# Explain the term, Mid value, Open End Classes and Cumulative Frequency Distribution.

**Mid -value: **It is the average of the lower limit and the upper limit of a class.Example:

Lower limit of the first class is 0 and the upper limit is 10. Therefore, mid-value of the first class is 0+10 / 2 i.e., 5. Similarly; other mid—values have been worked out

**Open-end classes :** These are the classes in which either the lower limit of the first class is not given or the upper limit of the last class is not given

or both are not given. A distribution with such classes is known as frequency distribution with open end classes. Example:

###### In the first class, lower limit is not given. In the last class, upper limit is not given. Both these classes are open end classes.

**Cumulative frequency distribution :** It is a distribution in which frequencies are added up either downwards or upwards. There are two types of cumulative frequency distributions less than type cumulative frequency distribution and more than type cumulative frequency distribution.

**Steps:**

- First we write the upper limits i.e., 10, 20, ……. etc. and before all these upper limits, we write the words less than.
- First cumulative frequency is same as first frequency i.e., 5.
- Second cumulative frequency = 5 + 7 =12

Third cumulative frequency = 12 + 8 = 20

Fourth cumulative frequency = 20 + 5 = 25

Fifth cumulative frequency = 25 + 12 = 37

Last cumulative frequency = 37 + 13 = 50

###### Cumulative frequencies are obtained by adding frequencies downwards.

Conversion of an ordinary frequency distribution into more than type cumulative frequency distribution.

**Steps:**

- First we write the lower limits i.e., 0, 10, ……etc. and before all these lower limits, we write the words more than.
- Last cumulative frequency is same as last frequency i.e.., 13.
- Second last cumulative frequency = 13+ 12 = 25

Third last cumulative frequency =25 + 5 = 30

Fourth last cumulative frequency = 30 + 8 = 38

Fifth last cumulative frequency = 38 + 7 = 45

First cumulative frequency = 45 + 5 = 50