Connecting | Class 7 Mathematics Notes

5.2 Representative Values

This section focuses on how to summarize and compare groups of numerical data using representative values. It begins with a comparison of cricket players' performances based on runs scored in matches. Different perspectives are presented: comparing individual match scores, total runs, and consistency (difference between maximum and minimum scores). The section highlights the difficulty in comparing groups of numbers directly and introduces the concept of a single representative number. The total sum of values is one way, but it may not be appropriate when group sizes differ. To address this, the arithmetic mean or average is introduced as a balanced representative value calculated by dividing the total sum by the number of values. Examples include calculating the average runs scored by players in matches and understanding the average as a fair-share or equal-share. The section also connects the concept of average to ancient Indian mathematics, where terms like samamiti and samarajju reflect the idea of an equalizing measure. Several activities encourage students to calculate averages in different contexts, such as bouncing a ball, counting flowers, running times, and school enrolment. The section concludes with a discussion on comparing data sets using averages and other measures like minimum, maximum, and range, illustrated through the example of onion prices in two towns.

📊 Diagram: Shreyas says, "Both their performances are similar since Yashasvi scored more in the first and second matches, whereas Shubman scored more in the third and fourth"; Table showing runs scored by Shubman and Yashasvi in matches; Images illustrating data examples; Try This activity figure.

🧪 Activity: Calculate the average number of bounces Shreyas can make with a ball on a bat over 8 attempts; Track the number of flowers blooming daily for a week and find the average; Compare running times of two friends over a week; Find the mean enrolment in a school over six years.

🔗 Connection: This section's discussion on averages sets the stage for understanding data variability and other measures like median and outliers, which are covered in the next sections.