Student-teacher ratio expresses the relationship between the

Q) Student-teacher ratio expresses the relationship between the number of students enrolled in a school and the number of teachers employed by the school. This ratio is important for a number of reasons. It can be used as a tool to measure teachers’ workload as well as the allocation of resources. A survey was conducted in 100 secondary schools of a state and the following frequency distribution table was prepared :

Based on the above, answer the following questions :
(i) What is the lower limit of the median class ?
(ii) What is the upper limit of the modal class ?
(iii) (a) Find the median of the data.
OR
(iii) (b) Find the modal of the data.

Ans: (i) Median Class:

We know that the median class is the class where the cumulative frequency crosses 50% of the total number of events.

Here in the given table, we need to calculate cumulative frequency and identify the median class and to do that, let’s re-organize the data:

at which it is crossing 50% of frequencies i.e. 45, at class “50-60”. Hence, our Median class

Here Sum of all frequencies (i.e. number of schools) is 100. hence, its 50% is 50. Now, if we look in the last column (cum freq), we can clearly see that the 50% of cumulative frequency (i.e. 50) is crossed at class “35 – 40”. Hence, our median class is 35-40.

Therefore, the lower limit of the Median class is 35.

(ii) Upper limit of Modal Class:

We know that the modal class is the class with the highest frequency.

In the given table of the question, class “35 – 40” has maximum students (30) i.e. highest frequency of 12. Hence, the modal class is “35 – 40”.

Therefore, the Upper limit of the Modal class is 40.

(iii) (a) Median Value:

We just identified the Median class as ” 35 – 40″.

Next, we know that the Median of a grouped data is given by the formula:

Median = L+ $\left [\frac{\frac{n}{2}-c_f}{f}\right]$ x h