Question
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:
Relist the cards in the correct order right here using their point values:
Find the mean of the data set and put your answer below showing your work.
Find the median of the data set and put your answer below showing your work.
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.
Relist the cards in the correct order right here using their point values:
Find the mean of the new data set and put your answer below showing your work.
Find the median of the new data set and put your answer below showing your work.
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.
How did the outlier (the Joker card) affect the mean? (2 complete sentences)
How did the outlier affect the median? (2 complete sentences)
How did the outlier affect the mode? (1 complete sentences)
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:
Relist the cards in the correct order right here using their point values:
Find the mean of the data set and put your answer below showing your work.
Find the median of the data set and put your answer below showing your work.
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.
Relist the cards in the correct order right here using their point values:
Find the mean of the new data set and put your answer below showing your work.
Find the median of the new data set and put your answer below showing your work.
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.
How did the outlier (the Joker card) affect the mean? (2 complete sentences)
How did the outlier affect the median? (2 complete sentences)
How did the outlier affect the mode? (1 complete sentences)
Answers
GPT-4o mini
Let's go through the project step by step, starting with Part 1.
### Part 1: Original Set of Cards
**Given Cards:**
To solve this, I will assign hypothetical card values, as you haven’t provided specific cards pulled from a deck.
Assuming the following six cards were pulled:
- 3
- 5
- 7
- 10 (10 points for a face card)
- 2
- 8
**Card Values in Order:**
2, 3, 5, 7, 8, 10
**Mean:**
To find the mean, you sum all the card values and divide by the number of cards.
\[
\text{Mean} = \frac{2 + 3 + 5 + 7 + 8 + 10}{6} = \frac{35}{6} \approx 5.83
\]
**Median:**
To find the median, you need to find the middle value when arranged in order. Since there are six cards (even number), you average the two middle numbers.
- The two middle numbers are 5 and 7.
\[
\text{Median} = \frac{5 + 7}{2} = \frac{12}{2} = 6
\]
**Mode:**
To find the mode, identify the number that appears most frequently. In this case, all numbers appear once, meaning there is no mode.
\[
\text{Mode} = \text{None}
\]
### Part 2: New Set of Cards
**New Set of Cards:**
Now, we replace the lowest card (2) with a Joker card worth 19 points.
**New Cards:**
3, 5, 7, 8, 10, 19
**New Card Values in Order:**
3, 5, 7, 8, 10, 19
**Mean:**
\[
\text{Mean} = \frac{3 + 5 + 7 + 8 + 10 + 19}{6} = \frac{52}{6} \approx 8.67
\]
**Median:**
The two middle numbers are 7 and 8.
\[
\text{Median} = \frac{7 + 8}{2} = \frac{15}{2} = 7.5
\]
**Mode:**
Again, all numbers appear once, indicating there is no mode.
\[
\text{Mode} = \text{None}
\]
### Part 3: Comparison
Comparing the two sets:
- **Means:** The mean increased from approximately 5.83 to about 8.67 due to the outlier introducing a larger value.
- **Medians:** The median increased from 6 to 7.5, suggesting a moderate adjustment based on the new card values.
- **Modes:** Neither set has a mode, so the introduction of the outlier didn't affect this aspect.
The mean was affected the most by the outlier because adding a high value (19) significantly raised the average. The median also increased but less dramatically due to being calculated from the middle values, reducing the absolute effect of the outlier.
### Effects of the Outlier
**Effect on Mean:**
The outlier (Joker card worth 19 points) raised the mean significantly as it brought a high value into the average. Before the outlier, the mean was about 5.83, and it increased to approximately 8.67 after adding the Joker.
**Effect on Median:**
The outlier had a more moderate effect on the median. It increased from 6 to 7.5, indicating that while the high value shifted the center of the data, it did not skew it as dramatically as it did with the mean.
**Effect on Mode:**
The introduction of the Joker card did not affect the mode; both datasets had no mode, as no number was repeated in either set.
### Part 1: Original Set of Cards
**Given Cards:**
To solve this, I will assign hypothetical card values, as you haven’t provided specific cards pulled from a deck.
Assuming the following six cards were pulled:
- 3
- 5
- 7
- 10 (10 points for a face card)
- 2
- 8
**Card Values in Order:**
2, 3, 5, 7, 8, 10
**Mean:**
To find the mean, you sum all the card values and divide by the number of cards.
\[
\text{Mean} = \frac{2 + 3 + 5 + 7 + 8 + 10}{6} = \frac{35}{6} \approx 5.83
\]
**Median:**
To find the median, you need to find the middle value when arranged in order. Since there are six cards (even number), you average the two middle numbers.
- The two middle numbers are 5 and 7.
\[
\text{Median} = \frac{5 + 7}{2} = \frac{12}{2} = 6
\]
**Mode:**
To find the mode, identify the number that appears most frequently. In this case, all numbers appear once, meaning there is no mode.
\[
\text{Mode} = \text{None}
\]
### Part 2: New Set of Cards
**New Set of Cards:**
Now, we replace the lowest card (2) with a Joker card worth 19 points.
**New Cards:**
3, 5, 7, 8, 10, 19
**New Card Values in Order:**
3, 5, 7, 8, 10, 19
**Mean:**
\[
\text{Mean} = \frac{3 + 5 + 7 + 8 + 10 + 19}{6} = \frac{52}{6} \approx 8.67
\]
**Median:**
The two middle numbers are 7 and 8.
\[
\text{Median} = \frac{7 + 8}{2} = \frac{15}{2} = 7.5
\]
**Mode:**
Again, all numbers appear once, indicating there is no mode.
\[
\text{Mode} = \text{None}
\]
### Part 3: Comparison
Comparing the two sets:
- **Means:** The mean increased from approximately 5.83 to about 8.67 due to the outlier introducing a larger value.
- **Medians:** The median increased from 6 to 7.5, suggesting a moderate adjustment based on the new card values.
- **Modes:** Neither set has a mode, so the introduction of the outlier didn't affect this aspect.
The mean was affected the most by the outlier because adding a high value (19) significantly raised the average. The median also increased but less dramatically due to being calculated from the middle values, reducing the absolute effect of the outlier.
### Effects of the Outlier
**Effect on Mean:**
The outlier (Joker card worth 19 points) raised the mean significantly as it brought a high value into the average. Before the outlier, the mean was about 5.83, and it increased to approximately 8.67 after adding the Joker.
**Effect on Median:**
The outlier had a more moderate effect on the median. It increased from 6 to 7.5, indicating that while the high value shifted the center of the data, it did not skew it as dramatically as it did with the mean.
**Effect on Mode:**
The introduction of the Joker card did not affect the mode; both datasets had no mode, as no number was repeated in either set.