Centering

1

Characteristic of Data

Central Tendency

Variation Skewness

Central Value

2

Measure of Central Tendency

Mean Median Mode

“Single Value in the range of data set that is used to represent the entire data”

Central Value

3

Benefits of central Value

1) Represents entire population

2) Facilitates Comparison

3) Helps in decision making

Mean (Arithmetic Mean)“Arithmetic mean is average of magnitude of all the data points in a sample/population. It is calculated by dividing the sum of the values of all observations in the given data set by the number of observation in that set.”

Table A37616    32240    44974    35904    25910    36428 N 2227870 SUM 74231942649 Mean 33741.7724065    42421    41726    36245    23436    17112    27306    30900    25091    42607    43573    43650    30437    30159    

Mean =Sum of all the value

Total no: of values

Table B34075    24550    28687    38223    29900    16413 N 22

42237 SUM162533

839676 Mean 7387916169    24036    19704    38340    28997    31330    21632    19806    29647    30443    42058    28596    

1000000

   

40819    

Median“Median is a middle value of any given data set when data is arranged in sequential order i.e. ascending or descending”

Median =N+1

2th item

When n is odd

Table A

 12342  

 13213  N 17

 13987(N+1)

/2 9

 14123  

 14567  

 14987  

 15873  

 15998  

 16008  

 16547  

 16985  

 17845  

 18000  

 18765  

 18967  

 19823  

 19921  

Table B

 12342  

 13213  N 16

 13987(N+1)

/2 8.5

 14123  

 14567  

 14987  

 15873  

 15998  

 16008  

 16547  

 16985  

 17845  

 18000  

 18765  

 18967  

 19823  

   

Table AMedian = 16008

Table BMedian = 8.5th item

Median = 15998+16008

2

Median = 16003

Comparison of Mean and Median

6

Table A37616    32240    44974    35904    25910    36428    27870    42649    24065    

42421 Mean33741.772

741726 Median 3407236245    23436    17112    27306    30900    25091    42607    43573    43650    30437    30159    

Table B37616    32240    44974    35904    25910    36428    27870    42649    24065    42421 Mean 77825.454541726 Median 36074.536245    23436    17112    27306    30900    25091    42607    43573    43650    30437    

1000000

   

“We use mean as a measure of central tendency in case of normal data and median in case of non normal data”

Mode

7

“Mode is the highest repeated number in any data set”

Quality Score

85854567557585909285

Highest repeated number =85Mode = 85