The table below shows the number of days per year during which the wind reaches a certainspeed expressed in km/hour. Use the table to answer the questions that follow.Wind Speed (km/h) Number of Days0 but less than 10 9710 but less than 20 10720 but less than 30 9130 but less than 45 4545 but less than 60 1860 but less than 80 7(a) Draw a histogram for this distribution.(6 marks)(b) Calculate, correct to one decimal place, the modal wind speed.(4 marks)(c) Form the cumulative frequency distribution.(2 marks)(d) Hence, construct the ogive.(6 marks)(e) From the ogive, estimate the median wind speed.(2 marks)(f) Use an appropriate formula to check your answer to part (e) of this question.

(a) To draw a histogram for this distribution, you would need to create a bar chart with the wind speed ranges on the x-axis and the number of days on the y-axis. Each bar would represent a wind speed range and its height would correspond to the number of days.

(b) The modal wind speed is the wind speed range with the highest frequency. In this case, it is the range "10 but less than 20" with 107 days. So, the modal wind speed is somewhere in this range. Since we don't have exact values, we can't calculate it to one decimal place.

(c) The cumulative frequency distribution is calculated by adding up the frequencies as you move along the wind speed ranges. Here it is:

0 but less than 10: 97 10 but less than 20: 97 + 107 = 204 20 but less than 30: 204 + 91 = 295 30 but less than 45: 295 + 45 = 340 45 but less than 60: 340 + 18 = 358 60 but less than 80: 358 + 7 = 365

(d) To construct the ogive, you plot the cumulative frequencies against the upper limit of each wind speed range on a graph. Then, you join the points with a smooth curve.

(e) The median wind speed is the wind speed that corresponds to the middle value of the cumulative frequency distribution. Since there are 365 days in a year, the middle value would be the 182.5th day. You would estimate this value from the ogive.

(f) To check your answer to part (e), you could use the formula for the median of a grouped frequency distribution: Median = L + [(N/2 - CF)/f] * c. Here, L is the lower class boundary of the group containing the median, N is the total number of observations, CF is the cumulative frequency of the group before the median group, f is the frequency of the median group, and c is the class width. However, since we don't have exact values for the wind speeds, we can't use this formula here.