Let's calculate the Mean, Median, and Mode for the given data:

Data:

66, 64, 63, 68, 66, 64, 64, 64, 71, 80, 74, 77, 73, 66, 65, 64, 67, 73, 79, 67

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1. Mean:

The mean is the sum of all values divided by the number of values.

First, we sum the data:

$66 + 64 + 63 + 68 + 66 + 64 + 64 + 64 + 71 + 80 + 74 + 77 + 73 + 66 + 65 + 64 + 67 + 73 + 79 + 67 = 1328$

Now, divide the sum by the number of data points, which is 20:

$\text{Mean} = \frac{1328}{20} = 66.4$

Mean = 66.4

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2. Median:

The median is the middle value when the data is ordered. If there is an even number of values, the median is the average of the two middle numbers.

First, let's order the data in ascending order:

$63, 64, 64, 64, 64, 64, 65, 66, 66, 66, 67, 67, 68, 71, 73, 73, 74, 77, 79, 80$

There are 20 values, so the median will be the average of the 10th and 11th numbers.

The 10th value is 66 and the 11th value is 67.

Now, calculate the median:

$\text{Median} = \frac{66 + 67}{2} = \frac{133}{2} = 66.5$

Median = 66.5

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3. Mode:

The mode is the value that occurs most frequently in the data.

From the ordered list:

$63, 64, 64, 64, 64, 64, 65, 66, 66, 66, 67, 67, 68, 71, 73, 73, 74, 77, 79, 80$

The value 64 appears 5 times, which is more frequent than any other number.

Mode = 64

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Final Answers:

• Mean = 66.4
• Median = 66.5
• Mode = 64

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Would you like further details on how these calculations are done, or do you have any questions?

Additional Questions:

1. How do you calculate the range of a data set?
2. What are outliers, and how do they affect statistical measures?
3. How is the variance different from the standard deviation?
4. What is the difference between population and sample data in statistics?
5. How do you interpret the results when you have more than one mode?

Tip:

Always double-check the order of your data when calculating the median and mode. Misordering can lead to incorrect results!