Mean, Median, Mode and Range Central Tendency

1. Republic of the Philippines
Department of Education
CARAGA ADMINISTRATIVE REGION
DIVISION OF AGUSAN DEL NORTE
LAS NIEVES DISTRICT II
ALTERNATIVE LEARNING SYSTEM
Yanie S. Gamuza –ALS Teacher

2. Objectives:
♦ define mean, median, mode, range and other
related terms;
♦ describe the differences among mean, median,
mode and range;
♦ use mean, median and mode and range to
analyze and interpret data to solve problems
in daily life.

3. - in statistics, a central tendency (or measure of
central tendency) is a central or typical value for a
probability distribution. It may also be called a
center or location of the distribution. Colloquially,
measures of central tendency are often called
averages.

4. 1. Mean
- also known as the arithmetic mean,
is the average of a set of
numeric data. This is the number that
best represents a group of numbers.
The mean (often called the average) is
most likely the measure of central
tendency that you are most familiar
with.
To find the mean,
we use the following
formula

5. 2. Median
- is the value that divides a given set of
data or distribution into two equal
halves wherein 50% of the values are
above it and 50% are below it. The
median is the midpoint (or middle value)
of a set of numbers.
- It is found by ordering the set of
numbers and then finding the middle
value in the set.
To find the mean,
we use the following
formula

6. 3. Mode
-is the value or category that occurs
with the highest frequency in a given
set of data. It is the most common (or
the data point that appears most
often) in a set of data. It can be found
by putting the data into an ordered
list and seeing which data point
occurs most often.
To find the mode,
we use the following
formula

7. 4. Range
- is a measure of variability in a set
of data. The range is computed by
using the formula:
- -The range is the gap between the
smallest and largest data point. It is
found by putting the data into an
ordered list and find the difference
between the largest and smallest
amount.
To find the mode,
we use the following
formula

8. Find the mean of 5, 7, 8 and 4
Step 1) Add up the numbers to give a total
of 5+7+8+4=24
Step 2) Divide the total by the number of
data points. 24 ÷ 4 = 6
Answer: the mean is 6.

9. Find the median of 23, 27, 16, 31
Step 1) Put the numbers in order: 16, 23, 27, 31
Step 2) There is an even number of values in the set,
so the median is the average of the middle two
values.
(23+27) ÷ 2 = 25 Answer: the mean is 25

10. Find the median of
90 89 77 72 84 100 98 71
Step 1) Order the numbers in the
set from smallest to largest.
Step 2) Find the middle number.
84 is the median

11. Find the mode of 3, 6, 4, 3, 2, 4, 7, 8, 6, 3, 9
Step 1) Put the data into an ordered list. This gives us: 2,
3, 3, 3, 4, 4, 6, 6, 7, 8, 9
Step 2) Check the number of data points in both lists is the
same. Both lists have 11 data points.
Step 3) The mode is the number which occurs most often.
Answer: the mode is 3.

12. 2.Findtherangeof14,21,9,32,27,15,12,30
Step1)Putthedataintoanorderedlist.Thisgivesus:9,12,14,15,21,27,30,32
Step2)Checkthenumberofdatapointsinbothlistsisthesame.Bothlistshave8data
points.
Step3)Therangeisthedifferenceorgapbetweenthelargestandsmallestnumbers.
Answer: 32-9=rangeis23.