A frequency table shows the value 1 occurring 5 times, 2 occurring 8 times, 3 occurring 4 times, and 4 occurring 3 times. What is the mean…

Find the total of all values and divide by the number of values. The total is $1(5)+2(8)+3(4)+4(3)=5+16+12+12=45$, and the number of values is $5+8+4+3=20$. The mean is $\frac{45}{20}=2.25$, choice B. Choice C ($2.5$) averages the four distinct values, $\frac{1+2+3+4}{4}$, without weighting by how often each occurs. Choice A ($2.0$) is the most common value, not the mean. Choice D ($4.5$) is $\frac{45}{10}$, dividing by the wrong count. In a frequency table, the frequencies are the weights.