Can someone help me figure this out?
1. Find the first and third quartiles, Q1 and Q3 of the following numbers:
347,242,146,391,249,567,277,218,319
and
0.16,0.08,0.27,0.20,0.22,0.32,0.25,0.18,0.28,0.27
2. Which of the following numbers are integers?
75,9.82,-1/14,-498,0.71
The calculation of the quartiles is sometimes not quite clear (especially if the number of observations of a sample is not divisible by four). We therefore provide exact instructions how to calculate the quartiles. Assuming a sample of N observations the quartiles are defined as follows ("round" stands for the rounding to the nearest integer):
1. quartile: the value of the sorted series of observations having the position x = round(0.25*(N+1))
2. quartile (median): if N is even, Q2 is the mean of the two values at the positions N/2 and N/2+1; if N is odd, Q2 is the value at the position (N+1)/2
3. quartile: the value of the sorted series having the position x = round(0.75*(N+1))
Example:
To find the quartiles, follow these steps:
Step 1: Sort the given numbers in ascending order.
For the first set of numbers: 146, 218, 242, 249, 277, 319, 347, 391, 567.
For the second set of numbers: 0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32.
Step 2: Find the positions of the quartiles.
For the first set of numbers:
- The first quartile, Q1, will have a position of x = round(0.25*(N+1)). In this case, x = round(0.25*(9+1)) = round(0.25*10) = round(2.5) = 3. This means the value at position 3 is Q1.
- The third quartile, Q3, will have a position of x = round(0.75*(N+1)). In this case, x = round(0.75*(9+1)) = round(0.75*10) = round(7.5) = 8. This means the value at position 8 is Q3.
For the second set of numbers:
- The first quartile, Q1, will have a position of x = round(0.25*(N+1)). In this case, x = round(0.25*(10+1)) = round(0.25*11) = round(2.75) = 3. This means the value at position 3 is Q1.
- The third quartile, Q3, will have a position of x = round(0.75*(N+1)). In this case, x = round(0.75*(10+1)) = round(0.75*11) = round(8.25) = 8. This means the value at position 8 is Q3.
Step 3: Find the values of Q1 and Q3.
For the first set of numbers: Q1 = 242, Q3 = 391.
For the second set of numbers: Q1 = 0.18, Q3 = 0.28.
So the first and third quartiles for the two sets of numbers are:
1. First set: Q1 = 242, Q3 = 391.
2. Second set: Q1 = 0.18, Q3 = 0.28.
Now let's move on to the second question.
To determine if a number is an integer, you need to check if it has a decimal part. If the decimal part is zero, then the number is an integer.
Let's check each number:
1. 75 - This is an integer because it does not have a decimal part.
2. 9.82 - This is not an integer because it has a decimal part.
3. -1/14 - This is not an integer because it is a fraction and fractions are not considered integers.
4. -498 - This is an integer because it does not have a decimal part.
5. 0.71 - This is not an integer because it has a decimal part.
So, the integers in the given list are: 75 and -498.
I hope this helps!