Question

the dot plot below shows the number of days with different temperatures last month.

temperature (in degrees fahrenheit)

what is the mean of the data set shown?
a. 8
b. 81
c. 2,430
d. 5.13

Explanation:

Step1: Count the number of dots for each temperature

• 68: 1 dot
• 70: 2 dots
• 74: 2 dots
• 76: 4 dots
• 78: 1 dot
• 80: 5 dots
• 82: 3 dots
• 84: 5 dots
• 86: 1 dot
• 88: 3 dots
• 92: 3 dots

Step2: Calculate the total sum of (temperature × number of days)

\[

$$\begin{align*} &68\times1 + 70\times2 + 74\times2 + 76\times4 + 78\times1 + 80\times5 + 82\times3 + 84\times5 + 86\times1 + 88\times3 + 92\times3\\ =& 68 + 140 + 148 + 304 + 78 + 400 + 246 + 420 + 86 + 264 + 276\\ \end{align*}$$

\]
Now sum these values:
\(68+140 = 208\); \(208 + 148=356\); \(356+304 = 660\); \(660+78 = 738\); \(738+400 = 1138\); \(1138+246 = 1384\); \(1384+420 = 1804\); \(1804+86 = 1890\); \(1890+264 = 2154\); \(2154+276 = 2430\)

Step3: Calculate the total number of days (sum of dots)

\(1 + 2+2 + 4+1 + 5+3 + 5+1 + 3+3= 30\)

Step4: Calculate the mean (total sum / total number of days)

Mean \(=\frac{2430}{30}=81\)

Answer:

B. 81