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2. The test scores, of 16 students are listed below: 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. (b) Find the first quartile of the above data,

2. The test scores, of 16 students are listed below: 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. (b) Find the first quartile of the above data,

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 26PFA
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### Analyzing Test Scores of Students **Problem Statement:** 2. The test scores of 16 students are listed below: 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. (b) Find the first quartile of the above data. **Options:** - ⃝ 87 - ⃝ 88.5 - ⃝ 58.5 - ⃝ 57 **Explanation:** To find the first quartile (Q1) of a data set, which is the median of the lower half of the data, follow these steps: 1. Arrange the data in ascending order (already provided in the problem): 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. 2. Since there are 16 data points (an even number), the lower half consists of the first 8 numbers (first eight values): 44, 46, 51, 57, 60, 63, 65, 70. 3. Find the median of these first 8 numbers: - The median is the average of the 4th and 5th numbers when arranged in ascending order. - The 4th number is 57 and the 5th number is 60. 4. Calculate the median (First Quartile): \[ Q1 = \frac{57 + 60}{2} = 58.5 \] Therefore, the first quartile (Q1) of the given data is **58.5**. The correct option is: - ⃝ **58.5**
Transcribed Image Text:### Analyzing Test Scores of Students **Problem Statement:** 2. The test scores of 16 students are listed below: 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. (b) Find the first quartile of the above data. **Options:** - ⃝ 87 - ⃝ 88.5 - ⃝ 58.5 - ⃝ 57 **Explanation:** To find the first quartile (Q1) of a data set, which is the median of the lower half of the data, follow these steps: 1. Arrange the data in ascending order (already provided in the problem): 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. 2. Since there are 16 data points (an even number), the lower half consists of the first 8 numbers (first eight values): 44, 46, 51, 57, 60, 63, 65, 70. 3. Find the median of these first 8 numbers: - The median is the average of the 4th and 5th numbers when arranged in ascending order. - The 4th number is 57 and the 5th number is 60. 4. Calculate the median (First Quartile): \[ Q1 = \frac{57 + 60}{2} = 58.5 \] Therefore, the first quartile (Q1) of the given data is **58.5**. The correct option is: - ⃝ **58.5**
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