Vaaneeidn
Answered

Get the most out of your questions with the extensive resources available on IDNLearn.com. Ask any question and get a detailed, reliable answer from our community of experts.

Daisy measured the heights of 20 plants. The table gives some information about the heights ([tex]\(h\)[/tex] in cm) of the plants.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Height of plants (\(h\)) & Frequency \\
\hline
\(0 \ \textless \ h \ \textless \ 10\) & 1 \\
\hline
\(10 \ \textless \ h \ \textless \ 20\) & 4 \\
\hline
\(20 \ \textless \ h \ \textless \ 30\) & 7 \\
\hline
\(30 \ \textless \ h \ \textless \ 40\) & 2 \\
\hline
\(40 \ \textless \ h \ \textless \ 50\) & 3 \\
\hline
\(50 \ \textless \ h \ \textless \ 60\) & 3 \\
\hline
\end{tabular}
\][/tex]

Using the midpoints of each group, work out an estimate for the mean height of a plant.

Answer: ______ cm

Sagot :

GinnyAnsweridn
To estimate the mean height of the plants, we need to use the midpoint of each height interval and the frequencies provided in the table. Here's a detailed, step-by-step solution:

### Step 1: Determine the Midpoints of each Interval
The midpoint of an interval is calculated as the average of the lower and upper boundaries of that interval.

For the given intervals:
- [tex]\(0 < h < 10\)[/tex]: Midpoint = [tex]\(\frac{0 + 10}{2} = 5\)[/tex]
- [tex]\(10 < h < 20\)[/tex]: Midpoint = [tex]\(\frac{10 + 20}{2} = 15\)[/tex]
- [tex]\(20 < h < 30\)[/tex]: Midpoint = [tex]\(\frac{20 + 30}{2} = 25\)[/tex]
- [tex]\(30 < h < 40\)[/tex]: Midpoint = [tex]\(\frac{30 + 40}{2} = 35\)[/tex]
- [tex]\(40 < h < 50\)[/tex]: Midpoint = [tex]\(\frac{40 + 50}{2} = 45\)[/tex]
- [tex]\(50 < h < 60\)[/tex]: Midpoint = [tex]\(\frac{50 + 60}{2} = 55\)[/tex]

These midpoints represent the average height within each interval.

### Step 2: List the Frequencies for each Interval
From the given data, the frequencies for each interval are:
- [tex]\(0 < h < 10\)[/tex]: Frequency = 1
- [tex]\(10 < h < 20\)[/tex]: Frequency = 4
- [tex]\(20 < h < 30\)[/tex]: Frequency = 7
- [tex]\(30 < h < 40\)[/tex]: Frequency = 2
- [tex]\(40 < h < 50\)[/tex]: Frequency = 3
- [tex]\(50 < h < 60\)[/tex]: Frequency = 3

### Step 3: Calculate the Total Number of Plants
The total number of plants is the sum of the frequencies:
[tex]\[ 1 + 4 + 7 + 2 + 3 + 3 = 20 \][/tex]

### Step 4: Calculate the Weighted Sum of the Midpoints
To find the weighted sum, multiply each midpoint by its corresponding frequency and then sum these products:
[tex]\[ (5 \times 1) + (15 \times 4) + (25 \times 7) + (35 \times 2) + (45 \times 3) + (55 \times 3) = 5 + 60 + 175 + 70 + 135 + 165 = 610 \][/tex]

### Step 5: Calculate the Estimated Mean Height
The estimated mean height is found by dividing the weighted sum of the midpoints by the total number of plants:
[tex]\[ \text{Mean Height} = \frac{\text{Weighted Sum}}{\text{Total Number of Plants}} = \frac{610}{20} = 30.5 \][/tex]

### Conclusion
The estimate for the mean height of a plant is:
[tex]\[ \boxed{30.5 \text{ cm}} \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.