Question

Find the mean, median, mode and range for the following data set. 1, 3, 5, 9, 8, 5, 8, 6 Mean: Median: Mode: Range:

Answer 1

mean=

5.625

median=5.5

mode=5and8

Explanation:

mean=1+3+5+5+6+8+8+9/8

45/8

5.625

median=1,3,5,5,6,8,8,9

5+6/2

11/2

5.5

mode=

5and8

1. range=9-1=8

Answer 2

`\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}`

Find the mean, median, mode and range for the following data set. 1, 3, 5, 9, 8, 5, 8, 6

`\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and How to solve:-}}}`

In order to find the mean of a data set, we add all the numbers in the data set and add them, then we divide by how many there are:-

• 1+3+5+9+8+5+8+6

`\bigstar` On simplification,

• 18+8+5+8+6
• 45

`\bigstar` Now, divide by 8, because there are 8 numbers in the data set:-

`\bold{(45)/(8)\:;written\:as\:decimal\Longrightarrow5,625}}}`

We've found the mean, but we also need to find the median, mode, and range!

The median is the number in the middle, but we should first arrange the data from least to greatest:-

1, 3, 5, 5, 6, 8, 8, 9

Now pick the number in the middle, which is:-

5,6. There are 2 numbers in the middle!

So what we do is we find the mean of the two numbers in the middle:-

5+6=11

11/2
`\Longleftarrow` median

Now, we don't need to find the mean anymore - the mode and range don't require the mean.

The median requires the mean only when there's an even amount of numbers in the data set.

The mode of a dataset is the number we see the most.

Here we see the number 1 once, the number 3 once, the number 5 appears twice, 6 appears one time only, 8 appears twice and, last but not least, 9 appears once.

So this data set has two modes - 5 and 8.

In order to find the range, we take the smallest number (1) and subtract it from the largest number (9), which results in

8 (range)

Good luck with your studies.

`\rule{300}{1}`