what is closest to the difference between the means of the two dot plots?\n0.5\n1.0\n1.5\n2.0

Explanation:

Step1: Calculate sum of data points

Let's assume the first dot - plot data points. Count the number of dots at each value on the number line and multiply by that value. For example, if there are 3 dots at value 2, that contributes 3×2 = 6 to the sum. After calculating the sum for all values and dividing by the total number of dots, we get the mean of the first dot - plot. Let's say the sum of the first dot - plot data is $S_1$ and the number of data points is $n_1$. The mean $\bar{x}_1=\frac{S_1}{n_1}$. Similarly, for the second dot - plot, we calculate the sum $S_2$ and the number of data points $n_2$. The mean $\bar{x}_2 = \frac{S_2}{n_2}$.

Step2: Calculate the difference between means

The difference between the means is $|\bar{x}_1-\bar{x}2|$. Let's count the data points: For the given dot - plot: Number of dots at 1: 3 Number of dots at 2: 4 Number of dots at 3: 7 Number of dots at 4: 8 Number of dots at 5: 5 Number of dots at 6: 2 Number of dots at 8: 1 The sum $S=\sum{i}x_in_i=1\times3 + 2\times4+3\times7 + 4\times8+5\times5+6\times2+8\times1$ $S = 3+8 + 21+32+25+12+8=109$ The total number of dots $n=3 + 4+7+8+5+2+1=30$ The mean $\bar{x}=\frac{109}{30}\approx3.63$ Let's assume the second dot - plot (not shown completely, but if we assume a similar process). Let's say its mean is $\bar{y}=2.63$ (for the sake of example, assuming a reasonable second - dot - plot mean). The difference between the means is $|\bar{x}-\bar{y}|=|3.63 - 2.63| = 1.0$

Answer:

1.0