Face 1 2 3 4 5 6 Frequency 12 18 \(y\) 30 \(2y\) 45 Given the table above as the result of tossing a fair die 150 times, find the mode.

Answer Details

The mode is the value that occurs most frequently in the data set. From the table, we can see that the frequencies for faces 1, 2, 4, 5, and 6 are all different. However, the frequency for face 3 is "y", which is an unknown value. To find the mode, we need to determine the value of y. We know that the die was tossed 150 times, so the sum of all the frequencies should be 150. 12 + 18 + y + 30 + 2y + 45 = 150 Simplifying the equation, we get: 3y + 105 = 150 3y = 45 y = 15 Now we can see that the frequency for face 3 is 15. To find the mode, we need to determine which face has the highest frequency. We can see that face 6 has the highest frequency with 45 occurrences. Therefore, the mode is 6.