Question 1: A class survey recorded the number of books students read in a month: 2, 3, 4, 3, 5. Calculate the estimated mean number of books read per student.

Answer: 3.4

Question 2: Given the grouped data: Class interval 0-4, frequency 5; 5-9, frequency 8; 10-14, frequency 12; calculate Σfx.

Answer: Σfx= (2*5)+(7*8)+(12*12)= (10)+(56)+(144)=210

Question 3: Using the previous data, find the estimated mean using Σfx/Σf.

Answer: 210/25=8.4

Question 4: A table shows exam scores grouped as 50-59, 60-69, 70-79, with frequencies 4, 10, and 6 respectively. The midpoints are 54.5, 64.5, 74.5. Calculate Σfx and find the estimated mean.

Answer: Σfx= (54.5*4)+(64.5*10)+(74.5*6)= 218+645+447=1310; Σf=4+10+6=20; mean=1310/20=65.5

Question 5: A survey records the hours spent on homework: 1, 2, 2, 3, 4, 4, 5. Calculate the estimated mean.

Answer: 2.9

Question 6: In a grouped frequency table, the total sum of fx is 480, and the total frequency Σf is 60. Determine the estimated mean.

Answer: 8

Question 7: A class recorded students' ages in groups: 10-14, 15-19, 20-24 with frequencies 7, 12, 9. The midpoints are 12, 17, 22. Calculate Σfx and the estimated mean age.

Answer: Σfx= (12*7)+(17*12)+(22*9)= 84+204+198=486; Σf=7+12+9=28; mean=486/28≈17.36

Question 8: A data set shows the number of hours students sleep: 5, 6, 7, 8, 9, 10, with frequencies 2, 5, 8, 7, 3. Calculate the estimated mean sleep hours.

Answer: 7.2

Question 9: Identify and correct the mistake: A student calculates the estimated mean as Σfx divided by total frequency, but they mistakenly sum the fx values as 300 and total frequency as 50, giving a mean of 10. The actual Σfx is 250. What is the correct estimated mean?

Answer: 250/50=5

Question 10: Given grouped data: Class interval 0-10, frequency 6; 10-20, 9; 20-30, 5. The midpoints are 5, 15, 25. Calculate the estimated mean and interpret its meaning in context.

Answer: Σfx= (5*6)+(15*9)+(25*5)=30+135+125=290; Σf=6+9+5=20; mean=290/20=14.5; Average score around 14.5 in the data.