Question

The successive annual rainfall magnitudes at a place for a period of 10 years from 2001 to 2010, both inclusive, are 30.3, 41.0, 33.5, 34.0, 33.3, 36.2, 33.6, 30.2, 35.5 and 36.3 cm. The mean and median values of this annual rainfall series are, respectively
1. 33.8 cm and 34.39 cm
2. 34.39 cm and 33.8 cm
3. 34.39 cm and 40.2 cm
4. 33.8 cm and 40.2 cm

Answer 1

Correct Answer - Option 2 : 34.39 cm and 33.8 cm

Concept:

Mean of rainfall = sum of all annual rainfall for a given period/ Total period

To find median, following two step procedures is adopted:

Step 1: Arrange the given data (annual rainfall) in an increasing order.

Step 2:

If data points are odd then median will the middle data point value.

If there is an even number of data, the median is the average of the middle two numbers.

Calculation:

\({\rm{Mean}} = {\rm{\;}}\frac{{30.3\; + {\rm{\;}}41.0\; + \;33.5,{\rm{\;}} + {\rm{\;}}34.0,\; + {\rm{\;}}33.3 \;+ {\rm{\;}}36.2\; + {\rm{\;}}33.6\; + {\rm{\;}}30.2\; + \;35.5\; + {\rm{\;}}36.3{\rm{\;}}}}{{10}}\)

Mean = 34.39 cm

The increasing order of annual rainfall data is 30.2, 30.3, 33.3, 33.5, 33.6, 34.0, 35.5, 36.2, 36.3, 41.0.

There are total 10 data points i.e. even number, so median is the average of the middle two numbers.

Median = (33.6 + 34.0)/2

Median = 33.8 cm