2. STATISTICS
• Is a mathematical science pertaining to the
collection , presentation ,summarising ,analysis,
interpretation or explanation of data.
3. CENTRAL TENDENCY
• The tendency of the obseravtions to cluster round some central
value is known as central tendency
• are also called as averages.
• For any group of data ,that value is used to represent the whole set
of observations.
• It is used when to compare 2 or more minor set of observations.
4. • It is measured by
• ARITHMETIC MEAN
• MEDIAN
• MODE
• HARMONIC MEAN
• GEOMETRIC MEAN
Averages of position
Mathematical averages
5. ARITHMETIC MEAN
• It is the average of the data.
• It is obtained by summing up of all observations
by number of observations.
It is denoted by X.
6. • UNGROUPED DATA
• MEAN = SUM OF ALL OBSERVATIONS
NO: OF OBSERVATIONS
1 1 2
n
i
i n
X
X X X
X
n n
7. ????
• CALCULATE THE MEAN OF:
1.BP OF 8 INDIVIDUALS- 83, 75, 81, 79 .71 ,75 ,95 ,77
2. WEIGHT OF 5 INFANTS- 5,3,6,4,7
3.No of teeth erupted at 2yrs in 6 children
- 3 ,5 ,8 ,9 ,7 ,4
8. GROUPED DATA
• To find the Arithmetic Mean of 1,2,3,1,2,3,2.
• The arithmetic mean = 1+2+3+1+2+3+2/7 = 14/7 = 2
• In this case there are two 1's, three 2's and two 3’s.
• The number of times each number occurs is called its frequency.
X value Frequency ΣfX
1 2 1 * 2 = 2
2 3 2 * 3 = 6
3 2 3 * 2 = 6
9. • Step 1: Find Σf.
Σf = 7
• Step 2: Now, find ΣfX.
ΣfX = ((1*2)+(2*3)+(3*2)) = 14
Step 3: Now, Substitute in the above
formula
• Arithmetic mean = ΣfX / Σf = 14/7 = 2
10. • MERITS
• Simple To Calculate
• Easy To Understand
• Useful For Further Statistical Analysis
• Uses all information in the data
• DEMERITS
• Values of all items necessary for calculation
• May be ridiculous some times e.g. Average number of
children =4.76
• Influenced by extreme values
• Cannot be obtained for qualitative data.
11. MEDIAN
• It is the value of middle observation after placing the
observations in either ascending or descending order.
• Half the values lie above it and half below it.
12. • If n or N is odd, the median is the middle
number.
• If n or N is even, the median is the average
of the two middle numbers
13. Example 1: To find the median of 4,5,7,2,1 [ODD].
Step 1: Count the total numbers given.
There are 5 elements or numbers in the
distribution.
Step 2: Arrange the numbers in ascending order.
1,2,4,5,7
Step 3: The total elements in the distribution (5) is
odd.
The middle position can be calculated using the
formula. (n+1)/2
So the middle position is (5+1)/2 = 6/2 = 3
The number at 3rd position is = Median = 4
14. Example 2 : To find the median of 5,7,2,1,6,4.
step 1 : count the total numbers given.
there are 6 numbers in the distribution.
step 2 :arrange the numbers in ascending order.
1,2,4,5,6,7.
step 3 :the total numbers in the distribution is 6
(even).
so the average of two numbers which are respectively in
positions n/2 and (n/2)+1 will be the median of the given data.
Median = (2+1)/2 = 1.5.
15. Grouped series
simply divide the total observation by 2
If the number of observations is 200 then
median will be 100th observation.
If the number of observations is 201 then
median will be 101th observation
16. ADVANTAGES:
1.There will be only one median for a given
data set.
2 .It is unaffected by the extreme values.
DISADVANTAGES:
1.It doesn't take in to consideration all the
observations.
17. MODE
• A measure of central tendency
• Value that occurs most often
• Not affected by extreme values
• Used for either numerical or categorical data
PROPERTIES:
1. There could be more than one mode for a given data.
2. It is un affected by extreme values.
3. It does not use all the observations in the given data.
