Measure of C Tendency

1. MEASURES OF CENTRAL
TENDENCY
NIGHAT KANWAL

2. OBJECTIVES
At the end of presentation the learner's would be able to:
 Describe the measures of central tendency
 Discuss the mean, median and mode with examples
 Enlist the distribution shapes of the data

3. MEASURES OF CENTRAL
TENDENCY
A measure of central tendency is a single value that
attempt to describe a set of data by identify the central
position within the set of data .
As such, measure of central tendency are sometimes
called measure of central location .
The most common of central tendency are
Mean
Median
mode

4. MEAN
The statistical mean refers to the mean or average that
is used to derived the central tendency of the data in
question. This is also known as arithmetic average.
The mean can be used for both continuous and discrete
numeric data.
Mean assumes numerical values and requires interval
data.
The mean cannot be calculated for categorical data, as
the value cannot be summed.
Mean affected by high or low values (outliers).

5. MEAN CALCULATED BY
The mean is the sum of the value of each observation in a
data set divided by the number of observation.

6. CALCULATING THE MEAN FOR
DRIVING SPEED OF CARS
Example : Find the mean driving speed for 6
different cars on the same highway.
66 mph, 57 mph, 71 mph, 54 mph, 69 mph, 58 mph
Formula: Sum of the value/ number of cases
Solution: 66 + 57 + 71 + 54 + 69 + 58 = 375
375/6
Answer: The mean driving speed is 62.5 mph.

7. MEDIAN
• The median represents the middle of the ordered
sample data
• When the sample size is odd, the median is the middle
value
• When the sample size is even, the median is the
midpoint of the two middle values
• Median requires ordering of values and can be used
with both interval and ordinal data
• Median not effected by outliers.

8. EXAMPLE
Find the median value of the set of numbers {4, 12, 15, 3, 7,
10}.
First, arrange the numbers in order from least to greatest.
3, 4, 7, 10, 12, 15
We have an even number of terms in our set, so we must
take the average of the two middle terms.
Formula = M1 + M2 / 2
= 7+10/2
=8.5
Our median is 8.5

9. MODE
• The mode is the value that occur most frequently
• It is the least useful of the three measures of central
tendency

10. EXAMPLE
The following is the number of problems that Ms. Matty
assigned for homework on 10 different days. What is the
mode?
8, 11, 9, 14, 9, 15, 18, 6, 9, 10
Solution: Ordering the data from least to greatest, we
get:
6, 8, 9, 9, 9, 10, 11 14, 15, 18
Answer: The mode is 9.

13. REFERENCES
 (n.d.). Retrieved from mean, median, mode and range
(examples solutions, worksheet, videos):
http:/www.onlinemathlearning.com
 frost, j. (n.d.). statistics by Jim. Retrieved from
https:/statisticsbyjim.com.