Draw a cumulative frequency curve (ogive) and find the median number of eggs laid by chickens based on the provided frequency distribution.

~Gracina~, let's knock this out. To solve this problem, we first need to prepare a cumulative frequency table. Step 1: Prepare the Cumulative Frequency Table We need to determine the class boundaries and then calculate the cumulative frequencies. | No. of eggs | Class Boundaries | No. of Chicken (f) | Cumulative Frequency (cf) | | :---------- | :--------------- | :------------------- | :-------------------------- | | | 44.5 | 0 | 0 | | 45-49 | 44.5 - 49.5 | 10 | 10 | | 50-54 | 49.5 - 54.5 | 36 | 10 + 36 = 46 | | 55-59 | 54.5 - 59.5 | 64 | 46 + 64 = 110 | | 60-64 | 59.5 - 64.5 | 52 | 110 + 52 = 162 | | 65-69 | 64.5 - 69.5 | 28 | 162 + 28 = 190 | | 70-74 | 69.5 - 74.5 | 10 | 190 + 10 = 200 | The total number of chickens, N = 200. a) Draw a Cumulative Frequency Curve (Ogive) Step 2: Explain how to draw the Ogive To draw the cumulative frequency curve, plot the cumulative frequency (cf) against the upper class boundaries. The points to plot are: (44.5, 0), (49.5, 10), (54.5, 46), (59.5, 110), (64.5, 162), (69.5, 190), and (74.5, 200). Connect these points with a smooth curve. The x-axis represents the number of eggs, and the y-axis represents the cumulative frequency. b) Use your graph to find Since I cannot draw a graph, I will calculate the values using interpolation formulas, which yield the same results as reading from a precisely drawn ogive. i) The median Step 3: Calculate the Median The median is the value at the (N)/(2)-th position. Median position = (200)/(2) = 100. From the cumulative frequency table, the 100th value falls in the 55-59 class (cumulative frequency 110). Median class: 55-59 (boundaries 54.5 - 59.5). Lower boundary of median class (L) = 54.5 Frequency of median class (f_m) = 64 Cumulative frequency of class before median class (cf_b) = 46 Class width (c) = 59.5 - 54.5 = 5 Median = L + ((N)/(2) - cf_bf_m)c Median = 54.5 + ((100 - 46)/(64))5 Median = 54.5 + ((54)/(64))5 Median = 54.5 + 4.21875 = 58.72 eggs ii) The interquartile range Step 4: Calculate the First Quartile (Q_1) The first quartile is the value at the (N)/(4)-th position