measures of central tendency from Alia.pdf

Quantitative reasoning

1. Lecture: 7

2. Measure of Central
Tendency or Averages
A data set can be summarized into a single
value, such a value usually in the centre and
around which the whole data have a tendency
to concentrate.

3. Types of Averages:
Mean
Best known & most widely used average,
describing the center of a frequency
distribution.
Median
The middle value/point of a set of ordered
numbers below which 50% of the distribution
falls.
Mode
The most frequent value or category in a
distribution.

4. Mean
It is the arithmetic average of a set of
numbers.
Sum of the values of all the observations in a
data set divided by the total number of
observations.
Mathematically:
The Sample Mean
 and The Population Mean

5. Example
Age of the patients coming to the clinic
57,86,42,38,90,66

= 57+86+42+38+90+66
6
= 379
6
= 63.167 year

6. Example
Score on a exam

68 90 77 79 80 92
= 68+90+77+79+80+90
6
= 486
6
= 81

7. Median
Middle value in an ordered array of numbers.

8. Procedure for calculating
median
Arrange the observations in an ordered
array.(ascending or descending order)

If there is an odd number of terms, the
median is the middle term of the ordered
array.

lf there is an even number of terms, the
median is the average of the middle two
terms

9. Median: example with an
odd number of terms
Ordered Array
Age of the patients coming to the clinic
3, 4, 5, 7, 8, 9, 11, 14, 15, 16, 16, 17, 19, 19,
20, 21, 22
There are 17 terms in the ordered array.
Position of median= (n+1)/2= (17+1)/2 = 9
The median is the 9th term, 15.

10. Median: Example with an
even number of terms
Ordered Array
Age of the patients coming to the clinic
3, 4, 5, 7, 8, 9, 11, 14, 15, 16, 16, 17, 19, 19,
20, 21,
There are 16 terms in the ordered array.
Position of median= (n+1)/2= (16+1)/2 = 8.5
The median is between the 8
th
and 9
th
term,
14.5.

11. Mode
The mode is the observation that occurs most
frequently.

For a sample of five salaries
6,000, 10,000, 14,000, 50,000, 10,000
the mode is equal to $10,000.

12. Mean, Median and Mode
for grouped data

13. Cont..
For grouped data, we cannot find the exact
Mean, Median and Mode, we can only
give estimates.

To estimate the Mean use the midpoints of
the class intervals.

15. CD

16. Thank you