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The purpose of this project is to solve for mean, median and mode and find out how an outlier affects the data.

Here is the point system: All numbered cards are worth exactly what they are numbered. Kings, Queens, and Jacks are all worth 10 points. Aces are worth 1 point.

Part 1: Your teacher pulled 6 cards from the deck. They are as follows:



1. Relist the cards in the correct order right here using their point values:

2. Find the mean of the data set and put your answer below showing your work.

3. Find the median of the data set and put your answer below showing your work.

4. Find the mode (which number appears the most) of the data set and put your answer below showing your work.

Part 2: Now take your lowest card and throw it out of the set. You will replace it with a Joker card which is worth 19 points. And you will still only have 6 cards total.
1. Relist the cards in the correct order right here using their point values:

2. Find the mean of the new data set and put your answer below showing your work.



3. Find the median of the new data set and put your answer below showing your work.

4. Find the mode of the new data set and put your answer below showing your work.

Part 3: Compare the two sets and describe. Be sure to include which one was affected the most.

1. How did the outlier (the Joker card) affect the mean? (2 complete sentences)

2. How did the outlier affect the median? (2 complete sentences)

3. How did the outlier affect the mode? (1 complete sentences)

1 answer

To assist you with this project, we'll first need the specific six card values that your teacher pulled from the deck in Part 1. Since that information wasn’t provided, I will create an example set of cards to illustrate the necessary calculations. Please replace my example cards with the actual cards you have for your project.

Example Set of Cards:

  1. 3
  2. 5
  3. 7
  4. 10 (Jack)
  5. 10 (Queen)
  6. 1 (Ace)

Part 1

  1. Relist the cards in the correct order right here using their point values:

    • Ordered Set: 1, 3, 5, 7, 10, 10

  2. Find the mean of the data set and put your answer below showing your work:

    • Calculation: \[ \text{Mean} = \frac{1 + 3 + 5 + 7 + 10 + 10}{6} = \frac{36}{6} = 6 \]
    • Mean: 6

  3. Find the median of the data set and put your answer below showing your work:

    • Ordered Set: 1, 3, 5, 7, 10, 10
    • Calculation: \[ \text{Median} = \frac{5 + 7}{2} = \frac{12}{2} = 6 \]
    • Median: 6

  4. Find the mode (which number appears the most) of the data set and put your answer below showing your work:

    • Calculation: The number 10 appears most frequently (twice).
    • Mode: 10

Part 2

Now take your lowest card (1) and throw it out of the set. You will replace it with a Joker card which is worth 19 points. You will still only have 6 cards total.

  1. Relist the cards in the correct order right here using their point values:

    • Ordered Set: 3, 5, 7, 10, 10, 19

  2. Find the mean of the new data set and put your answer below showing your work:

    • Calculation: \[ \text{Mean} = \frac{3 + 5 + 7 + 10 + 10 + 19}{6} = \frac{54}{6} = 9 \]
    • Mean: 9

  3. Find the median of the new data set and put your answer below showing your work:

    • Ordered Set: 3, 5, 7, 10, 10, 19
    • Calculation: \[ \text{Median} = \frac{7 + 10}{2} = \frac{17}{2} = 8.5 \]
    • Median: 8.5

  4. Find the mode of the new data set and put your answer below showing your work:

    • Calculation: The number 10 appears most frequently (twice).
    • Mode: 10

Part 3: Compare the two sets and describe. Be sure to include which one was affected the most.

  1. How did the outlier (the Joker card) affect the mean?

    • The mean increased from 6 to 9 after including the Joker card. The outlier shifted the average higher because it added a significant amount of value that was not present in the original set.

  2. How did the outlier affect the median?

    • The median decreased from 6 to 8.5. This change indicates that the outlier affected the center of the dataset, but less dramatically than it did the mean since the new median remained lower than the outlier value.

  3. How did the outlier affect the mode?

    • The mode remained unchanged at 10, as this value continued to appear the most frequently in both datasets.

Summary

In conclusion, the outlier (Joker card) had a more pronounced effect on the mean than on the median and did not affect the mode at all. The mean rose significantly, while the median showed a smaller increase, demonstrating the sensitivity of the mean to outliers compared to the median.

Feel free to replace the example values with your actual card values as needed!