To find the measures of central tendency for the data set:

6, 5, 4, 1, 7, 8, 3, 3, 2, 3

We will calculate the mean, median, and mode.

1. Mean (Average)

The mean is calculated by summing all the data points and dividing by the total number of points.

$\text{Mean} = \frac{6 + 5 + 4 + 1 + 7 + 8 + 3 + 3 + 2 + 3}{10} = \frac{42}{10} = 4.2$

So, the mean is 4.2.

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2. Median (Middle Value)

To find the median, we first arrange the data in ascending order: $1, 2, 3, 3, 3, 4, 5, 6, 7, 8$

Since there are 10 numbers (an even number), the median is the average of the 5th and 6th numbers in this ordered list.

$\text{Median} = \frac{3 + 4}{2} = \frac{7}{2} = 3.5$

So, the median is 3.5.

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3. Mode (Most Frequent Value)

The mode is the value that appears most frequently. In this case, the number 3 appears three times, which is more frequent than any other number.

So, the mode is 3.

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Summary:

• Mean: 4.2
• Median: 3.5
• Mode: 3

Would you like further details on how to calculate or interpret these measures? Feel free to ask any questions!

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Here are some related questions to explore further:

1. How do outliers affect the mean and median?
2. What is the difference between the median and mode in a data set?
3. How do you calculate the range of a data set, and what does it represent?
4. Can a data set have multiple modes? If so, how do you describe it?
5. What are the other measures of central tendency besides mean, median, and mode?

Tip: When the data has outliers or extreme values, the median is often a more reliable measure of central tendency than the mean.