Select the correct answer.
The table shows the number of hours Hazel worked per week at her part-time job for the last 20 weeks.
| 9 | 22 | 16 | 12 | 16 | 10 | 22 | 16 | 17 | 8 |
| 20 | 18 | 10 | 20 | 25 | 6 | 14 | 10 | 14 | 20 |
Identify the five number summary (lowest value, first quartile, median, third quartile, and highest value) for the corresponding box plot.
A. $6,12,18,22,25$
B. $6,12,16,20,25$
C. $6,10,17,22,25$
D. $6,10,16,20,25$
Answer (2)
Sort the data: [ 6 , 8 , 9 , 10 , 10 , 10 , 12 , 14 , 14 , 16 , 16 , 16 , 17 , 18 , 20 , 20 , 20 , 22 , 22 , 25 ]
Find the minimum and maximum: 6 and 25 .
Calculate the median: 2 16 + 16 = 16 .
Calculate Q1 and Q3: 2 10 + 10 = 10 and 2 20 + 20 = 20 .
The five-number summary is 6 , 10 , 16 , 20 , 25 .
Explanation
Understand the problem and provided data We are given a dataset of 20 values representing the number of hours Hazel worked per week for the last 20 weeks. Our goal is to identify the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum, which corresponds to a box plot.
Sort the data First, we need to sort the data in ascending order to easily identify the required values. The sorted data is: [ 6 , 8 , 9 , 10 , 10 , 10 , 12 , 14 , 14 , 16 , 16 , 16 , 17 , 18 , 20 , 20 , 20 , 22 , 22 , 25 ]
Identify minimum and maximum Now we can identify the minimum and maximum values directly from the sorted data: Minimum = 6 Maximum = 25
Calculate the median (Q2) Next, we calculate the median (Q2) of the sorted data. Since there are 20 values (an even number), the median is the average of the 10th and 11th values: Median = 2 16 + 16 = 16
Calculate the first quartile (Q1) Now, we calculate the first quartile (Q1), which is the median of the lower half of the data (the first 10 values). Since there are 10 values, Q1 is the average of the 5th and 6th values: Q1 = 2 10 + 10 = 10
Calculate the third quartile (Q3) Then, we calculate the third quartile (Q3), which is the median of the upper half of the data (the last 10 values). Since there are 10 values, Q3 is the average of the 15th and 16th values: Q3 = 2 20 + 20 = 20
Present the five-number summary Finally, we present the five-number summary as: minimum, Q1, median, Q3, maximum: 6 , 10 , 16 , 20 , 25 This corresponds to option D.
Examples
Understanding the five-number summary is crucial in many real-world scenarios. For instance, in analyzing student test scores, the five-number summary helps educators quickly grasp the distribution of scores, identify outliers, and compare performance across different classes. Similarly, in finance, it can be used to analyze stock prices, providing a concise overview of price ranges and central tendencies, aiding investment decisions. This statistical tool offers a simple yet powerful way to summarize and interpret data in various fields.
A current of 15.0 A flowing for 30 seconds results in a total charge of 450 C . This transfers approximately 2.81 × 1 0 21 electrons through the device during this time period.
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