11. use the following data for questions #10 - #15
what is the mean of this distribution?
34, 34, 65, 33, 35, 54, 57, 48, 42, 33, 36, 38, 44, 35, 36, 32, 36, 37, 44, 45
a. 25.2
b. 55.1
c. 39.4
d. 40.9

Question

Accepted Answer

# Explanation:
## Step1: Count the number of data points
There are $n = 20$ data points.
## Step2: Sum up all the data points
$$
\begin{align*}
\sum x&=34 + 34+65 + 33+35 + 54+57+48+42+33+36+38+44+35+36+32+36+37+44+45\
&=(34\times2)+65+(33\times2)+35+(54 + 57)+48+42+(36\times3)+38+44+(35)+32+37+(44)+45\
&=68+65 + 66+35+111+48+42+108+38+44+35+32+37+44+45\
&=(68+65)+(66+35)+111+(48+42)+108+(38+32)+(44+35)+(37+44)+45\
&=133+101+111+90+108+70+79+81+45\
&=(133+101)+111+90+108+70+79+81+45\
&=234+111+90+108+70+79+81+45\
&=(234+111)+90+108+70+79+81+45\
&=345+90+108+70+79+81+45\
&=(345+90)+108+70+79+81+45\
&=435+108+70+79+81+45\
&=(435+108)+70+79+81+45\
&=543+70+79+81+45\
&=(543+70)+79+81+45\
&=613+79+81+45\
&=(613+79)+81+45\
&=692+81+45\
&=(692+81)+45\
&=773+45\
&=818
\end{align*}
$$
## Step3: Calculate the mean
The formula for the mean $\bar{x}=\frac{\sum x}{n}$. Substitute $\sum x = 818$ and $n = 20$ into the formula: $\bar{x}=\frac{818}{20}=40.9$

# Answer:
d. $40.9$

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QUESTION IMAGE

Question

Explanation:

Step1: Count the number of data points

Step2: Sum up all the data points

Step3: Calculate the mean

Answer: