Question

colin keeps track of how many goals he scores at each game throughout the season. these amounts are represented in the following dot plot. goals per game dot plot with 0:1 dot, 1:1 dot, 2:5 dots, 3:1 dot, 4:2 dots, 5:4 dots, 6:4 dots which statement correctly describes the data in this dot plot? show your work here options: mode > mean, mode < median, median < mode, median < mean

Explanation:

Step1: List all data points

From the dot plot, the data set is: $0, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6$

Step2: Calculate the mode

The mode is the most frequent value. Here, 2, 5, 6 each appear 4 times, so mode = 2, 5, 6 (we can use 2 for comparison as it's the lowest mode, or any, but we'll confirm with all)

Step3: Calculate the median

Total data points $n=17$. Median is the $\frac{n+1}{2} = 9$th value. Ordered data's 9th value is $4$. So median $=4$

Step4: Calculate the mean

Sum of data: $0+1+(2\times4)+3+(4\times2)+(5\times4)+(6\times4) = 0+1+8+3+8+20+24=64$. Mean $=\frac{64}{17}\approx3.76$

Step5: Compare values

• mode (2) < median (4); mode (5,6) > median (4)
• median (4) > mean ($\approx3.76$)
• mode (2) < mean ($\approx3.76$); mode (5,6) > mean ($\approx3.76$)

Now check options:

• mode > mean: False for mode=2
• mode < median: True for mode=2
• median < mode: False for mode=2
• median < mean: False, since $4>3.76$

Answer:

mode < median