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To estimate the mean height of the sunflowers using the frequency table, we will:

1. Find the midpoint of each height bracket (since the data is grouped).
2. Multiply each midpoint by its corresponding frequency.
3. Sum the products from step 2.
4. Divide this sum by the total frequency to estimate the mean.

Let’s go step by step:

**1. Midpoints of the height brackets:**
- \( 50 - 59 \): Midpoint = \( \frac{50 + 59}{2} = 54.5 \)
- \( 60 - 69 \): Midpoint = \( \frac{60 + 69}{2} = 64.5 \)
- \( 70 - 79 \): Midpoint = \( \frac{70 + 79}{2} = 74.5 \)
- \( 80 - 89 \): Midpoint = \( \frac{80 + 89}{2} = 84.5 \)
- \( 90 - 99 \): Midpoint = \( \frac{90 + 99}{2} = 94.5 \)

**2. Multiply each midpoint by the frequency:**
- \( 54.5 \times 3 = 163.5 \)
- \( 64.5 \times 5 = 322.5 \)
- \( 74.5 \times 4 = 298 \)
- \( 84.5 \times 7 = 591.5 \)
- \( 94.5 \times 4 = 378 \)

**3. Sum the products:**
\( 163.5 + 322.5 + 298 + 591.5 + 378 = 1753.5 \)

**4. Divide by the total frequency (which is \( 3 + 5 + 4 + 7 + 4 = 23 \)):**
\[
\frac{1753.5}{23} \approx 76.24
\]

Rounding to the nearest whole number, the estimated mean height is **76 cm**.

Would you like further details or have any other questions?

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Here are 5 related questions to explore:
1. How would the mean change if the frequency of the tallest bracket increased?
2. What would be the effect of introducing another bracket for shorter sunflowers (e.g., 40–49 cm)?
3. How can we calculate the median height from this grouped data?
4. How does grouping data into intervals affect the precision of the mean?
5. What would the mode be in this frequency table?

**Tip:** Grouped data estimates the mean by assuming each value is represented by the midpoint of its range, which can slightly skew the results if the data is not evenly distributed.

A gardener was measuring the different heights of sunflowers in his allotment. The frequency table shows the number of sunflowers in the different height brackets. Use the information in the table to estimate the mean height of sunflowers in the allotment. Round your answer to the nearest whole number.

Learn how to estimate the mean height of sunflowers using a frequency table. This problem covers statistical concepts such as grouped data and mean calculation, making it suitable for students in Grades 6-8.

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