

Answer 1

Given: Following data- 6, 4, 5, 8, 3, 7, 1, 4

Required: To determine the mean, median, mode, and range.

Step-by-step 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,

`\begin{gathered} Mean=(6+4+5+8+3+7+1+4)/(8) \\ =(38)/(8) \\ =4.75 \end{gathered}`

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-

`1,3,4,4,5,6,7,8`

The two middle terms are 4 and 5.

Hence, the Median is

`\begin{gathered} Median=(4+5)/(2) \\ =(9)/(2) \\ =4.5 \end{gathered}`

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,

`Mode=4`

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,

`\begin{gathered} Range=8-1 \\ =7 \end{gathered}`

Final Answer:

Mean=4.75

Median=4.5

Mode=4

Range=7