Case Study – 1 Student-teacher ratio expresses the relationship between the number of students enrolled in a…

Question

Case Study – 1
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 :
Number of students per Teacher: $20-25$, $25-30$, $30-35$, $35-40$, $40-45$, $45-50$
Number of Schools: $5$, $15$, $25$, $30$, $15$, $10$
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
(b) Find the modal of the data.

Accepted Answer

No. of Students per teacher | No. of School | c.f.
$20-25$ | $5$ | $5$
$25-30$ | $15$ | $20$
$30-35$ | $25$ | $45$
$35-40$ | $30$ | $75$
$40-45$ | $15$ | $90$
$45-50$ | $10$ | $100$
(i) Median class is $35 - 40$
Lower limit of median class = $35$
(ii) Modal class is $35 - 40$
Upper limit of modal class = $40$
(iii) (a) Median class is $35 - 40$
Median = $$\begin{aligned}& 35 + \frac{(\frac{100}{2} - 45)}{30} \times 5 \\ & = \frac{215}{6}\end{aligned}$$ or $35.83$ approx.
OR
(iii) (b) Modal class is $35 - 40$
Mode = $$\begin{aligned}& 35 + \frac{30-25}{2\times30-25-15} \times 5 \\ & = 36.25\end{aligned}$$

Case Study – 1 Student-teacher ratio expresses the relationship between the number of students enrolled in a school…

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