DATA HANDLING
STORY OF REPRESNTATIVE VALUES
Once upon a time in the land of Mathematics, there was a bustling village known as "DataVille." In DataVille, every resident had a unique story to tell, and the villagers were curious to understand and summarize these stories in a meaningful way. To achieve this, they relied on a group of special characters known as the "Representative Values."
The leader of the Representative Values was the wise and friendly "Mean." Mean was like the storyteller of the village, always eager to share the average experience of the villagers. When the villagers gathered in the town square, Mean would stand up and eloquently describe the typical tale, capturing the essence of the collective experiences.
Right beside Mean was the calm and composed "Median." This character had a unique ability to find the middle ground. Whenever there was a sequence of stories, Median would carefully arrange them in order and highlight the one right in the middle. The villagers appreciated Median's perspective, as it provided a balanced representation of their narratives.
In the corner of the village, there lived a playful and lively character named "Mode." Mode was the one who always pointed out the most popular story in town. Whenever a particular tale was repeated more than others, Mode would joyfully declare it the "Story of the Day." The villagers loved this recognition of their common experiences.
Meanwhile, the vigilant "Range" character patrolled the outskirts of DataVille. Range was like a guardian, always keeping an eye on the extremes of the stories. When villagers spoke of their most exciting or challenging moments, Range would calculate the difference between the highest and lowest points, ensuring that the diversity of tales was acknowledged.
Further into the village, the Quartiles were a trio known as Q1, Q2, and Q3. They divided the stories into four equal parts, creating a narrative timeline that allowed everyone to understand the distribution of experiences. Villagers often referred to the quartiles when they wanted to explore the various chapters within the community.
Occasionally, there were rebels in DataVille – the "Outliers." These were the stories that stood out from the crowd, unique and different. The villagers appreciated the Outliers for adding a touch of unpredictability to their otherwise familiar narratives. Outliers reminded them that diversity was a cherished aspect of their community.
In the heart of the village, there was a character called "MAD," which stood for Mean Absolute Deviation. MAD was like a friendly neighbor who measured the average distance of each story from the central point. This character helped the villagers understand how much individual tales deviated from the common thread.
And so, in DataVille, the Representative Values worked harmoniously, each playing a distinct role in capturing the essence of the villagers' stories. Together, they painted a vivid picture of the community, making data handling in 7th class a delightful journey for all the young mathematicians in the village.
What is Representative value?
You might be aware of the term average and would have come across statements involving the term ‘average’ in your day-to-day life:
* Isha spends on an average of about 5 hours daily for her studies.
* The average temperature at this time of the year is about 40 degree celsius.
* The average age of pupils in my class is 12 years.
* The average attendance of students in a school during its final examination was 98 per cent
Many more of such statements could be there. Think about the statements given above.
Do you think that the child in the first statement studies exactly for 5 hours daily?
Or, is the temperature of the given place during that particular time always 40 degrees?
Or, is the age of each pupil in that class 12 years? Obviously not.
Then what do these statements tell you?
By average we understand that Isha, usually, studies for 5 hours. On some days, she may study for less number of hours and on the other days she may study longer.
Similarly, the average temperature of 40 degree celsius, means that, very often, the temperature at this time of the year is around 40 degree celsius. Sometimes, it may be less than 40 degree celsius and at other times, it may be more than 40°C.
Thus, we realise that average is a number that represents or shows the central tendency of a group of observations or data. Since average lies between the highest and the lowest value of the given data so, we say average is a measure of the central tendency of the group of data. Different forms of data need different forms of representative or central value to describe it
Let's explore the key representative values: