Question 1184365: In January of 2017, you planted a rare variety of tomato. In 2 month time, you recorded the number of tomatoes harvested every week from various plots. Your data contained
140, 140, 100, 120, 110, 130, 110, 110, 140, 100, 130, 80.
A. Find the mean, mode, median and range for your data set of number of tomatoes. B. If the number of tomatoes doubles each week in the year 2017, what will be the mean, mode, median and range for the 2017 data? C. If, instead, there are five more tomatoes per week in the year 2017, what will be the mean, mode, median and range for the 2017 data?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's the analysis of your tomato harvest data:
**A. Original Data Analysis:**
* **Mean:** (140 + 140 + 100 + 120 + 110 + 130 + 110 + 110 + 140 + 100 + 130 + 80) / 12 = 120 tomatoes
* **Mode:** 110 and 140 (both appear 3 times)
* **Median:** First, order the data: 80, 100, 100, 110, 110, 110, 120, 130, 130, 140, 140, 140. The median is the average of the two middle numbers: (110 + 120) / 2 = 115 tomatoes
* **Range:** 140 (highest) - 80 (lowest) = 60 tomatoes
**B. Doubling Each Week:**
If the number of tomatoes doubles each week, we multiply each data point by 2:
280, 280, 200, 240, 220, 260, 220, 220, 280, 200, 260, 160
* **Mean:** (280 + 280 + 200 + 240 + 220 + 260 + 220 + 220 + 280 + 200 + 260 + 160) / 12 = 240 tomatoes (the mean also doubles)
* **Mode:** 220 and 280 (both appear 3 times)
* **Median:** Order the data: 160, 200, 200, 220, 220, 220, 240, 260, 260, 280, 280, 280. Median: (220 + 240) / 2 = 230 tomatoes
* **Range:** 280 - 160 = 120 tomatoes (the range also doubles)
**C. Five More Tomatoes Each Week:**
If there are five more tomatoes each week, we add 5 to each data point:
145, 145, 105, 125, 115, 135, 115, 115, 145, 105, 135, 85
* **Mean:** (145 + 145 + 105 + 125 + 115 + 135 + 115 + 115 + 145 + 105 + 135 + 85) / 12 = 125 tomatoes (the mean increases by 5)
* **Mode:** 115 and 145 (both appear 3 times)
* **Median:** Order the data: 85, 105, 105, 115, 115, 115, 125, 135, 135, 145, 145, 145. Median: (115 + 125) / 2 = 120 tomatoes
* **Range:** 145 - 85 = 60 tomatoes (the range stays the same)
**Key Observations:**
* When the data is scaled (multiplied by 2), the mean, mode, median, and range all scale by the same factor.
* When a constant is added to the data, the mean, mode, and median increase by that constant, but the range remains unchanged.
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