Question

Distinguish between

1) Arithmetic mean and Mode
2) Arithmetic mean and median
3) Median and mode
4) Quartiles and Deciles
5) Deciles and Percentiles
6) Quartiles and Percentiles

Answer 1

1.

Basis of Difference	Arithmetic Mean	Mode
Definition	It refers to the value calculated by dividing the sum of the values of the given items by the total number of items.	It refers to the value that repeats itself the maximum number of times or that has the maximum frequency.
Further Algebraic treatment	It is capable of algebraic treatment.	It is not capable of algebraic treatment.
Scope	It has wide scope.	It has limited scope.
Ambiguity	It has a certain value.	Mode may have an ambiguous value in the sense that a series can have two or more modes simultaneously.
Affect of extreme values	Affected	Not affected
Type of average	Arithmetic average	Positional average

2.

Basis of Difference	Arithmetic Mean	Median
Definition	It refers to the value calculated by dividing the sum of the values of the given items by the total number of items.	It refers to the middlemost value of the given set of data arranged in an array (ascending or descending).
Algebraic treatment	It is capable of algebraic treatment.	It is not capable of algebraic treatment.
Necessity of array	It is not required.	It is essential.
Affect of extreme values	Affected	Not affected
Affect of open-ended classes	Cannot be calculated in case of open-ended classes	Can be calculated in case of open-ended classes
Type of average	Arithmetic average	Positional average

3.

Basis of Difference	Mode	Median
Definition	It refers to the value that repeats itself the maximum number of times or that has the maximum frequency.	It refers to the middlemost value of the given set of data arranged in an array (ascending or descending).
Division of data	It does not divide data into parts.	It divides data into equal parts.
Necessity of array	It is not required.	It is essential.
Ambiguity	It has an ambiguous value.	It has a certain value.

4.

Basis of Difference	Quartiles	Deciles
Definition	Quartiles are the values of a given set of data that divide the whole data or observations into 4 parts.	Deciles are the values of a given set of data that divide the whole data or observations into 10 parts.
Number of equal parts created	4	10
Number of dividing points	3	9
Formula	$Q_1={\left(\frac{N+1}{4}\right)}^{th}observation$	$D_1={\left(\frac{N+1}{10}\right)}^{th}item$

5.

Basis of Difference	Percentiles	Deciles
Definition	These are the values of a given set of data that divide the whole data or observations into 100 equal parts.	These are the values of a given set of data that divide the whole data or observations into 10 equal parts.
Number of equal parts created	100	10
Number of dividing points	99	9
Formula	$P_1={\left(\frac{N+1}{100}\right)}^{th}item$	$D_1={\left(\frac{N+1}{10}\right)}^{th}item$

6.

Basis of Difference	Quartiles	Percentiles
Definition	These are the values of a given set of data that divide the whole data or observations into 4 equal parts.	These are the values of a given set of data that divide the whole data or observations into 100 equal parts.
Number of equal parts created	4	100
Number of dividing points	3	99
Formula	$Q_1={\left(\frac{N+1}{4}\right)}^{th}observation$	$P_1={\left(\frac{N+1}{100}\right)}^{th}item$