The Bough and Bud Company combined an insect spray with a growth hormone to produce the MOP
(More Oranges Production) Treatment, which was expected to increase the number of oranges
produced by each tree.
The data below shows the number of oranges produced by each tree in two separate samples of trees.
One group of trees (Group A) had been given the MOP treatment. The other (Group B) was kept under
identical conditions but was not given this treatment.
Group A (given the MOP treatment)
34 29 27 82 21 48 55 43 29 76
42 33 56 73 55 29 77 46 31 27
52 28 35 24 50 38 34 48 71 58
Group B (no special treatment)
32 37 56 39 33 61 45 52 38 60
32 44 33 54 40 64 41 29 30 61
41 32 38 32 42 48 56 63 57 33
You have been asked to write a report on the effectiveness or otherwise of this new treatment.
To determine the effectiveness of the MOP treatment on increasing the number of oranges produced by each tree, we can analyze the data provided for Group A (given the MOP treatment) and Group B (no special treatment). Let's start by calculating some key statistics for each group.
1. Calculate the mean (average) number of oranges produced for Group A and Group B:
- For Group A: Sum all the values and divide by the total number of observations (30).
- For Group B: Sum all the values and divide by the total number of observations (30).
2. Calculate the median number of oranges produced for Group A and Group B:
- Arrange the values in ascending order.
- If the total number of observations is odd, the median is the middle value.
- If the total number of observations is even, the median is the average of the two middle values.
3. Calculate the range of the number of oranges produced for Group A and Group B:
- Subtract the smallest value from the largest value in each group.
4. Calculate the standard deviation of the number of oranges produced for Group A and Group B:
- The standard deviation measures the amount of variation or dispersion in the data.
- Calculate the deviation of each observation from the mean.
- Square the deviations, sum them up, and divide by the total number of observations.
- Take the square root of the result to obtain the standard deviation.
After calculating these statistics, we can compare the results between Group A and Group B to determine the effectiveness of the MOP treatment.