Question

below are the dot plots for two data sets. (a dot plot is sometimes called a \line plot\.) data set a dot plot with number line from 1 to 9, dots: 4 has 1, 5 has 2, 6 has 2, 7 has 2, 8 has 2, 9 has 1 data set b dot plot with number line from 1 to 9, dots: 4 has 1, 5 has 3, 6 has 3, 7 has 3, 8 has 1 find the mean of each data set.

Explanation:

Data Set A

Step1: Count the number of dots for each value

• At 4: 1 dot
• At 5: 2 dots
• At 6: 2 dots
• At 7: 2 dots
• At 8: 2 dots
• At 9: 1 dot

Total number of data points: \(1 + 2 + 2 + 2 + 2 + 1 = 10\)

Step2: Calculate the sum of the data

\(4\times1 + 5\times2 + 6\times2 + 7\times2 + 8\times2 + 9\times1\)
\(= 4 + 10 + 12 + 14 + 16 + 9\)
\(= 65\)

Step3: Calculate the mean

Mean = \(\frac{\text{Sum}}{\text{Number of data points}} = \frac{65}{10} = 6.5\)

Data Set B

Step1: Count the number of dots for each value

• At 4: 1 dot
• At 5: 3 dots
• At 6: 3 dots
• At 7: 3 dots
• At 8: 1 dot

Total number of data points: \(1 + 3 + 3 + 3 + 1 = 11\) Wait, no, let's recount: 1 (at 4) + 3 (at 5) + 3 (at 6) + 3 (at 7) + 1 (at 8) = 11? Wait, no, looking at the dot plot:

Wait, Data Set B:

• 4: 1 dot

• 5: 3 dots (since there are three dots)

• 6: 3 dots

• 7: 3 dots

• 8: 1 dot

Wait, total: 1 + 3 + 3 + 3 + 1 = 11? Wait, no, maybe I miscounted. Wait, the dot plot for Data Set B:

At 4: 1 dot

At 5: 3 dots (three dots)

At 6: 3 dots (three dots)

At 7: 3 dots (three dots)

At 8: 1 dot

Wait, that's 1 + 3 + 3 + 3 + 1 = 11? Wait, no, maybe I made a mistake. Wait, let's check again.

Wait, Data Set B:

• 4: 1

• 5: 3

• 6: 3

• 7: 3

• 8: 1

Total: 1 + 3 + 3 + 3 + 1 = 11.

Step2: Calculate the sum of the data

\(4\times1 + 5\times3 + 6\times3 + 7\times3 + 8\times1\)
\(= 4 + 15 + 18 + 21 + 8\)
\(= 66\)

Step3: Calculate the mean

Mean = \(\frac{66}{11} = 6\)

Answer:

Mean of Data Set A: \(6.5\)

Mean of Data Set B: \(6\)