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The number of tomatoes, of a certain size, that each plant produces is given in the tables below.

Plants given water only

\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Number of tomatoes per plant & 30 & 31 & 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 \\
\hline
Frequency & 2 & 3 & 3 & 4 & 4 & 2 & 1 & 0 & 0 & 0 & 1 \\
\hline
\end{tabular}

Plants given new food

\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Number of tomatoes per plant & 30 & 31 & 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 \\
\hline
Frequency & 3 & 3 & 1 & 1 & 0 & 0 & 0 & 4 & 4 & 1 & 3 \\
\hline
\end{tabular}

a) Calculate the mean, median, and mode of the number of tomatoes produced per plant for each set of data.

b) Calculate the range for each set of data.

c) Comment on any differences that you found in parts a) and b) and decide whether the new food affects the number of tomatoes produced per plant.



Answer :

GinnyAnswer
Sure! Let's go through each part of the question step-by-step.

### Part (a): Calculate the Mean, Median, and Mode for Each Set of Data

#### Plants Given Water Only
1. Mean:
- The mean number of tomatoes per plant for plants given water only is [tex]\(33.15\)[/tex].

2. Median:
- The median number of tomatoes per plant for plants given water only is [tex]\(33.0\)[/tex].

3. Mode:
- The mode of the number of tomatoes per plant for plants given water only is [tex]\([33, 34]\)[/tex].

#### Plants Given New Food
1. Mean:
- The mean number of tomatoes per plant for plants given new food is [tex]\(35.35\)[/tex].

2. Median:
- The median number of tomatoes per plant for plants given new food is [tex]\(37.0\)[/tex].

3. Mode:
- The mode of the number of tomatoes per plant for plants given new food is [tex]\([37, 38]\)[/tex].

### Part (b): Calculate the Range for Each Set of Data

The range is the difference between the maximum and minimum values.

#### Plants Given Water Only
- The range for the number of tomatoes per plant for plants given water only is [tex]\(10\)[/tex].

#### Plants Given New Food
- The range for the number of tomatoes per plant for plants given new food is also [tex]\(10\)[/tex].

### Part (c): Comment on Differences and the Effect of the New Food

1. Mean Comparison:
- The mean number of tomatoes per plant increased from [tex]\(33.15\)[/tex] with regular water to [tex]\(35.35\)[/tex] with the new food. This indicates that, on average, plants given the new food produced more tomatoes.

2. Median Comparison:
- The median number of tomatoes per plant also increased from [tex]\(33.0\)[/tex] with regular water to [tex]\(37.0\)[/tex] with the new food. This suggests a general shift in the distribution of tomato production to higher values when using the new food.

3. Mode Comparison:
- The mode shifted from [tex]\([33, 34]\)[/tex] with regular water to [tex]\([37, 38]\)[/tex] with the new food. This shift indicates that the most frequent number of tomatoes produced per plant increased with the new food.

4. Range Comparison:
- The range remained the same ([tex]\(10\)[/tex]) for both sets of data. This suggests that the spread or variability of the data did not change with the new food.

### Conclusion:

Based on the calculations for mean, median, and mode:
- The new food appears to have increased both the average and the most frequent number of tomatoes produced per plant.
- Despite these increases, the distribution of tomato production (as indicated by the range) remained constant.

Thus, the new food seems to have positively affected the number of tomatoes produced per plant by increasing the overall and most frequently occurring tomato counts while maintaining the variability within the same range.

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