| 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)$= 30$
| 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 $Σfi= N= 80$ and $Σfi di = 430$.
Using the formula for mean,
$= 30 + 430/80$
$= 30 + 5.375$
$= 35.375$
$= 35.38$
Thus, the mean of this data is $35.38$. It can also be interpreted as that on an average the age of a patients admitted to hospital was $35.38$ years.
It is also observed that maximum class frequency is $23$ and it belongs to class interval $35 – 45$
So, modal class is $35 – 45$ with the Lower limit (l) of modal class $= 35$
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.