Question

1. what is the mode of the following data set? 2, 3, 3, 5, 7, 8, 8, 9

a. 3
b. 8
c. 5
d. 3 and 8

1. what is the mean of the following numbers?

4, 6, 8, 10, 12
a. 6
b. 8
c. 10
d. 12

1. if the median of a dataset is 15, which of the following is true?

a) most values are less than 15
b) half of the values are less than 15

Explanation:

Step1: <Find the mode>

Mode is the number that appears most frequently. In the data set \(2,3,3,5,7,8,8,9\), the number \(3\) appears \(2\) times and the number \(8\) appears \(2\) times.

Step2: <Check other options>

Option A (\(3\)) and Option B (\(8\)) only consider one of the modes. Option C (\(5\)) appears only once.

Step3: <Calculate the mean>

Mean formula: \(\text{Mean}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). For the data set \(4,6,8,10,12\), \(n = 5\) and \(\sum_{i=1}^{5}x_{i}=4 + 6+8 + 10+12=40\). Then \(\text{Mean}=\frac{40}{5}=8\).

Answer:

1. D. 3 and 8
2. B. 8