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Calculate an estimate of the mean height of the students. Give your answer in centimetres (cm). Bight(5) \( 120
Ask by Carter Rodriquez. in Spain
Feb 03,2025

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The estimated mean height of the students is 137 cm.

Solución

To estimate the mean height of the students based on the provided frequency distribution, follow these steps: ### **1. Organize the Data** Assume the data represents a frequency distribution table with class intervals and corresponding frequencies: | **Height Interval (cm)** | **Frequency (f)** | |--------------------------|-------------------| | 120 < x ≤ 130 | 2 | | 130 < x ≤ 140 | 12 | | 140 < x ≤ 150 | 6 | | **Total** | **20** | ### **2. Determine the Midpoint for Each Class Interval** The midpoint (\( m \)) of each class interval is calculated as: \[ m = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \] | **Height Interval (cm)** | **Midpoint (m)** | |--------------------------|------------------| | 120 < x ≤ 130 | 125 | | 130 < x ≤ 140 | 135 | | 140 < x ≤ 150 | 145 | ### **3. Calculate the Product of Midpoint and Frequency** Compute \( m \times f \) for each class: | **Midpoint (m)** | **Frequency (f)** | **\( m \times f \)** | |------------------|-------------------|----------------------| | 125 | 2 | 250 | | 135 | 12 | 1,620 | | 145 | 6 | 870 | ### **4. Sum the Products and Total Frequencies** \[ \sum (m \times f) = 250 + 1,620 + 870 = 2,740 \] \[ \sum f = 2 + 12 + 6 = 20 \] ### **5. Calculate the Mean Height** \[ \text{Mean Height} = \frac{\sum (m \times f)}{\sum f} = \frac{2,740}{20} = 137 \text{ cm} \] ### **Conclusion** The estimated mean height of the students is **137 centimeters**.

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To calculate the estimated mean height of the students, we need to find the midpoint for each height interval, multiply it by the frequency of students in that interval, and then divide by the total number of students. 1. **Calculate Midpoints**: - For \( 120 < x \leq 130 \): Midpoint = \( (120 + 130) / 2 = 125 \) cm - For \( 130 < x \leq 140 \): Midpoint = \( (130 + 140) / 2 = 135 \) cm - For \( 140 < x \leq 150 \): Midpoint = \( (140 + 150) / 2 = 145 \) cm 2. **Multiply Midpoints by Frequencies**: - \( 125 \times 2 = 250 \) - \( 135 \times 12 = 1620 \) - \( 145 \times 6 = 870 \) 3. **Calculate Total**: - Sum of products = \( 250 + 1620 + 870 = 2740 \) 4. **Calculate Total Frequency**: - Total students = \( 2 + 12 + 6 = 20 \) 5. **Estimate Mean Height**: - Mean height = \( 2740 / 20 = 137 \) cm Thus, the estimated mean height of the students is **137 cm**!

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