Question

consider the data represented in the dot plot.
what is the mean of the data to the nearest tenth?
enter the answer.
mean =

Explanation:

Step1: Count the frequency of each value

Value 1 has 1 dot, value 2 has 1 dot, value 3 has 2 dots, value 4 has 2 dots, value 5 has 2 dots, value 7 has 1 dot, value 9 has 1 dot, value 10 has 1 dot, value 11 has 2 dots, value 12 has 2 dots.

Step2: Calculate the sum of the products of values and their frequencies

Sum = \(1\times1 + 2\times1+3\times2 + 4\times2+5\times2+7\times1+9\times1+10\times1+11\times2+12\times2\)
\[

$$\begin{align*} &=1+2 + 6+8+10+7+9+10+22+24\\ &=(1 + 2)+(6+8)+10+7+9+10+(22+24)\\ &=3+14+10+7+9+10+46\\ &=(3+14)+10+7+9+10+46\\ &=17+10+7+9+10+46\\ &=(17+10)+7+9+10+46\\ &=27+7+9+10+46\\ &=(27+7)+9+10+46\\ &=34+9+10+46\\ &=(34+9)+10+46\\ &=43+10+46\\ &=(43+10)+46\\ &=53+46\\ &=99 \end{align*}$$

\]

Step3: Calculate the total number of data - points

Total number of data - points \(n=1 + 1+2+2+2+1+1+1+2+2=15\)

Step4: Calculate the mean

Mean \(\bar{x}=\frac{99}{15}=6.6\)

Answer:

6.6