Each year, actors, actresses, directors, producers, and many other talented individuals are nominated for the Academy of Motion Picture Arts and Sciences' Academy Awards, which are also called the Oscars. The table below shows five recent years and the movies each year that received the greatest number of nominations.

Detra and her brother studied this data and made a list of conclusions. Determine whether or not each of these conclusions is supported by the data in the table.

Of these 5 movies, the median number of nominations is 9.	Interactive popup. Assistance may be required. Hint The median is found by listing the numbers in order from least to greatest, and then identifying the middle number in the list.
	Interactive popup. Assistance may be required. Check Your Answer The conclusion is not supported by the data. The median number is 11, not 9.
The King's Speech received 50% more nominations than No Country for Old Men.	Interactive popup. Assistance may be required. Hint A percent increase is found by subtracting the two values, and then dividing the difference by the original value.
	Interactive popup. Assistance may be required. Check Your Answer The conclusion is valid. The King's Speech received 12 nominations, and No Country for Old Men received 8 nominations. 12 – 8 = 4, and 4 ÷ 8 = 0.50 = 50%.
The King's Speech received 4 over 3 4 3 times the nominations as Avatar.	Interactive popup. Assistance may be required. Hint Multiply the number of nominations received by Avatar by 4 over 3 4 3 .
	Interactive popup. Assistance may be required. Check Your Answer The conclusion is valid. The King's Speech received 12 nominations, and Avatar received 9 nominations. 9 × 4 over 3 4 3 = 12.

Practice

The population of Texas for recent years, according to the U.S. Census Bureau, is shown in the table.

Based on the information presented in the table, decide which of the following conclusions are valid or invalid.