For the following frequency distribution, draw an ogive and then use it to estimate the median.

C.I.	f
450 - 550	40
550 - 650	68
650 - 750	86
750 - 850	120
850 - 950	90
950 - 1050	40
1050 - 1150	6

For the same distribution, as given above, draw a histogram and then use it to estimate the mode.

Cumulative frequency distribution table is as follows :

Here no. of terms = 450, which is even.

By formula,

Median = $\dfrac{n}{2}$ th term = 225.

Steps of construction of ogive :

1. Take 2 cm = 100 units (C.I.) on x-axis.

2. Take 1 cm = 50 units (frequency) on y-axis.

3. A kink is shown near x-axis as it starts from 450. Plot the point (450, 0) as ogive starts on x-axis representing lower limit of first class.

4. Plot the points (550, 40), (650, 108), (750, 194), (850, 314), (950, 404), (1050, 444) and (1150, 450).

5. Join the points by a free-hand curve.

6. Draw a line parallel to x-axis from point I (frequency) = 225, touching the graph at point J. From point J draw a line parallel to y-axis touching x-axis at point K.

From graph, K = 780

Hence, median = 780.

Steps :

1. Draw a histogram of the given distribution.

2. Inside the highest rectangle, which represents the maximum frequency (or modal class), draw two lines AC and BD diagonally from the upper corners A and B of adjacent rectangles.

3. Through point K (the point of intersection of diagonals AC and BD), draw KL perpendicular to the horizontal axis.

4. The value of point L on the horizontal axis represents the value of mode.

∴ Mode = 803.

Hence, mode = 803.