I was elected as the mayor of a small village in 1850. On the first day of my office I decided with my staff to prepare a report to analyze the age distribution of the population of my village. My staff went on a survey, met all the people in the village and compiled their age in a record book. Upon analyzing I noticed that my village had 101 people in total and the age of the youngest member was 1 Year, and the oldest person had lived for 102 years.

Below is the graph of the population age for each member of the village.

I was amazed,I had been elected to lead the population with ages varying from 1 to 102 Years. This difference between this maximum and the minimum ages is known as the range of the population age. The range of population age in my village was 102-1 = 101 Years. Big responsibility, isn’t it! I had to make the development policies keeping in mind the youngest and the oldest person.

Since the age variation was quite high I decided to calculate what the average age also referred to as the mean age of the village. For calculating mean I picked the ages of 101 people, summed them up and divided this sum by the total number of people which was 101 in my case. The output I obtained represented the mean age of the village. Mean age of 46 in my village indicated the population of the village was generally old (considering 46 years as old).

To get a bird size view of the age distribution of the population I lay down the data sheet and arranged the ages in ascending order starting from the 1year old boy to 102year old person.

Below graph shows the ages of the population displayed from youngest to oldest and the mean age

The 51st person in the population arranged in the ascending order of the ages lies in the middle of all and his age denotes the median of the population age which I find out was 45 years. On the other hand, had the population been 100 then the median or the middle age would have been the average of the age of 50th and 51st person. To see which age group is the maximum in the village I counted the maximum number of people having same age. In my village there were 19 people with the age of 25 Years and this was the maximum number of people having same age. Hence 25 which is the maximum number of times the variable of interest(population age in this case) repeats is called the mode. Since I had a sizeable population 25 years old I had to work towards creating employment opportunities for all of them.

Below graph shows the ages of the population displayed from youngest to oldest and the mean, median and mode of the age of the population

Another parameter that helped me quantify how spread or concentrated population age data was.I calculated the standard deviation. If the data is concentrated near the mean, we expect the standard deviation to be small. To calculate standard deviation, we square root the average squared difference between the mean of the data and each data value. By doing this we are checking how far from the mean our data lies on an average. You may wonder why we squared the difference.Squaring makes all the differences positive as we can expect some data values to be smaller than mean and some more than mean which would give us negative and positive difference values respectively.

I knew the mean which was 46, I calculated the difference of age of every villager and the mean age of the population. I squared this and calculated the mean of the the squared difference for the age of all the villagers. The square root of the result gave me the standard deviation.

That was a lot of in-depth analysis I carried out in the beginning which helped me draft the development policies for all the age groups and eventually my village got recognized as a smart village of India.