Question
\( 110,164,140,151,184,150,157, \quad 153,153,160 \) Mr. McGregor has 28 students in his class. He selects 10 students and records their heights in centimeters. The height of each student is shown. Based on the sample, what is the best estimate for the median height of his students? (A) 153 (B) 155 (C) 157 (D) 167
Ask by Bowen Ortiz. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The median height is 153 cm.
Solution
We start by arranging the sample data in increasing order:
\[
110, \quad 140, \quad 150, \quad 151, \quad 153, \quad 153, \quad 157, \quad 160, \quad 164, \quad 184
\]
Since there are 10 data values in the sample, the median is the average of the 5th and 6th values.
The 5th value is \(153\) and the 6th value is also \(153\).
Thus, the median is calculated as:
\[
\text{Median} = \frac{153 + 153}{2} = \frac{306}{2} = 153
\]
Based on the sample, the best estimate for the median height of Mr. McGregor's students is \(\boxed{153}\), which corresponds to option (A).
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Beyond the Answer
To find the median height from Mr. McGregor's sample, we first need to organize the heights in ascending order: 110, 140, 151, 153, 153, 157, 160, 164, 184, 150. The median is the middle value in a sorted list. Since there are 10 heights (an even number), the median will be the average of the 5th and 6th values. The 5th value is 153 and the 6th value is 157. Calculating the median: \( \text{Median} = \frac{153 + 157}{2} = \frac{310}{2} = 155 \). So, the best estimate for the median height is (B) 155!