Sure, let's work through these problems step-by-step.
### Part 5: Evaluate [tex]\(2^4 + 4 \times (6 - 2) \div 2\)[/tex]
First, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (left to right), and Addition and Subtraction (left to right).
1. Calculate the exponent: [tex]\(2^4 = 16\)[/tex].
2. Evaluate the expression in parentheses: [tex]\(6 - 2 = 4\)[/tex].
3. Perform the multiplication and division from left to right:
- Multiply: [tex]\(4 \times 4 = 16\)[/tex]
- Divide: [tex]\(16 \div 2 = 8\)[/tex]
4. Finally, perform the addition:
- Add: [tex]\(16 + 8 = 24\)[/tex]
So, the result of [tex]\(2^4 + 4 \times (6 - 2) \div 2\)[/tex] is [tex]\(\boxed{24.0}\)[/tex].
### Part 6: The mass in kilograms of 8 sheep in a pen were [tex]\(14, 15, 20, 7, 18, 25, 17, 10\)[/tex]. Determine the interquartile deviation of the data.
To find the interquartile deviation, follow these steps:
1. Sort the data in increasing order:
- Sorted sheep masses: [tex]\(7, 10, 14, 15, 17, 18, 20, 25\)[/tex]
2. Find the median to divide the data into lower and upper halves.
- Since there are 8 data points (an even number), the median will be the average of the 4th and 5th values.
- Median = [tex]\(\frac{15 + 17}{2} = 16\)[/tex]
3. Divide the data into lower and upper halves:
- Lower half: [tex]\(7, 10, 14, 15\)[/tex]
- Upper half: [tex]\(17, 18, 20, 25\)[/tex]
4. Find the first quartile (Q1), which is the median of the lower half:
- Lower half sorted: [tex]\(7, 10, 14, 15\)[/tex]
- Median of the lower half (Q1): [tex]\(\frac{10 + 14}{2} = 12\)[/tex]
5. Find the third quartile (Q3), which is the median of the upper half:
- Upper half sorted: [tex]\(17, 18, 20, 25\)[/tex]
- Median of the upper half (Q3): [tex]\(\frac{18 + 20}{2} = 19\)[/tex]
6. Calculate the interquartile range (IQR):
- [tex]\(IQR = Q3 - Q1 = 19 - 12 = 7\)[/tex]
Therefore, the interquartile deviation of the given data is [tex]\(\boxed{7.0}\)[/tex].
