The tech company wants to change the reward system so that the median number of rewards is increased and the interquartile range is increased. They make some changes and take a new sample of 500 customers. The cumulative frequency graph for the new data is shown. Use the graph to find the median and interquartile range for the new sample.

This question requires reading values from a cumulative frequency graph. The total frequency (the maximum value on the y-axis) is 500. 1. **Median (Q2)**: The median is found at the 50% point of the data. * Position = 0.5 × 500 = 250. * On the graph, locating 250 on the vertical axis, moving horizontally to the curve, and then vertically down to the horizontal axis gives a value of **2 rewards**. 2. **Lower Quartile (Q1)**: The lower quartile is found at the 25% point. * Position = 0.25 × 500 = 125. * On the graph, locating 125 on the vertical axis, moving across to the curve, and down to the horizontal axis gives a value of **1 reward**. 3. **Upper Quartile (Q3)**: The upper quartile is found at the 75% point. * Position = 0.75 × 500 = 375. * On the graph, locating 375 on the vertical axis, moving across to the curve, and down to the horizontal axis gives a value of **3 rewards**. 4. **Interquartile Range (IQR)**: The IQR is the difference between the upper and lower quartiles. * IQR = Q3 - Q1 = 3 - 1 = **2**.