Question

Classes and frequency are given as follows

Classes	Frequency
$600 - 640$	$16$
$640 - 680$	$45$
$680 - 720$	$156$
$720 - 760$	$284$
$760 - 800$	$172$
$800 - 840$	$59$
$840 - 880$	$18$

Prepare a cumulative frequency table by less than method and draw an ogive.

Answer 1

Hint: We will make a cumulative frequency table by less than type. Thereafter, we will take the upper limit and cumulative frequency and plot these points on a graph to get less than ogive.

Complete step-by-step answer:
We will draw a cumulative frequency distribution table by less than method.
Cumulative frequency: Cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution. It means that you are adding up a value and all the values that came before it in less than type method, we will take upper limit

Classes	Frequency
$600 - 640$	$16$
$640 - 680$	$45$
$680 - 720$	$156$
$720 - 760$	$284$
$760 - 800$	$172$
$800 - 840$	$59$
$840 - 880$	$18$

Now, we will convert it by less type method.

Classes	Frequency	Cumulative frequency
Less than $640$	$16$	$16$
Less than $680$	$45$	$16 + 45 = 61$
Less than $720$	$156$	$61 + 156 = 217$
Less than $760$	$284$	$217 + 284 = 501$
Less than $800$	$172$	$501 + 172 = 673$
Less than $840$	$59$	$673 + 59 = 732$
Less than $880$	$18$	$732 + 18 = 750$
	$\sum {f = 750} $

Now, plot the points $(640,16),(680,61),(720,217),(760,501),(800,673),(840,732),(880,750)$.Take upper class limit of class interval on x-axis and their respective frequency on y-axis, ogive can be drawn as follows

Note: In statistics, an ogive, also known as a cumulative frequency polygon, can refer to one of two things: any hand drawn graphic of a cumulative distribution function. any empirical cumulative distribution function.