Comparing Distributions, Medians, and Means

Class A and Class B both have a mean score of 80. Class A has a standard deviation of 4, while Class B has a standard deviation of 16. Which class is more uniform?

Class A is more uniform because a smaller standard deviation indicates that scores cluster closer to the average.

Find the mean and the median of the following test scores: 65, 75, 80, 85, 95.

Mean is 80 (400 divided by 5). Median is 80 (the third value in the ordered list).

If the score 95 in the previous set is replaced with 120, what is the new mean and the new median?

New mean is 85 (425 divided by 5). The median remains 80.

A student scored 70, 82, and 76 on three quizzes. What score must they get on the fourth quiz to reach an overall average of 80?

92. Required total is 4 times 80 = 320. Current sum is 70 + 82 + 76 = 228. Missing score is 320 - 228 = 92.

A student needs an average of 85 across four exams. Their first three scores are 60, 65, and 70. Can they reach their goal on a test graded out of 100?

No. Required total is 4 times 85 = 340. Current sum is 195. They would need 340 - 195 = 145, which is impossible on a 100-point test.

Group 1 has 10 students with an average of 70. Group 2 has 30 students with an average of 90. Can you calculate the combined average by doing (70 + 90) / 2? Why or why not?

No. The groups are different sizes. You must compute the weighted mean: (10*70 + 30*90) / 40 = (700 + 2700) / 40 = 3400 / 40 = 85.

True or False: A high standard deviation always means that the class received high marks.

False. Standard deviation measures the spread of marks around the average, not how high or low the scores are.