This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to Question 2: 2.1 Estimate the median travel time. Step 1: Identify the total number of employees, N = 60. Step 2: The median corresponds to the (N)/(2) position, which is (60)/(2) = 30. Step 3: Locate 30 on the cumulative frequency (y-axis) and read the corresponding time on the x-axis from the ogive. Reading from the graph, a cumulative frequency of 30 corresponds to a travel time of 60 minutes. The estimated median travel time is 60 minutes. 2.2 Estimate the lower quartile. Step 1: The lower quartile (Q1) corresponds to the (N)/(4) position, which is (60)/(4) = 15. Step 2: Locate 15 on the cumulative frequency (y-axis) and read the corresponding time on the x-axis from the ogive. Reading from the graph, a cumulative frequency of 15 corresponds to a travel time of 40 minutes. The estimated lower quartile is 40 minutes. 2.3 Estimate the interquartile range. Step 1: The upper quartile (Q3) corresponds to the (3N)/(4) position, which is (3 × 60)/(4) = 45. Step 2: Locate 45 on the cumulative frequency (y-axis) and read the corresponding time on the x-axis from the ogive. Reading from the graph, a cumulative frequency of 45 corresponds to a travel time of 80 minutes. Step 3: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. IQR = 80 - 40 = 40 The estimated interquartile range is 40 minutes. 2.4 Draw a box and whisker diagram. Step 1: Determine the five-number summary for the box-whisker plot. • Minimum time = 5 minutes (given) • Lower Quartile (Q1) = 40 minutes (from 2.2) • Median (Q2) = 60 minutes (from 2.1) • Upper Quartile (Q3) = 80 minutes (from 2.3) • Maximum time = 120 minutes (given) To construct the box-whisker plot: • Draw a number line (scaled line) that covers the range from 0 to 120 minutes. • Mark the minimum value (5) and the maximum value (120) with whiskers. • Draw a box from the first quartile (Q1 = 40) to the third quartile (Q3 = 80). • Draw a vertical line inside the box at the median (Q2 = 60). 2.5 What percentage of the employees will be allowed to work from home for part of the day? Step 1: Identify the threshold for working from home. Employees who travel for an hour or more (60 minutes or more) are allowed to work from home. Step 2: Determine the number of employees who travel less than 60 minutes. From the ogive, at 60 minutes on the x-axis, the cumulative frequency is 30. This means 30 employees travel 60 minutes or less. Step 3: Calculate the number of employees who travel more than 60 minutes. Total employees = 60. Number of employees travelling more than 60 minutes = Total employees - (Cumulative frequency at 60 minutes) 60 - 30 = 30 employees Step 4: Calculate the percentage of employees who will work from home. Percentage = Number of employees travelling 60 minTotal number of employees × 100\% Percentage = (30)/(60) × 100\% = 50\% The percentage of employees who will be allowed to work from home is 50\%. 3 done, 2 left today. You're making progress.