Question

question 1: the dot plot shows the number of goals scored in each soccer game this season. which statement about the data is correct? dot plot titled goals scored per game with dots above values 0,1,2,3,4,5,6; multiple - choice options below the plot

Explanation:

To determine which statement about the dot - plot is correct, we analyze the spread and center of the data (goals scored per game) from the dot - plot:

Step 1: Analyze the spread of data

• The spread of data can be thought of as the range or the distribution of the data points. For the "mean > median" or "mean < median" to be determined, we also need to consider the skewness of the data.
• If the data is symmetric, the mean and median are approximately equal. If the data is skewed to the right (tail on the right - hand side), the mean is greater than the median because the mean is pulled in the direction of the skew. If the data is skewed to the left (tail on the left - hand side), the mean is less than the median.
• Looking at the dot - plot, we can see that the data has a longer tail on the right (more spread out towards the higher number of goals). This means the data is skewed to the right.

Step 2: Relate skewness to mean and median

• In a right - skewed distribution, the mean is greater than the median. This is because the few larger values (in the right - tail) increase the value of the mean, while the median (the middle value) is less affected by these extreme values on the right.
• Now let's analyze the other options:
• "mean = median": This is true for symmetric distributions. Since our data is right - skewed, the mean and median are not equal.
• "mean < median": This is true for left - skewed distributions. Our data is right - skewed, so this is not correct.
• "median > mean": This is also a statement for left - skewed data. Our data is right - skewed, so this is incorrect.

Answer:

mean > median