AGB 311: Agribusiness statistics Assignment 1 (Units 1 and 5) Due date (ODL): 29th October, 2023 1) In a study to examine consumer preference for milk in Kabwe, a randomly selected number of consumers were asked to indicate the number of times each of them drunk a full cup of milk in the past one month. The data below presents the number of times each responded indicated. 5, 9, 0, 3, 1, 1, 6, 0, 5, 9, 0, 3 Treating this data as ungrouped data, determine the following: a) Mean (1) b) Median (1) c) Mode (1) d) Mean absolute deviation (1) e) Variance (1) f) Standard deviation (1) g) What shape of distribution is exhibited by the data above? Explain. (1) h) Use a bar graph to depict the dataset above (1) i) Interpret your answer in part c above. (1) 2) The manager of a local agro-store is studying the number of items purchased by customers in the late afternoon hours of each day of the week. Listed below is the number of items for a sample of 20 customers. 3, 23, 7, 17, 12, 18, 2, 20, 9, 16, 4, 17, 8, 19, 3, 18, 5, 9, 17, 3, 20, 7, 13, 2, 14 a) Develop a frequency distribution using a class width of 5. (Note: The lower limit of the first class must be 1 (one)). b) Using the frequency distribution developed in part a above, determine the following 1) Mean (1) 2) Median (1) 3) Mode (1) 4) Mean absolute deviation (1) 5) Variance (1) 6) Standard deviation (1) 7) What shape of distribution is exhibited by the data above? Explain. (1) 8) Present the data above in a histogram (1) 9) Interpret your answer in part 6 above? (1) 3) The use of family members as a source of labor is one of the oldest concepts of farm management. Several studies have attempted to model the relationship between household size and area cultivated for food production. The argument is that the number of family members of a farming household affects the area cultivated by the household. Assuming that a study in Mpongwe district revealed the following data: Area cultivated (ha) Number of household members 3 4 2 1 1 3 1 4 Use this data to, a) Plot the best straight line to fit this data (1) b) Determine the least square regression equation for this data (4) c) Interpret the regression equation in part b above. (2) d) Would you agree that the number of household members is statistically significant in influencing the area farming households cultivate? Test this at the 5% level of significance. (5) e) By how much are variations in the area cultivated explained by variations in the household size? (3) 4) In a bid to understand drivers of cassava farming in Chibombo district, an agribusiness and agricultural economics research class of 2022 took a trip to collect data from small holder farmers in Chibombo district. Among many other things, they wanted to determine whether the number of years individual farming households have been growing cassava is influenced by the gender of the head of the house. Assume that part of the data collected by the students is as presented in the table below: Gender of the household head Number of years the household has been growing cassava 0 4 1 4 0 2 0 3 1 4 1 1 0 3 1 4 Use this data to, a) Plot the best straight line to fit this data (1) b) Determine the least square regression equation for this data (4) c) Interpret the regression equation in part b above. (2) d) Is gender of the household head statistically significant in influencing how long the household has been engaged in cassava farming in Chibombo district? Test this at the 5% level of significance. (5) e) By how much are variations in the number of years the household has been growing cassava explained by variations in the gender of the household head? (3) THE END.