Cherry makes gourmet chocolates and sells them at markets and craft fairs. In one evening at a market, she sold packages of the following sizes: 175 g, 170 g. 185 g. 250 g. 75 g, 100 g, 100 g, 175 g. 100 g, 75 g, 250 g, 175 g, 250 g, 175 g
a) Calculate the mean, median, and mode package sizes.
b) Cherry is deciding on how many packages of each size she should bring to the next market. Which measure of central tendency should she use to help her decide? Explain your answer
a) To calculate the mean package size, we add up all the package sizes and divide by the total number of packages:
Total weight = 175 + 170 + 185 + 250 + 75 + 100 + 100 + 175 + 100 + 75 + 250 + 175 + 250 + 175
Total weight = 2195
Mean = Total weight / Number of packages
Mean = 2195 / 14
Mean = 156.79 g
To find the median package size, we need to first arrange the package sizes in ascending order: 75, 75, 100, 100, 100, 170, 175, 175, 175, 175, 185, 250, 250, 250
Since there are 14 packages, the median is the average of the 7th and 8th terms: (175 + 175) / 2 = 175 g
The mode is the package size that appears most frequently. In this case, the mode is 175 g as it appeared 4 times, more than any other size.
b) Cherry should use the mode as the measure of central tendency to help her decide how many packages of each size she should bring to the next market. This is because the mode represents the most common package size sold in the previous market, indicating the most popular choice among customers. By bringing more of the mode package size, Cherry can maximize her sales potential at the next market.