The box plots below show attendance at a local movie theater and high school basketball games: Two box plots shown. The top one is labeled Movies. Minimum at 60, Q1 at 65, median at 95, Q3 at 125, maximum at 150. The bottom box plot is labeled Basketball games. Minimum at 90, Q1 at 95, median at 125, Q3 at 145, maximum at 150. Which of the following best describes how to measure the spread of the data? The IQR is a better measure of spread for movies than it is for basketball games. The standard deviation is a better measure of spread for movies than it is for basketball games. The IQR is the best measurement of spread for games and movies. The standard deviation is the best measurement of spread for games and movies.
The Correct Answer and Explanation is :
To evaluate the spread of the data represented in the box plots for attendance at movies and basketball games, we need to consider both the interquartile range (IQR) and standard deviation as measures of spread.
Box Plot Summary
- Movies:
- Minimum: 60
- Q1: 65
- Median: 95
- Q3: 125
- Maximum: 150
- IQR = Q3 – Q1 = 125 – 65 = 60
- Basketball Games:
- Minimum: 90
- Q1: 95
- Median: 125
- Q3: 145
- Maximum: 150
- IQR = Q3 – Q1 = 145 – 95 = 50
Analysis of Spread
- Interquartile Range (IQR):
The IQR measures the middle 50% of the data and is less affected by outliers and extreme values. In this case:
- For movies, the IQR is 60, indicating a wider spread in attendance compared to basketball games, where the IQR is 50. Thus, the IQR indicates that the movies have a larger variation in attendance.
- Standard Deviation:
The standard deviation provides a measure of how much individual data points differ from the mean. However, it is sensitive to extreme values. Given the data:
- The attendance for movies has a wider range of values with a lower minimum (60) compared to basketball games (90). Therefore, the standard deviation for movies may be higher due to this increased variability.
Conclusion
While both IQR and standard deviation can measure spread, the IQR is generally more reliable in this scenario due to the presence of outliers (the minimum attendance for movies). Consequently, the IQR is the best measurement of spread for games and movies. It provides a clearer understanding of the central tendency and variability without being skewed by extreme values. Therefore, among the given options, stating that “the IQR is the best measurement of spread for games and movies” is correct.