1. **Problem statement:** We have a sample of 760 potatoes with weights measured and a cumulative frequency curve given. We need to find: - (a) Number of potatoes weighing more than 200 grams. - (b) Median weight. - (c) Lower quartile. - (d) Upper quartile. - (e) Draw a box and whisker diagram using the given scale. 2. **Key concepts and formulas:** - The cumulative frequency curve shows the number of potatoes with weight less than or equal to a given value. - To find the number of potatoes with weight more than a certain value, subtract the cumulative frequency at that weight from the total number of potatoes. - Median corresponds to the 50th percentile (760/2 = 380th potato). - Lower quartile (Q1) corresponds to the 25th percentile (760/4 = 190th potato). - Upper quartile (Q3) corresponds to the 75th percentile (3*760/4 = 570th potato). 3. **Step-by-step solution:** **(a) Number of potatoes weighing more than 200 grams:** - From the graph, cumulative frequency at 200 grams is approximately 425. - Total potatoes = 760. - Number weighing more than 200 grams = $760 - 425 = 335$. **(b) Median weight:** - Median position = 380th potato. - From the graph, find the weight corresponding to cumulative frequency 380. - The curve shows cumulative frequency 380 corresponds to about 190 grams. - So, median weight $\approx 190$ grams. **(c) Lower quartile (Q1):** - Position = 190th potato. - From the graph, cumulative frequency 190 corresponds to about 140 grams. - So, lower quartile $\approx 140$ grams. **(d) Upper quartile (Q3):** - Position = 570th potato. - From the graph, cumulative frequency 570 corresponds to about 280 grams. - So, upper quartile $\approx 280$ grams. **(e) Box and whisker diagram:** - Minimum weight = 20 grams. - Lower quartile = 140 grams. - Median = 190 grams. - Upper quartile = 280 grams. - Maximum weight = 400 grams. Draw a box from 140 to 280 grams with a line at 190 grams inside the box. Draw whiskers from 20 to 140 grams and from 280 to 400 grams. This diagram visually represents the distribution of potato weights. **Final answers:** - Number of potatoes weighing more than 200 grams: $335$ - Median weight: $190$ grams - Lower quartile: $140$ grams - Upper quartile: $280$ grams