Michael records the number of miles he runs each week for nine weeks. 6, 11, 13, 8, 15, 9, 11, 5, 9 Which box plot represents the data?
The correct answer and explanation is :
To determine which box plot represents Michael’s weekly mileage data, we must calculate the five-number summary, which includes:
- Minimum
- First Quartile (Q1)
- Median (Q2)
- Third Quartile (Q3)
- Maximum
Step 1: Arrange the data in ascending order
5, 6, 8, 9, 9, 11, 11, 13, 15
Step 2: Identify the five-number summary
- Minimum: 5
- Maximum: 15
- Median (Q2): The middle value is the 5th number: 9
- Lower Half: 5, 6, 8, 9
- Q1 (Median of lower half): (6 + 8)/2 = 7
- Upper Half: 11, 11, 13, 15
- Q3 (Median of upper half): (11 + 13)/2 = 12
Final Five-Number Summary:
- Minimum: 5
- Q1: 7
- Median (Q2): 9
- Q3: 12
- Maximum: 15
What should the box plot look like?
- The left whisker extends from 5 to 7
- The box goes from 7 to 12, with a line at 9 (the median)
- The right whisker extends from 12 to 15
Explanation:
A box plot, also called a box-and-whisker plot, graphically represents the distribution of a data set. It shows central tendency and variability without displaying all individual data points.
- The box represents the interquartile range (IQR), which contains the middle 50% of the data (from Q1 to Q3).
- The line inside the box is the median, showing the data’s center.
- The whiskers extend from the box to the minimum and maximum values, showing the full data range.
This plot helps detect skewness and outliers. In this case, the data are fairly symmetric, and no extreme outliers exist.
The correct box plot will have:
- Whiskers at 5 and 15
- Box from 7 to 12
- Line at 9