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#### Each person in a random sample of ten ninth graders was asked two questions: How many hours did you spend watching TV last night? What is the total value of the coins you have with you today?

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0 1.Construct a dot plot of the data on Hours of TV. Would you describe this data distribution as approximately symmetric or as skewed?

2.If you wanted to describe a typical number of hours of TV watched for these ten students, would you use the mean or the median? Calculate the value of the measure you selected.

3.Here is a dot plot of the data on Total Value of Coins. Calculate the values of the mean and the median for this data set.

4.Why are the values of the mean and the median that you calculated in Problem 3 so different? Which of the mean and the median would you use to describe a typical value of coins for these ten students? Sangeetha Pulapaka
0

Step 1: Construct a dot plot

https://www.qalaxia.com/viewDiscussion?messageId=5ccac7d09a8f715227163337

: Recall what is symmetric data or skewed data in a data plot,

https://www.qalaxia.com/viewDiscussion?messageId=5ccbcfcb9a8f7152271633e2

The dot plot is approximately symmetric

Step 2:

Recall when to use mean or median if data is symmetric

If the dot plot is symmetric/ approximately symmetric we use mean

If the dot plot is skewed to the left or the right we use median

Here we would use mean.

Recall on how to calculate mean

https://www.qalaxia.com/viewDiscussion?messageId=5cc92d629a8f715227163212

Arrange the given data in ascending order we get

0, 1 ,1, 2, 2, 2, 3, 3, 4, 4

The value of mean = \frac{22}{10} = 2.2 hours

Step 3:

Calculate mean and median from the dot plot of coins given

Recall on how to calculate median

https://www.qalaxia.com/viewDiscussion?messageId=5cc9345c9a8f71522716321e

Arrange the data in the given dot plot in ascending order 0.0, 0.0, 0.10, 0.15, 0.25, 0.36, 0.54, 0.89, 1.37, 2.19

The sum is 5.65

Mean = \frac{5.85}{10} = 0.585 or about 59 cents

Median is the average of the two middle numbers

Median = \frac{0.25 +0.36}{2}

= 0.305  or about 31 cents.

Step 4:

Write which is a better estimate for the given data  - the mean or the median

The values of the mean and median are different because the data distribution is skewed, and the mean is pulled up by the large values in the data set. Because the data distribution is skewed, the median would be a better choice for describing a typical value.

https://www.engageny.org/resource/high-school-algebra-i