What is the Mean?

What is the Median?

What is the Mode?

What is Range?

What might central Tendency questions look like?

Student Explanation

Mean is the average. To get this number you must add the numbers and divide by the amount of numbers that you added.


For example: what is the mean of 14, 33,26,18?


First add the values
$14 + 33 + 26 + 18 = 91$

Then divide by 4 because there are 4 numbers in your data set
$\[91 \div 4 = 22.75\]$

Therefore most of the numbers are close to 22.75


















Mode is the value that appears the most in a data set.

For example:
Find the mode for the data set 36, 36,36,29, 14.

The mode is 36 because it appears the most.

You may have more than one mode if two or more number appear the same amount of times in a data set.
for example 14 and 12 are the modes of the following data set because they both appear three times:

14,14,14,11, 11, 12,12,12















Median is the middle value in a data set after the numbers are placed in order. If there are two number in the middle add them and divide by two.

For example: Find the median of the data set 14,14,14,11, 11, 12,12,12

First place them in order:
$11,11,12,12,12,14,14,14$

Then cross off numbers until you reach the center of the numbers

$\[\not 1\not 1,\not 1\not 1,\not 1\not 2,12,12,\not 1\not 4,\not 1\not 4,\not 1\not 4\]$

We can see that the median is 12 but just to show that adding and dividing by two works
$12 + 12 = 24$


$\[24 \div 2 = 12\]$

So the median is 12













Range is the value that you get after subtracting the highest and lowest numbers in a data set. This number is the difference of the highest and the lowest numbers.

In the previous data set you subtract the highest and lowest numbers
$\[14 - 11 = 3\]$

Therefore the range is 3.

How could central tendency questions look?

1. If you had the data set 92, 91, 93, 92, 99, which measure of central tendency and range would change the most if you added 90 to the data set?

A. Mean

B. Median

C. Mode
D. Range



In the above question find what the mean, median, mode, and range are without 90 then compare what they are with 90.

Without 90:
Mean - 93.4
Median-92
Mode-92
Range- 8

With 90:
Mean - 92.8
Median-92
Mode-92
Range- 9

The mean changed by 0.6, the median did not change, the mode did not change, and the range changed by 1. The range changed the most.

2. If the range is 34, the mean is 26, the mode is 55, and the median is 53, and the highest number is 58, what measure of central tendency or range could you use to find the value of the lowest number in the data set?

A. Mean

B. Median

C. Mode
D. Range

3. If the range is 49, the mean is 70, the mode is 75, and the median is 73, and the sum of the numbers in the data set is 400, what measure of central tendency or range could you use to find the value of the lowest number in the data set?

A. Mean

B. Median

C. Mode
D. Range



4. If the range is 65, the mean is 91, the mode is 95 , and the median is 96, and the lowest number is 12, what measure of central tendency or range could you use to find the value of the highest number in the data set?

A. Mean

B. Median

C. Mode
D. Range



Student explanation:

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