Nutball12williamsidn
Answered

From tech troubles to travel tips, IDNLearn.com has answers to all your questions. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.

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

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

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

Sagot :

GinnyAnsweridn
To determine an estimate for the mean height of the plants, we follow these steps:

1. Identify the Midpoints of Each Height Interval:
To find the midpoint of each interval, we take the average of the lower and upper bounds of each height group. The intervals and their midpoints are:
- [tex]\( 0 \leq h < 10 \)[/tex]: Midpoint [tex]\( = \frac{0 + 10}{2} = 5 \)[/tex]
- [tex]\( 10 \leq h < 20 \)[/tex]: Midpoint [tex]\( = \frac{10 + 20}{2} = 15 \)[/tex]
- [tex]\( 20 \leq h < 30 \)[/tex]: Midpoint [tex]\( = \frac{20 + 30}{2} = 25 \)[/tex]
- [tex]\( 30 \leq h < 40 \)[/tex]: Midpoint [tex]\( = \frac{30 + 40}{2} = 35 \)[/tex]
- [tex]\( 40 \leq h < 50 \)[/tex]: Midpoint [tex]\( = \frac{40 + 50}{2} = 45 \)[/tex]
- [tex]\( 50 \leq h < 60 \)[/tex]: Midpoint [tex]\( = \frac{50 + 60}{2} = 55 \)[/tex]

2. List the Frequencies Corresponding to Each Interval:
The frequencies provided in the table are:
- [tex]\( 0 \leq h < 10 \)[/tex]: Frequency [tex]\( = 1 \)[/tex]
- [tex]\( 10 \leq h < 20 \)[/tex]: Frequency [tex]\( = 4 \)[/tex]
- [tex]\( 20 \leq h < 30 \)[/tex]: Frequency [tex]\( = 7 \)[/tex]
- [tex]\( 30 \leq h < 40 \)[/tex]: Frequency [tex]\( = 2 \)[/tex]
- [tex]\( 40 \leq h < 50 \)[/tex]: Frequency [tex]\( = 3 \)[/tex]
- [tex]\( 50 \leq h < 60 \)[/tex]: Frequency [tex]\( = 3 \)[/tex]

3. Calculate the Total Number of Plants:
The total number of plants is the sum of all frequencies:
[tex]\[ \text{Total Number of Plants} = 1 + 4 + 7 + 2 + 3 + 3 = 20 \][/tex]

4. Calculate the Weighted Sum of the Midpoints:
We multiply each midpoint by its corresponding frequency and then sum these products. This gives us the weighted sum:
[tex]\[ \text{Weighted Sum} = (5 \times 1) + (15 \times 4) + (25 \times 7) + (35 \times 2) + (45 \times 3) + (55 \times 3) \][/tex]
[tex]\[ = 5 + 60 + 175 + 70 + 135 + 165 = 610 \][/tex]

5. Calculate the Estimate for the Mean Height:
The mean height is obtained by dividing the weighted sum 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]

Thus, the estimated mean height of the plants is:
[tex]\[ \boxed{30.5 \text{ cm}} \][/tex]
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.