Question

How many articles have cost at least Rs.50?

Cost (In Rs.)	Frequency
$10 - 20$	$22$
$20 - 30$	$18$
$30 - 40$	$35$
$40 - 50$	$115$
$50 - 60$	$38$
$60 - 70$	$22$

A. $22$
B. $60$
C. $35$
D. $115$

Answer 1

Hint: According to the question we have to determine how many articles have cost at least Rs.50. So, first of all we have to draw a cumulative frequency table for the given data but before that we have to understand about the cumulative frequency as mentioned below:
Cumulative frequency: Cumulative frequency is the frequency which is used to determine the number of observations that lie above and or below a particular value in the data set and we can calculate the cumulative frequency by adding each frequency from a frequency distribution table to the sum of its predecessors.
Now, as we have to understand about the cumulative frequency so we have to draw the table for the given data set.
Now, as mentioned in the question , how many articles have cost at least Rs.50 so we have to check for the cost Rs.50.

Complete step-by-step solution:
Step 1: First of all we have to draw a cumulative frequency table which can be obtain by adding each frequency from a frequency distribution table to the sum of its predecessors as mentioned in the solution hint. Hence,

Cost (In Rs.)	Frequency	Cumulative frequency
$10 - 20$	$22$	$22$
$20 - 30$	$18$	$22 + 18 = 40$
$30 - 40$	$35$	$40 + 35 = 75$
$40 - 50$	$115$	$75 + 115 = 190$
$50 - 60$	$38$	$190 + 38 = 228$
$60 - 70$	$22$	$228 + 22 = 250$

Step 2: Now, we have to check for the cost for which we have to determine the number of articles with the help of the table as obtained in the solution step 1. So, as we can see that for cost Rs.50 the frequency is 38.
Step 3: As we have already obtained the frequency for the cost so, the articles which cost at least Rs.50 is:
$
   = 38 + 22 \\
   = 60
 $
Final solution: Hence, we have obtained the number of articles which have cost at least Rs.50 is 60.

Therefore option (B) is correct.

Note: To calculate the cumulative frequency by adding each frequency from a frequency distribution table to the sum of its predecessors.
The cumulative frequency of a variable is the number of values in the collection of the data less than or equal to the value of the variable.