Question

A study was conducted to find out the centration of sulphur dioxide (SO2) in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
0.03 0.08 0.08 0.09 0.04 0.17
0.16 0.05 0.02 0.06 0.18 0.20
0.11 0.08 0.12 0.13 0.22 0.07
0.08 0.01 0.10 0.06 0.09 0.18
0.11 0.07 0.05 0.07 0.01 0.04
(i) Make a grouped frequency distribution for this data with class intervals 0.00-0.04, 0.04-0.08 i.e so on.
(ii) For how many days has the concentration of SO2 more than 0.11 ppm?

Answer 1

Hint: A certain range of data can be grouped together in certain classes which are known as class intervals. We need to Calculate the number of variables lying between respective class intervals and note them down, to make a frequency distribution table.

Complete step-by-step answer:
A frequency distribution is a representation, either in a graphical or tabular format, that displays the number of observations within a given interval. The interval size depends on the data being analyzed and the goals of the analyst. The intervals must be mutually exclusive and exhaustive.

Concentration of SO2	Tally	Number of days
0.00-0.04	||||	4
0.04-0.08	|||| ||||	9
0.08-0.12	|||| ||||	9
0.12-0.16	||	2
0.16-0.20	||||	4
0.20-0.24	||	2

→ This is the frequency distribution table for class intervals 0.00-0.04, 0.04-0.08…….
(ii) Number of days when concentration of SO2 is more than 0.11 is the sum of numbers of days in following class interval that include: 0.12-0.16, 0.16-0.20 and 0.20-0.24
Therefore, for 8 days concentration of SO2 was more than 0.11 ppm.

Note: To calculate frequency for more than any stated value(as asked in ii) part of question), we are required to calculate the sum of frequencies of the class intervals occurring after the asked one.