Ex.3.1 Q8 Data Handling - NCERT Maths Class 7
Question
The rainfall (in mm) in a city on \(7\) days of a certain week as recorded as follows:
Day |
Mon |
Tue |
Wed |
Thurs |
Fri |
Sat |
Sun |
Rain fall (in \(\rm mm\)) |
\(0.0\) |
\(12.2\) |
\(2.1\) |
\(0.0\) |
\(20.5\) |
\(5.5\) |
\(1.0\) |
(i) Find the range of the rainfall in the above data.
(ii) Find the mean rainfall of the week.
(iii) On how many days was the rainfall less than the mean rainfall?
Text Solution
What is known?
Rainfall in \(\rm mm\)
What is unknown?
Range of the rainfall and mean rainfall
Reasoning:
Mean of the rainfall in \((\text{mm})\)
\(\begin{align}=\frac{\text{sum of rain falls (in mm) }}{\text{Number of days}}\end{align}\)
Steps:
(i)Highest of the rainfall (in \(\rm m\rm m\)) \(= 20.5\)
Lowest of the rainfall (in \(\rm m\rm m\)) \(= 0.0\)
Range of the rainfall = Highest rainfall – Lowest rainfall
\(= 20.5 – 0.0\\ = 20. 5 \rm\,mm\)
(ii)Total number of days \(= 7\)
Record of the rainfall (in \(\rm mm\)) \(= 0.0, 12.2, 2.1, 0.0, 20.5, 5.5, 1.0\)
Mean of the rainfall in \((\text{mm})\)
\[\begin{align} & =\frac{\left[ \begin{align} & 0.0+12.2+2.1+0.0+ \\ & 20.5+5.5+1.0 \\ \end{align} \right]}{7} \\ & =\frac{41.3}{7} \\ & =5.9 \\ \end{align}\]
(iii)On \(5\) days rainfall was less than the mean rainfall i.e., Monday, Wednesday, Thursday, Saturday and Sunday.