Question

1. the dot - plot below shows the number of goals jessica scored in each lacrosse game last season. which statement about the dot - plot is correct? 1) mean > mode 2) mean = median 3) mode = median 4) median > mean goals scored per game

Explanation:

Step1: Count data - points

Count the number of dots for each value. There are 3 dots at 0, 3 dots at 1, 4 dots at 2, 5 dots at 3, 2 dots at 4, 2 dots at 5 and 1 dot at 6. The total number of data - points is $3 + 3+4 + 5+2+2 + 1=20$.

Step2: Find the mode

The mode is the value that appears most frequently. The value 3 appears 5 times, which is more frequently than any other value. So the mode is 3.

Step3: Find the median

Since there are $n = 20$ data - points (an even number of data - points), the median is the average of the $\frac{n}{2}=10$th and $(\frac{n}{2}+1)=11$th ordered data - values. Arranging the data in ascending order, we count the cumulative number of data - points: 3 (for 0), $3 + 3=6$ (for 1), $6+4 = 10$ (for 2), $10 + 5=15$ (for 3). The 10th and 11th values are both 2. So the median is $\frac{2 + 2}{2}=2$.

Step4: Find the mean

The mean $\bar{x}=\frac{\sum_{i}x_{i}f_{i}}{\sum_{i}f_{i}}$, where $x_{i}$ is the value and $f_{i}$ is the frequency. $\sum_{i}x_{i}f_{i}=0\times3+1\times3 + 2\times4+3\times5+4\times2+5\times2+6\times1=0 + 3+8 + 15+8+10+6=50$. Since $\sum_{i}f_{i}=20$, the mean is $\frac{50}{20}=2.5$.

Step5: Compare mean, median and mode

We have mode = 3, median = 2, mean = 2.5. So mean < mode and median < mode and median < mean is incorrect. And mean>mode is incorrect. The correct relationship is mean>median.

Answer:

1. mean > mode