Question

Draw an Ogive for the following frequency distribution by less than the method and also find its median from the graph.

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of Students	7	10	23	51	6	3

(a) 36 marks
(b) 35 marks
(c) 34 marks
(d) 33 marks

Answer 1

Hint: To solve this question, we will first compute the frequency table and the cumulative frequency table. The corresponding values of the cumulative frequency are on the y axis and that of the class interval or “less than” value lies on the x-axis.

Complete step by step answer:
We are given the table as

Marks	Number of Students
0 – 10	7
10 – 20	10
20 – 30	23
30 – 40	51
40 – 50	6
50 – 60	3

The steps to draw a less than O – give are as given below.
1. Draw and mark the horizontal and vertical axis
2. Take the cumulative frequencies along the y-axis (vertical axis) and the upper-class limits on the x-axis (horizontal axis).
3. Against each upper-class limit, plot the cumulative frequencies.
4. Connect the points with a continuous curve.
Also, let us define an Ogive. The Ogive is defined as the frequency distribution graph of a series. The Ogive is a graph of a cumulative distribution that explains data value on the horizontal plane axis and the cumulative relative frequencies, the cumulative frequencies or the cumulative percent frequencies on the vertical axis.
Let us find the table having the cumulative frequency of our given data in terms of “less than” data.

Marks	Frequency	Cumulative Frequency
Less than 10	7	7
Less than 20	10	17
Less than 30	23	40
Less than 40	51	91
Less than 50	6	97
Less than 60	3	100

Finally, we will mark the Ogive using this cumulative frequency.

The median from an Ogive graph can be determined as: If N = total frequency, compute \[\dfrac{N}{2}\] and here N = 100. So, we get,
\[\Rightarrow \dfrac{N}{2}=\dfrac{100}{2}=50\]
Here, 50 on the y-axis would give an x-axis near to 34. You can observe this from the graph. So, hence, the median according to the graph is 34.
So, the correct answer is “Option C”.

Note: The method or process to find the median from the given set of data or from the given Ogive graph is by first calculating \[\dfrac{N}{2}\] where N is the total frequency and finally locate \[\dfrac{N}{2}\] on the y-axis, the corresponding point on the x-axis is our median.