How do you construct an ogive curve from grouped data, and what are the key steps involved in plotting it?

To draw an ogive curve, we first need to calculate the upper class boundaries and the cumulative frequencies.

We also include a starting point for the ogive: $(129.5, 0)$.

• Draw a graph with "Height (cm)" on the x-axis (using the upper class boundaries) and "Cumulative Frequency" on the y-axis.
• The x-axis should range from approximately 129.5 to 199.5.
• The y-axis should range from 0 to 100.
• Plot the points: $(129.5, 0)$, $(139.5, 10)$, $(149.5, 23)$, $(159.5, 39)$, $(169.5, 60)$, $(179.5, 78)$, $(189.5, 92)$, $(199.5, 100)$.
• Connect these points with a smooth curve to form the ogive.

The median is the value at the 50th percentile. For a total of 100 students, the median position is $\frac{100}{2} = 50$.
To find the median height, locate 50 on the cumulative frequency (y-axis), draw a horizontal line to the ogive, and then draw a vertical line down to the height (x-axis).
Using interpolation from the table (as a proxy for reading from the graph):
The 50th position falls in the 160-169 class.

Where $L = 159.5$, $N = 100$, $CF_b = 39$, $f_m = 21$, $c = 10$.

This asks for the height at the 30th percentile.
The position is $30\%$ of $100 = 0.30 \times 100 = 30$.
To find this height, locate 30 on the cumulative frequency (y-axis), draw a horizontal line to the ogive, and then draw a vertical line down to the height (x-axis).
Using interpolation:
The 30th position falls in the 150-159 class.

Where $L = 149.5$, Position $= 30$, $CF_b = 23$, $f_p = 16$, $c = 10$.