Question 1: A travel survey recorded the number of travelers from different regions. The cumulative frequency data shows the number of travelers at different distances. Using the data below, calculate the first quartile (Q1) of travelers by distance.

Answer: 15

Question 2: Determine the median (Q2) of the travel distances based on the cumulative frequency data provided in the table.

Answer: 30

Question 3: Calculate the third quartile (Q3) for the distances traveled by tourists. Use the cumulative frequency data from the map survey.

Answer: 45

Question 4: In a map survey, the cumulative frequency at 50 km is 60, at 70 km is 80, and total travelers are 80. Find Q2 (median) of the distribution.

Answer: 70

Question 5: A city’s transportation data shows cumulative travel frequency across zones. The cumulative frequency at 20 km is 25, at 40 km is 50, at 60 km is 70, and total travelers are 80. Find Q1 and Q3.

Answer: Q1=20, Q3=60

Question 6: A survey reports cumulative travel data. Identify the quartile position for a traveler who traveled 35 km, given the data shows cumulative frequencies: 10 at 10 km, 25 at 20 km, 45 at 30 km, and 60 at 40 km.

Answer: Q2 (median) is between 30 km and 40 km, likely around 35 km.

Question 7: A map shows cumulative frequency data for travelers from 0 to 100 km. Compute the interquartile range (IQR) using Q1 and Q3 values derived from the data.

Answer: IQR = Q3 - Q1

Question 8: Using the cumulative frequency data, identify the risk of misinterpreting the median if Q2 is incorrectly calculated as the midpoint of data points instead of using the actual data. Explain briefly.

Answer: Incorrect Q2 can lead to misjudging the median location, affecting data interpretation.

Question 9: Challenge: Given a set of cumulative frequency data for travel distances, find Q1, Q2, Q3, and then determine if the data is skewed based on the relative positions of the quartiles.

Answer: Students should calculate the quartiles and analyze their spacing.

Question 10: Mixed Review: For the cumulative frequency data, determine Q1 and Q3, then plot these quartiles on the map grid to visualize the spread of travel distances.

Answer: Q1 and Q3 plotted accordingly, showing data spread.

Question 11: Error Analysis: A student calculates Q2 as the average of the 25th and 75th data points rather than the median position. Explain why this might be wrong in the context of cumulative frequency data.

Answer: This method may not account for the actual data distribution; Q2 should be based on position, not data values.