From Raw Test Scores to Box-and-Whisker Visualizations

The cumulative frequency curve below shows the amount of weight loss, measured to the nearest kg, of 200 men in Glow Fitness Centre.

The corresponding cumulative frequency table for this distribution is as shown below.

1. Determine the value of \(a\).
2. Use your graph to find the
   1. median weight loss,
   2. interquartile range,
   3. \(44^{\mathrm{th}}\) percentile weight loss.
3. A second fitness centre, Saturn Fitness Centre also measured the amount of weight loss by \(200\) of their men. The box-and-whisker diagram below illustrates their weight loss achieved.
   
   1. Find the interquartile range.
   2. A physical instructor claimed that the weight loss program at Glow Fitness Centre is more effective than Saturn Fitness Centre. Explain if his statement is true.