On a certain​ exam, Tony corrected 2020 papers and found the mean for his group to be 6060. Alice corrected the remaining 1010 papers and found that the mean for her group was 8080. What is the mean of the combined group of 3030 ​students

Accepted Solution

Answer:The mean is 66.667 ( approx )Step-by-step explanation:Let x be the sum of Tony's group and y be the sum of Alice's group,We know that,[tex]Mean = \frac{\text{Total sum of observations}}{\text{Number of observations}}[/tex]According to the question,In Tony's group,Students = 20,Mean = 60,[tex]\implies \frac{x}{20}=60\implies x = 1200[/tex]In Alice's group,Students = 10,Mean = 80,[tex]\implies \frac{y}{10}=80\implies y = 800[/tex]Thus, the total sum of combined group of 30 students = 1200 + 800 = 2000,Hence, the mean of the combined group = [tex]\frac{2000}{30}[/tex][tex]\approx 66.667[/tex]