Question 1: The estimated mean of grouped data is calculated using the formula: Σfx divided by Σf. Here, Σfx is the sum of the products of each class midpoint and its frequency, and Σf is the total frequency. This method provides an approximation of the average value within grouped data.

Answer:

Question 1: Calculate the estimated mean for the following grouped data: Class intervals: 10-19, 20-29, 30-39 Frequencies: 5, 8, 7

Answer: 22.5

Question 2: Given class intervals 0-9, 10-19, 20-29 with frequencies 4, 6, 10, calculate the estimated mean.

Answer: 17

Question 3: A grouped frequency table has class intervals 50-59, 60-69, 70-79 with frequencies 3, 5, 2. Find the estimated mean.

Answer: 63.5

Question 4: Plot a graph of y=2x for x values from 0 to 10 on the grid.

Answer: Students will draw the line y=2x

Question 5: Construct a triangle with sides measuring 3cm, 4cm, and 5cm on the grid.

Answer: Students will draw the triangle

Question 6: A table shows class intervals 0-9, 10-19, 20-29 with frequencies 2, 5, 3. Find the estimated mean.

Answer: 16

Question 7: Calculate the estimated mean for class intervals 15-24, 25-34, 35-44 with frequencies 6, 10, 4.

Answer: 27

Question 8: A village survey recorded the following ages grouped in ranges: 20-29 (12 people), 30-39 (15 people), 40-49 (8 people). Calculate the estimated average age.

Answer: Approximately 34.5

Question 9: A class has the following frequency distribution: Class: 0-10, 11-20, 21-30 Frequencies: 4, 9, 7 Calculate the estimated mean using the class midpoints.

Answer: 20

Question 10: Identify and correct the mistake in this calculation of the estimated mean: Frequencies: 3, 7, 5 Midpoints: 5, 15, 25 Σfx = 3×5 + 7×15 + 5×25 = 15 + 105 + 125 = 245 Σf = 3 + 7 + 5 = 15 Estimated mean = 245/15 ≈ 16.33

Answer: The mistake is in the calculation of Σfx; actual sum is 15 + 105 + 125 = 245, which is correct, but the midpoints or frequencies may be inconsistent with the data or the segments misaligned. Students should identify the mismatch or re-verify the data.