The following data shows the number of potatoes in twenty 2 kg bags. One graph represents Farm A, the other represents Farm B
Farm A: 8,9,11,13,13,16,19,19,19,20,21,21,23,25,26,27,30,31,33,33
Farm B: 9,9,11,11,12,13,13,14,15,16,17,17,18,19,20,21,21,22,24,30
You are interested in larger potatoes for baking. Which farm would you choose purchase from? Justify your answer by using measures of central tendency.
Mean = ∑x/n
Calculate means. Whichever bags has the fewer potatoes, would have (on average) the larger potatoes.
To determine which farm to choose for purchasing larger potatoes for baking, we can analyze the measures of central tendency, such as the mean, median, and mode, for both Farm A and Farm B.
1. Mean:
The mean is the average value of a dataset. We can calculate it by summing all the values and dividing by the total number of values.
Farm A: To find the mean of Farm A, we add up all the values and divide by the total number of bags (20 in this case).
Mean of Farm A = (8 + 9 + 11 + 13 + 13 + 16 + 19 + 19 + 19 + 20 + 21 + 21 + 23 + 25 + 26 + 27 + 30 + 31 + 33 + 33) / 20
Mean of Farm A = 460 / 20
Mean of Farm A = 23
Farm B: Similarly, for Farm B, we add up all the values and divide by the total number of bags (also 20 in this case).
Mean of Farm B = (9 + 9 + 11 + 11 + 12 + 13 + 13 + 14 + 15 + 16 + 17 + 17 + 18 + 19 + 20 + 21 + 21 + 22 + 24 + 30) / 20
Mean of Farm B = 352 / 20
Mean of Farm B = 17.6
2. Median:
The median is the middle value of a dataset when arranged in ascending order. If the dataset has an even number of values, the median is the average of the two middle values.
Farm A: To find the median of Farm A, we arrange the values in ascending order:
8, 9, 11, 13, 13, 16, 19, 19, 19, 20, 21, 21, 23, 25, 26, 27, 30, 31, 33, 33
As the dataset has an odd number of values (20), the median is the value in the middle, which is the 10th value from the lowest:
Median of Farm A = 20
Farm B: Similarly, for Farm B, we arrange the values in ascending order:
9, 9, 11, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 24, 30
Again, the dataset has an odd number of values (20), so the median is the value in the middle, which is the 10th value from the lowest:
Median of Farm B = 16
3. Mode:
The mode is the value(s) that appear most frequently in a dataset.
Farm A: In Farm A, multiple values appear more than once, but no value appears more frequently than others. Therefore, we can say that Farm A does not have a single mode.
Farm B: In Farm B, the value 13 appears twice, which is the most frequent value in the dataset.
Mode of Farm B = 13
Based on the measures of central tendency, we can conclude the following:
- The mean of Farm A is 23, while the mean of Farm B is 17.6. This suggests that, on average, Farm A may have larger potatoes than Farm B.
- The median of Farm A is 20, while the median of Farm B is 16. This also indicates that Farm A may have larger potatoes, as the middle value is higher.
- The mode of Farm B is 13, which means there are some bags of potatoes that are similar in size to those in Farm A. However, this does not change the overall trend suggesting Farm A may have larger potatoes.
Therefore, based on the measures of central tendency, it is more likely that Farm A would be a better choice for purchasing larger potatoes for baking.