A school teacher wants to analyse results. Identify the appropriate statistical technique to be used along with its justification for the following cases:

1. Teacher wants to compare performance in terms of division secured by students in Class XII A and Class XII B where each class strength is same.

2. Teacher has conducted five unit tests for that class in months July to November and wants to compare the class performance in these five months.

1. Standard deviation is the statistical technique used for comparing the performance of students in Class XII A and Class XII B. It considers all division scores, measuring their spread around the given data. Smaller value of standard deviation means data are less spread while a larger value of standard deviation means data are more spread. By comparing standard deviations, the teacher can statistically assess the performance differences between the two classes, helping to identify trends and the overall variability in division scores.

2. To compare class performance in five unit tests from July to November, calculate the mean of students marks for each month. Compare the mean marks across successive months, if the mean increases, the class performance is improving, while a decrease indicates a lack of improvement.