Question

Tutorial: Mean, Median, Mode, Range, and Quartiles

Answer 1

\(\sf Mean~is~the~average.\)

You add all the numbers and divide by how many numbers there are.

\(\sf Median~is~the~middle~value. \)

You list the numbers in order of least to greatest, and find the middle value.

\(\sf Mode~is~the~number~that~is~repeated~the~most. \)

Find the number that's repeated the most.

\(\sf Range~is~the~difference~between~the~biggest~number~and~the~smallest~number. \)

Subtract the highest term from the smallest term.

\(\sf\Large\color{lime}{Examples:} \)

\(\sf Mean: \)

\(\sf 2, 5, 7, 10, 14, 15, 18 \)

Add all the terms:

\(\sf 2 + 5 + 7 + 10 + 14 + 15 + 18 = 71 \)

There are 7 numbers total.

Divide:

\(\sf 71 \div 7 = 10.14 \)

So the mean is approximately \(\sf 10.14. \)

\(\sf Median: \)

Median can be a little confusing. If you have an odd number of values, it's easy to spot the middle term:

\(\sf 1, 5, 6, 9, 11 \)

\(\sf \cancel 1, \cancel 5, 6, \cancel 9, \cancel {11} \)

The middle value is 6, so the median is 6.

However if you have an even number of values, it's a bit different:

\(\sf 2, 3, 5, 6, 7, 9 \)

\(\sf \cancel 2, \cancel 3, 5, 6, \cancel 7, \cancel 9 \)

There seems to be 2 middle numbers.

You have to find the mean of these two numbers to find the real median.

\(\sf 5 + 6 = 11 11 \div 2 = 5.5 \)

So the median is \(\sf 5.5\).

\(\sf Mode: \)

\(\sf 5, 5, 6, 6, 6, 9, 9, 10, 14, 15 \)

Here, you can see that 6 is repeated the most, so 6 is the Mode.

There can also be two modes.

If you didn't have those 6's in your values:

\(\sf 5, 5, 9, 9, 10, 14, 15 \)

Then the mode would be 5 AND 9, because they’re both repeated the same number of times, and they’re both repeated the most than any other term.

\(\sf Range: \)

\(\sf 6, 9, 11, 16, 21, 23, 27 \)

Locate the biggest and the smallest numbers:

\(\sf\color{red}6, 9, 11, 16, 21, 23, \color{red}{27} \)

Subtract them:

\(\sf 27 – 6 = 21 \)

So the Range here will be 21.

\(\sf\Large Quartiles :\)

Quartiles are usually associated with box and whisker plots. Similarly to the Mean, Median, Mode, and Range, they are another way we use to represent data sets.

\(\sf Q1:\)

The first Quartile is the middle value of the data from the beginning to the middle of the entire data set.

\(\sf Q2:\)

The second Quartile is the same as the Median.

\(\sf Q3:\)

The third Quartile is the middle value of the data from middle to the end of the entire data set.

\(\sf IQR: \)

The Interquartile Range is the difference between the third and first Quartiles.

\(\sf\Large\color{lime}{Examples}\):

Odd set of numbers:

\(\sf 3, 3, 9, 6, 4, 8, 5\)

Rearrange the data from least to greatest:

\(\sf 3, 3, 4, 5, 6, 8, 9\)

\(\sf\color{red}{3, 3, 4,} \color{lime}{ 5,}\color{blue}{ 6, 8, 9}\)

\(\sf\color{lime}{Q2 = 5}\)

\(\sf\color{red}{\cancel 3, 3, \cancel 4,}\)

\(\sf\color{red}{Q1 = 3}\)

\(\sf\color{blue}{ \cancel 6, 8, \cancel 9}\)

\(\sf\color{blue}{Q3 = 8}\)

\(\sf\color{yellow}{IQR = Q3- Q1}\)

\(\sf\color{yellow}{IQR = 8- 3}\)

\(\sf\color{yellow}{IQR = 5}\)

Even set of numbers:

\(\sf 2, 9, 8, 4, 7, 5, 6, 8\)

Rearrange the data from least to greatest:

\(\sf 2, 4, 5, 6, 7, 8, 8, 9\)

\(\sf\color{red}{2, 4, 5, 6,} \color{blue}{7, 8, 8, 9}\)

\(\sf\color{lime}{Q2 = \dfrac{6+7}{2}}\)

\(\sf\color{lime}{Q2 = 6.5}\)

\(\sf\color{red}{\cancel 2, 4, 5, \cancel 6,}\)

\(\sf\color{red}{Q1 = \dfrac{4+5}{2}}\)

\(\sf\color{red}{Q1 = 4.5}\)

\(\sf\color{blue}{ \cancel 7, 8, 8, \cancel 9}\)

\(\sf\color{blue}{Q3 = \dfrac{8+8}{2}}\)

\(\sf\color{blue}{Q3 = 8}\)

\(\sf\color{yellow}{IQR = Q3 - Q1}\)

\(\sf\color{yellow}{IQR = 8- 4.5}\)

\(\sf\color{yellow}{IQR = 3.5}\)

Here’s an example of what the characteristics of a box and whisker plot represents:

https://www.mathsisfun.com/data/images/box-whisker-plot.gif

Answer 2

really nice tutorial

Answer 3

3rd grade? Jesus what kinda unadvanced school did you go to bob? It's kindergarten for me XD

Answer 4

This works for people like me. *o*

Answer 5

Nice done greenie ;)

Answer 6

Nicely done !!

Answer 7

nice

Answer 8

Great job ^^