Find the mean deviation from the median of the following data: Marks: 0 10 20 30 40 50 60 : : : : : : : : No of Students 20 18 15 10 5 3 1

Solution

Step 1: Compute the Median

The given data is discrete and ungrouped. To find the median, we first determine the total number of students and locate the median position.

• Total number of students ($N$): $$N=20+18+15+10+5+3+1=72$$
• Median position ($M$): $$M=\frac{N+1}{2}=\frac{72+1}{2}=36.5$$ Since the median position is 36.5, the median lies in the 20 marks class (cumulative frequency up to 20 marks = 20 + 18 = 38).

Thus, Median ($M_d$) = 20.

Step 2: Compute Mean Deviation from the Median

Mean deviation from the median is calculated using the formula:

$$\text{Mean Deviation}=\frac{\sum f|x-M_d|}{\sum f}$$

where:

• $f$ = frequency of each class,
• $x$ = midpoint of each class,
• $M_d$ = median.

Since the data is discrete, the midpoint of each class is the class value itself.

Compute $|x-M_d|$ and $f|x-M_d|$ for each class:

Sum of $f|x-M_d|$: $$400+180+0+100+100+90+40=910$$

Total number of students ($N$) = 72.

Thus, the mean deviation from the median is:

$$\text{Mean Deviation}=\frac{910}{72}\approx 12.64$$

Mean deviation from the median = 12.64 (rounded to two decimal places).