| Ages (in years): | 5 – 15 | 15 – 25 | 25 – 35 | 35 – 45 | 45 – 55 | 55 – 65 |
| No of students: | 6 | 11 | 21 | 23 | 14 | 5 |
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Solution:
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.
To find the mean:
For the given data let the assumed mean (A)
| Age (in years) | Number of patients fi | Class marks xi | di = xi – 275 | fidi |
| 5 – 15 | 6 | 10 | – 20 | -120 |
| 15 – 25 | 11 | 20 | – 10 | -110 |
| 25 – 35 | 21 | 30 | 0 | 0 |
| 35 – 45 | 23 | 40 | 10 | 230 |
| 45 – 55 | 14 | 50 | 20 | 280 |
| 55 – 65 | 5 | 60 | 30 | 150 |
| N = 80 | Σfi di = 430 |
It’s observed from the table that 
and 
.
Using the formula for mean,
Thus, the mean of this data is 
. It can also be interpreted as that on an average the age of a patients admitted to hospital was years.
It is also observed that maximum class frequency is 
and it belongs to class interval 
So, modal class is with the Lower limit (l) of modal class 
And, Frequency (f) of modal class = 23
Class size (h) = 10
Frequency (f1) of class preceding the modal class = 21
Frequency (f2) of class succeeding the modal class = 14
Mode
Therefore, the mode is 36.8. This represents that maximum number of patients admitted in hospital were of 36.8 years.
Hence, it’s seen that mode is greater than the mean.