Question

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Answer 1

Here, Maximum frequency is `10`.
So, Modal class will be corresponding class to `10` that is , `30-35`.
Now, Mode can be given by formula,
`Mode = l+(f_1-f_0)/(2f_1-f_0-f_2)**h`
Here, `l =` Lower limit of modal class `= 30`
`f_1 = ` Frequency of Modal class `= 10`
`f_2 = ` Frequency of Pre Modal class `= 9`
`f_3 = ` Frequency of Succeeding Modal class `= 3`
`h =` Class interval `= 5`
Putting these values in Mode formula,
`Mode = 30+(10-9)/(20-3-9)**5 = 30+5/8 = 30.625`
So, `Mode = 30.625`, indicates maximum number of states have `30.625` students per teacher.
Here, we can use step deviation method to find the mean of given data.
First we have to construct a table for the given data. Please refer to video for creating complete table.
We know, Mean,`(barX) = a+(sumf_iu_i)/(sumf_i)**h`
Here, `a =` assumed mean `= 32.5`
`sumf_iu_i = -23`
`sumf_i = 35`
`h =` = step size `=5`
Putting these values in formula,
`barX = 32.5+(-23)**5/35 = 32.5-23/7 = 29.22 `
So, `Mean = 29.22`, indicates average number of students per teacher is `30.625` .