Tales by Dots and LinesClass 8 Mathematics Case Study Questions

Virat, a star cricketer, played a T20 series consisting of 6 matches. His scores in five of the matches were 42, 55, 30, 78, and 25. The score for the fourth match was not recorded properly, but the team statistician announced that his average (mean) score for the entire 6-match series was 50 runs. Virat's performance is crucial for the team's morale and strategy. The coach wants to analyze his consistency and performance under pressure. The median score is often used alongside the mean to understand the 'typical' performance, as it is less affected by unusually high or low scores. The analysis will help in planning for the upcoming final match of the tournament.

A mathematics teacher, Mrs. Sharma, conducted a class test for 40 students. The test was out of 10 marks. To analyze the performance, she created a frequency table of the marks obtained. The table shows how many students scored each possible mark. She wants to calculate the class average (mean) to get an overall sense of performance and the median to find the 'middle' score. This will help her identify if the test was too difficult or if certain topics need to be retaught. Understanding the distribution of scores is a key part of effective teaching and assessment.

The data is as follows:

The line graph below shows the average monthly maximum temperatures for two cities, City A and City B, over a period of one year. Such graphs are used by meteorologists to compare climate patterns between different locations. The horizontal axis represents the months from January to December, and the vertical axis represents the temperature in degrees Celsius ($^{\circ}$C). By analyzing the trends, peaks, and troughs, we can infer information about the seasons in each city and how they differ. For example, a city with a large temperature variation might experience more distinct seasons compared to one with a flatter temperature curve. The data points are: City A: (Jan, 15), (Feb, 18), (Mar, 22), (Apr, 28), (May, 35), (Jun, 38), (Jul, 34), (Aug, 33), (Sep, 30), (Oct, 25), (Nov, 20), (Dec, 16) City B: (Jan, 28), (Feb, 29), (Mar, 31), (Apr, 32), (May, 31), (Jun, 30), (Jul, 29), (Aug, 29), (Sep, 30), (Oct, 30), (Nov, 29), (Dec, 28)