Question

at the beginning of ms. carrolls gym class, the students voted for the game they wanted to play. there were 4 votes for kickball, 4 votes for basketball, 4 votes for soccer, and 8 votes for volleyball. select all of the statements that describe the data. the modes of the data are kickball, basketball, and soccer. there were more votes for soccer than for kickball. there were exactly 20 students in the class. fewer than half of the students voted for volleyball.

Explanation:

Step1: Calculate total number of votes

Total votes = \(4 + 4+4 + 8=20\)

Step2: Analyze mode

Mode is the value that appears most frequently. Kickball, basketball and soccer each have 4 votes (tied for most frequent if we consider non - unique maximum in a sense, as 4 is the value that repeats for three different games and 8 is a single value. In some definitions, if multiple values have the same highest frequency among non - unique cases, they can be considered modes).

Step3: Compare soccer and kickball votes

Soccer has 4 votes, kickball has 4 votes. So the statement “There were more votes for soccer than for kickball” is incorrect.

Step4: Check half of the class

Half of 20 is 10. Volleyball has 8 votes. \(8<10\)

Answer:

The modes of the data are kickball, basketball, and soccer.
There were exactly 20 students in the class.
Fewer than half of the students voted for volleyball.