1. Tabulation : The arrangement of the raw data under various heads in the form of a table is called tabulation.

## 2. Tange of a Data : The difference between the largest and the smallest observations is called the range.

## 3. Frequency : The number of observation in a particular class is called its frequency.

## 4. Cumulative Frequency : The cumulative frequency of a particular class is the sum of all frequencies up to this class.

## 5. Frequency Distribution : The distribution of frequency in various classes is known as frequency distribution.

## 6. Types of Frequency Distribution :

## (i). Exclusive or Continuous Form : Here, the classes are of the form 0 – 10 , 10 – 20 , 20 – 30 ……………..etc.

Here , 10 – 20 means 10 and more but less than 20

Thus , in 10 – 20 we include 10 and exclude 20.

Here in 10 – 20 , we have

lower limit = 10 Upper limit = 20

True lower limit = 10 True upper limit = 20

Class Size = (20 – 10 ) = 10

(ii). Inclusive or Discontinuous form : Here, the classes are of the form 0 -10, 11- 20, 21 – 30 ……………etc.

Here , 11 – 20 means 11 and more but less than 20 and 20

Thus, in 11 – 20 both 11 and 20 are included.

in 11 – 20 , we have

lower limit = 11 Upper limit = 20

True lower limit = 10.5 True upper limit = 20.5

Class size = (20.5 – 10.5) = 10

(iii). Class mark of a Class :

(iv). Range = (maximum value ) – ( minimum value )

## 7. Arithmetic Mean : The average of a given set of numbers is called the arithmetic mean.

## 8. Properties of Arithmetic Mean.

9. Mean for an ungrouped frequency distribution :

(a). Direct Method :

(b). Assumed – Mean Method : When the product ( f _{i }× x_{i} ) involves large numbers then we use the assumed – mean method.

Steps :

(c). Step – Deviation Method : When the values of x_{i} and f_{i } are large and the values of x_{i }are equally spaced , we use the step – deviation method for finding the mean.

Steps :

## 10. Median : It is the value of the middle most observation.

## 11. Mode is the most frequently occurring observation.

12. Mode = 3 (median ) – 2 ( mean )

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