Statistics Class 10

 📝 Statistics 

● The mean for grouped data can be found by :
(i) Direct Method 
`\overline x = frac{\sum f_ix_i}{\sum f_i}`

(ii) Assumed mean method 

`\overline x =  a + frac{\sum f_id_i}{\sum f_i}`

(iii) Step deviation method 

`\overline x =  a +  h ×frac{\sum f_iu_i}{\sum f_i}`

with the assumption that the frequency of a class is centered at its mid-point, called its class mark.

● The mode for grouped data can be found by using the formula:

Mode = `l + (frac{f_1 - f_0} {2f_1-f_0-f_2}) × h` 

where `l` = lower limit of the modal class,

`h` = size of the class interval (assuming all class sizes to be equal),

`f_1` = frequency of the modal class,

`f_0` = frequency of the class preceding the modal class,

`f_2` = frequency of the class succeeding the modal class.

●The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.

● The median for grouped data is formed by using the formula:

Median `= l +  (\frac {n/2-cf}{f})  × h` 

● Representing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the less than type and of the more than type.