I am having a hard time with these problems and could you show me how to work them so next time i will know how.
find the first and third quartiles of Q and Q of the set of numbers 11,12,16,14,14,14,8,12,10,18
find any outliers ( if any) in the set of numbers 2,8,5,6,9,7,4,4,5,4,3
represent the quantity with a real number: an altitude of 400 feet(ft) above sea level.
represent the quantity with a real number: a decrease in population of 25,000
put the numbers in order.
8,10,11,12,12,14,14,14,16,18
The mean is 13. There is no universally accepted method of getting quartiles with an odd number of data, despite what your text or instructor says. IT is common to round up.
So, bottom quartile ends at 11, third quartile 14 ends.
8,10,11,12,14,14,14,16,18
Sure! I'll explain how to solve each problem step by step.
Problem 1:
To find the first and third quartiles, you need to arrange the numbers in ascending order. Here is the set of numbers in ascending order: 8, 10, 11, 12, 12, 14, 14, 14, 16, 18.
First Quartile(Q1):
To find Q1, you need to calculate the median of the lower half of the data set. In this case, the lower half consists of the first five numbers: 8, 10, 11, 12, 12. Since there is an odd number of values, the median will be the middle number, which is 11. So, Q1 is 11.
Third Quartile(Q3):
To find Q3, you need to calculate the median of the upper half of the data set. In this case, the upper half consists of the last five numbers: 14, 14, 14, 16, 18. Again, since there is an odd number of values, the median will be the middle number, which is 14. So, Q3 is 14.
Therefore, the first quartile (Q1) is 11 and the third quartile (Q3) is 14.
Problem 2:
To find any outliers in a data set, you can use a box plot or calculate the interquartile range (IQR).
To find the outliers using the IQR method, follow these steps:
1. Arrange the numbers in ascending order: 2, 3, 4, 4, 4, 5, 5, 6, 7, 8, 9.
2. Find Q1 and Q3 as we did in the previous problem. Q1 is 4, and Q3 is 7.
3. Calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 7 - 4 = 3.
4. Determine the lower bound by subtracting 1.5 times the IQR from Q1: Lower Bound = Q1 - 1.5 * IQR = 4 - 1.5 * 3 = -1.5.
5. Determine the upper bound by adding 1.5 times the IQR to Q3: Upper Bound = Q3 + 1.5 * IQR = 7 + 1.5 * 3 = 11.5.
6. Any values below the lower bound or above the upper bound are considered outliers.
In this case, there are no numbers below -1.5 or above 11.5, so there are no outliers in the set.
Problem 3:
To represent the quantity of altitude of 400 feet above sea level with a real number, you can simply use 400. Since the question specifies "above" sea level, a positive value is used.
Problem 4:
To represent the quantity of a decrease in population of 25,000 with a real number, you can use -25,000. Since the question mentions a decrease, a negative value is used.