Question

the following list shows the number of goals scored by a soccer team in each of 9 games: 0, 0, 1, 1, 1, 3, 3, 4, 5. how does the median number of goals scored compare with the mean number of goals scored? a) the median is equal to the mean. b) the median is less than the mean by 1. c) the median is greater than the mean by 1. d) the median is less than the mean by 2. e) the median is greater than the mean by 2.

Explanation:

Step1: Organize the data

The data set is: \(0, 0, 1, 1, 1, 3, 3, 4, 5\) (9 values, so the median is the 5th value).

Step2: Find the median

The 5th value in the ordered list is \(1\)? Wait, no, wait: ordered list is \(0, 0, 1, 1, 1, 3, 3, 4, 5\). The middle (5th) term is \(1\)? Wait, no, 9 terms: positions 1 - 9. The median is the \((9 + 1)/2 = 5\)th term. So 5th term is \(1\)? Wait, no, let's count: 1st: 0, 2nd: 0, 3rd: 1, 4th: 1, 5th: 1, 6th: 3, 7th: 3, 8th: 4, 9th: 5. So median is \(1\)? Wait, no, wait, no—wait, the data is [0, 0, 1, 1, 1, 3, 3, 4, 5]. Wait, no, wait, the number of terms is 9, so median is the 5th term. So 5th term is 1? Wait, no, that can't be. Wait, no, let's re - order: 0, 0, 1, 1, 1, 3, 3, 4, 5. Yes, 5th term is 1. Wait, but let's calculate the mean.

Step3: Calculate the mean

Sum of the data: \(0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5\)
\(= (0 + 0)+(1 + 1 + 1)+(3 + 3)+(4 + 5)\)
\(= 0+3 + 6+9\)
\(= 18\)
Mean \(=\frac{18}{9}=2\)

Step4: Compare median and mean

Median is \(1\), mean is \(2\). So median (\(1\)) is less than mean (\(2\)) by \(2 - 1=1\)? Wait, no: median is \(1\), mean is \(2\). So median is less than mean by \(1\)? Wait, no, \(2-1 = 1\). Wait, but let's check the options. Option B: "The median is less than the mean by 1". Wait, but wait, did I make a mistake in median? Wait, no, the data is 9 values: 0,0,1,1,1,3,3,4,5. The 5th term is 1. Mean is 18/9 = 2. So median (1) is less than mean (2) by 1. So option B? Wait, but wait, let's re - check the data. Wait, the list is: 0, 0, 1, 1, 1, 3, 3, 4, 5. Number of terms: 9. Median is the 5th term: 1. Mean: (0+0 + 1+1+1+3+3+4+5)/9=(02 + 13+3*2 + 4+5)/9=(0 + 3+6 + 4+5)/9=(18)/9 = 2. So median (1) is less than mean (2) by 1. So option B.

Answer:

B. The median is less than the mean by 1.