Question

1)Given the following data set, find the mean, median, mode, and midrange.5, 6, 7, 7, 7, 8, 9, 10

Answer 1

Given:

`5,\text{ 6, 7, 7, 7, 8, 9 , 10}`

mean of the dataset

The mean is the average of the dataset and can be found using the formula:

`mean\text{ = }\frac{Sum\text{ of the numbers}}{Total\text{ number of numbers}}`

Substituting the given values:

`\begin{gathered} mean\text{ = }\frac{5\text{ + 6 + 7 + 7 + 7 +8 + 9 + 10}}{8} \\ =\text{ }(59)/(8) \\ =7.375 \end{gathered}`

Answer:

Mean = 7.375

Median of the dataset

The median is the value that lies at the center.

First, we arrange the data in ascending order

5, 6, 7, 7, 7, 8, 9, 10

Next, we find the value at the center

`\begin{gathered} Median\text{ = }(7+7)/(2) \\ =(14)/(2) \\ =\text{ 7} \end{gathered}`

Answer:

Median =

Mode of the dataset

The mode is the value with the highest frequency

Mode = 7

Mid-range of the dataset

The mid-range can be calculated using the formula:

`Mid-range\text{ = }\frac{Max(x)\text{ + Min\lparen x\rparen}}{2}`

Substituting the given values:

`\begin{gathered} Mid-range\text{ = }\frac{5\text{ + 10}}{2} \\ =\text{ }(15)/(2) \\ =\text{ 7.5} \end{gathered}`