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 130, Q1 at 162, median at 185, Q3 at 195, maximum at 290. The bottom box plot is labeled Basketball games. Minimum at 85, Q1 at 170, median at 200, Q3 at 225, maximum at 230.
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.
I think it is THE IQR is the best measurement of spread for games and movies. Please help
What was it?
Based on the given information, the interquartile range (IQR) is a better measure of spread for both movies and basketball games. The IQR represents the range of the middle 50% of the data, which helps to identify the spread of the data within that range. Comparing the IQR values, we can see that the IQR for movies is 195-162=33, while the IQR for basketball games is 225-170=55. Therefore, the IQR is a better measure of spread for basketball games compared to movies.
Based on the given information, the best measure of spread for both movies and basketball games is the Interquartile Range (IQR).
The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). In the box plots, the IQR for movies is 195 - 162 = 33, and for basketball games, it is 225 - 170 = 55.
The IQR is a good measure of spread because it focuses on the middle 50% of the data, capturing the range of values where most of the observations lie. It is less influenced by outliers in the data, providing a robust measure of spread.
On the other hand, standard deviation is a measure of the average distance of each data point from the mean. While it is a commonly used measure of spread, it is more sensitive to outliers and can be affected by extreme values in the data. Thus, in this case, the IQR is a better choice for measuring the spread of the data for both movies and basketball games.
To summarize, the statement "The IQR is the best measurement of spread for games and movies" accurately captures the best measure of spread for both sets of data.