Question

2 which expression is equal to: b + 4 a 48 b 4b c b + b + b + b d 4 + b 3 goals per soccer game: 3, 0, 1, 3, 4, 3, 2, 0 mean = _ median = _ mode(s) = _ range = _

Explanation:

Question 2

Step1: Analyze each option

• Option A: \(48\) is a constant, not related to \(b + 4\).
• Option B: \(4b=b + b+ b + b\), which is multiplication, not addition.
• Option C: \(b + b+ b + b = 4b\), not \(b + 4\).
• Option D: By commutative property of addition \(a + b=b + a\). So \(4 + b=b + 4\).

Step1: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Here \(n = 8\) and \(\sum_{i=1}^{8}x_{i}=3 + 0+1 + 3+4 + 3+2 + 0=16\). Then \(\bar{x}=\frac{16}{8}=2\).

Step2: Calculate the median

First, order the data: \(0,0,1,2,3,3,3,4\). Since \(n = 8\) (even), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}=\frac{2 + 3}{2}=2.5\).

Step3: Calculate the mode

The mode is the most - frequently occurring value. The value \(3\) occurs \(3\) times, more frequently than other values.

Step4: Calculate the range

The range \(R=\text{Max}-\text{Min}\). Here \(\text{Max}=4\) and \(\text{Min}=0\), so \(R = 4-0=4\).

Answer:

D. \(4 + b\)

Question 3