https://file.aiquickdraw.com/mathbot/file/1728646137603y1i3cucp.jpg

Let's break down the questions one by one based on the image you provided.

### Question 1
For the set of numbers: \(1, 2, 5, 5, 8, 9, 10, 5, 3, 8\)

**(a) List them in ascending order:**
The numbers in ascending order are:
\[ 1, 2, 3, 5, 5, 5, 8, 8, 9, 10 \]

**(b) How many numbers are in the set?**
There are 10 numbers in the set.

**(c) Calculate the:**
- **i. Mean:**
  The mean is calculated as the sum of the numbers divided by the count:
  \[
  \text{Mean} = \frac{1 + 2 + 3 + 5 + 5 + 5 + 8 + 8 + 9 + 10}{10} = \frac{56}{10} = 5.6
  \]
- **ii. Mode:**
  The mode is the most frequent number in the set. The number 5 appears the most (3 times).
  \[
  \text{Mode} = 5
  \]
- **iii. Median:**
  The median is the middle value of the set. Since there are 10 numbers (even count), the median is the average of the 5th and 6th numbers:
  \[
  \text{Median} = \frac{5 + 5}{2} = 5
  \]
- **iv. Range:**
  The range is the difference between the largest and smallest numbers:
  \[
  \text{Range} = 10 - 1 = 9
  \]

**(d) If each number in the set is doubled, what is the new mean?**
Doubling all the numbers doubles the sum. The new sum is \(56 \times 2 = 112\), and the count remains the same (10).
\[
\text{New Mean} = \frac{112}{10} = 11.2
\]

---

### Question 2
There are four spinners labeled A, B, C, D, each with different numbers.

**(a) Which spinner has the lowest probability of landing on the number 1 in a single spin?**
- **Spinner D** has 6 sections, and only 1 of them is the number 1, so the probability is \( \frac{1}{6} \), which is the lowest probability.

**(b) Which spinner has a 50% probability of landing on the number 1 in a single spin?**
- **Spinner B** has 2 sections, and one of them is the number 1. The probability is \( \frac{1}{2} \) or 50%.

**(c) List the spinners in order, from the most likely to land on the number 1 to the least likely:**
- Spinner B: \( \frac{1}{2} \)
- Spinner C: \( \frac{1}{3} \)
- Spinner A: \( \frac{1}{4} \)
- Spinner D: \( \frac{1}{6} \)

---

### Question 3
This question is about the probability of drawing specific cards from a standard 52-card deck.

**(a) Probability of drawing a red card:**
There are 26 red cards (hearts and diamonds).
\[
P(\text{red}) = \frac{26}{52} = \frac{1}{2}
\]

**(b) Probability of drawing a black card:**
There are 26 black cards (spades and clubs).
\[
P(\text{black}) = \frac{26}{52} = \frac{1}{2}
\]

**(c) Probability of drawing a heart:**
There are 13 hearts in the deck.
\[
P(\text{heart}) = \frac{13}{52} = \frac{1}{4}
\]

**(d) Probability of drawing an ace:**
There are 4 aces in the deck.
\[
P(\text{ace}) = \frac{4}{52} = \frac{1}{13}
\]

**(e) Probability of drawing a king:**
There are 4 kings in the deck.
\[
P(\text{king}) = \frac{4}{52} = \frac{1}{13}
\]

**(f) Probability of drawing a red 7:**
There are 2 red 7s (one in hearts and one in diamonds).
\[
P(\text{red 7}) = \frac{2}{52} = \frac{1}{26}
\]

---

Would you like any more details or explanations for any of these problems?

Here are some additional practice questions:
1. If the set of numbers in Question 1 had an additional number, 6, how would the mean change?
2. If a spinner has 8 sections, how would the probability of landing on a specific number compare with the spinners in Question 2?
3. What is the probability of drawing a face card (jack, queen, or king) from a standard deck?
4. If each number in the set in Question 1 is multiplied by 3, what would the new mean and range be?
5. How would the mode of the set in Question 1 change if another 8 were added?

**Tip:** When working with probabilities, it's often helpful to reduce fractions to their simplest form to better compare outcomes!

Solve questions related to ascending order, mean, mode, median, range, probabilities, and spinners from the provided set of numbers and spinners in the image.

Solve statistics and probability problems, including calculating the mean, mode, median, and range for a set of numbers, determining probabilities for spinners, and finding card probabilities in a standard deck. Suitable for Grades 6-8.

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