Question 1: Given the frequency table below, calculate the mean: | Class Interval | Frequency | |------------------|-----------| | 1 - 3 | 4 | | 4 - 6 | 6 | | 7 - 9 | 2 | Use the formula Σfx / Σf.

Answer: 4.88

Question 2: A student calculates the mean from a frequency table as 5.2. The total frequency is 20. The sum of fx (Σfx) is missing. What is the value of Σfx?

Answer: 104

Question 3: In a frequency table, a student mistakenly sums the class midpoints times frequencies but forgets to divide by the total frequency. What error have they made?

Answer: They calculated the sum of fx but did not divide by Σf to find the mean.

Question 4: The class intervals are 10-20, 20-30, 30-40 with respective frequencies 5, 8, 7. Find the mean using Σfx / Σf.

Answer: 26.09

Question 5: A table shows the ages of students: | Age | Frequency | |-----|-----------| | 10 | 3 | | 11 | 5 | | 12 | 2 | | 13 | 4 | Calculate the mean age.

Answer: 11.09

Question 6: Identify the error in this student's calculation: They obtained Σfx = 50 and Σf = 10, then calculated the mean as 5, which is correct. However, the actual Σfx was 60. What's the mistake?

Answer: They used the wrong sum for Σfx; it should be 60, not 50.

Question 7: A frequency table lists scores: 1-3 (3 students), 4-6 (5 students), 7-9 (4 students). The midpoints are 2, 5, 8 respectively. Calculate Σfx and then the mean.

Answer: Σfx = 2×3 + 5×5 + 8×4 = 6 + 25 + 32 = 63; mean = 63 / 12 = 5.25

Question 8: A teacher notes that some students mistakenly add the class midpoints times frequencies but forget to divide by total frequency. How can this mistake be corrected?

Answer: They need to divide the total Σfx by Σf to find the mean.

Question 9: A table shows the number of books read in a month: | Number of Books | Frequency | |-------------------|-----------| | 0 - 2 | 4 | | 3 - 5 | 6 | | 6 - 8 | 2 | Calculate the approximate mean number of books read using midpoints.

Answer: Approximate mean = (1 + 4 + 7)/2 = 2.5, 4.5, 7; Σfx = 2.5×4 + 4.5×6 + 7×2 = 10 + 27 + 14 = 51; total f= 12; mean= 51/12= 4.25

Question 10: Construct a frequency table with class intervals 0-10, 10-20, 20-30 and frequencies 3, 7, 5. Calculate the mean from the table.

Answer: Midpoints: 5, 15, 25; Σfx= 5×3 + 15×7 + 25×5= 15 + 105 + 125= 245; Σf= 15; mean= 245/15=16.33

Question 11: A student finds the mean from a frequency table as 8.5, but the total frequency was incorrectly summed as 12 instead of 15. How does this mistake affect the calculation?

Answer: The mean is underestimated because the total frequency is too low; dividing Σfx by 12 instead of 15 results in a higher mean than actual.