i am trying to find this answer there are 3 questions.
1. micheal kept the following records of her phone bills for 12 months:
$47, $42, $56, $46, $63, $49, $47, $40, $58, $63, $51, $62
Find the mean and median of michael's monthly phone bills.
A) mean: $52, median: $50 C) mean: $50, median: $52
B) mean: $52, median: $48 D) mean: $48, median: $50
2.Find the five-number summary of the following set of numbers. the answers at the bottom a,b,c,d.
0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27
A)0.08, 0.18, 0.223, 0.27, 0.32
C)0.08, 0.18, 0.225, 0.27, 0.28
B)0.08, 0.18, 0.235, 0.27, 0.32
D)0.08, 0.16, 0.23, 0.28, 0.32
Find the first and third quartiles, Q1 and Q3, of the following set of numbers.
14, 4, 13, 18, 8, 15, 8, 3, 11, 8
A) 4; 13 B) 4; 15
C) 8; 14 D) 3; 18
1.
The mean can be found by adding up each value and dividing by the number of values. The mean is the middle value when the values are put in order.
2.
The 5 number summary is the following: the minimum value, the 1st quartile, the median, the 3rd quartile, and the maximum.
The 1st quartile is the median of all values less than the median. Similarly, the 3rd quartile is the median of all values greater than the median.
thank you now i understand it, i didn't know what i was doing.
First, I will explain how to find the mean and median of a set of numbers.
1. To find the mean (also called the average) of a set of numbers, you need to add up all the numbers and then divide the sum by the total number of numbers.
For example, for Michael's monthly phone bills:
Add up all the bills: $47 + $42 + $56 + $46 + $63 + $49 + $47 + $40 + $58 + $63 + $51 + $62 = $644
Divide the sum by the total number of bills: $644 / 12 = $53.67 (rounded to the nearest cent)
So, the mean of Michael's monthly phone bills is $53.67.
2. To find the median of a set of numbers, you need to arrange the numbers in ascending order and then find the middle value. If there is an even number of values, you take the average of the two middle values.
For example, for Michael's monthly phone bills:
Arrange the bills in ascending order: $40, $42, $46, $47, $47, $49, $51, $56, $58, $62, $63, $63
There are 12 bills, so the middle two values are the 6th and 7th bills: $49 and $51
Take the average of the two middle values: ($49 + $51) / 2 = $50
So, the median of Michael's monthly phone bills is $50.
Now, I will explain how to find the five-number summary of a set of numbers.
1. The five-number summary consists of the minimum value, the first quartile (Q1), the median (Q2 or the second quartile), the third quartile (Q3), and the maximum value.
2. To find the minimum value, you need to identify the smallest number in the set.
For example, for the set of numbers: 0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27
The minimum value is 0.08.
3. To find the first quartile (Q1), you need to find the median of the lower half of the numbers. This means you arrange the numbers in ascending order and find the median of the numbers below the median.
For example:
Arrange the numbers in ascending order: 0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32
The lower half of the numbers is: 0.08, 0.16, 0.18, 0.20, 0.22
Find the median of the lower half: (0.18 + 0.20) / 2 = 0.19
So, the first quartile (Q1) is 0.19.
4. The median (Q2) is already found as part of the five-number summary.
For the set of numbers: 0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32
The median (Q2) is 0.22.
5. To find the third quartile (Q3), you need to find the median of the upper half of the numbers. This means you arrange the numbers in ascending order and find the median of the numbers above the median.
For example:
Arrange the numbers in ascending order: 0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32
The upper half of the numbers is: 0.25, 0.27, 0.27, 0.28, 0.32
Find the median of the upper half: (0.27 + 0.27) / 2 = 0.27
So, the third quartile (Q3) is 0.27.
6. To find the maximum value, you need to identify the largest number in the set.
For the set of numbers: 0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27
The maximum value is 0.32.
So, the five-number summary is 0.08, 0.19, 0.22, 0.27, 0.32.
For the last question, I will explain how to find the first and third quartiles (Q1 and Q3) of a set of numbers.
1. Like I explained earlier, the first quartile (Q1) is the median of the lower half of the numbers, and the third quartile (Q3) is the median of the upper half of the numbers.
2. To find the first quartile (Q1), you need to find the median of the lower half of the numbers. This means you arrange the numbers in ascending order and find the median of the numbers below the median.
For example, for the set of numbers: 14, 4, 13, 18, 8, 15, 8, 3, 11, 8
Arrange the numbers in ascending order: 3, 4, 8, 8, 8, 11, 13, 14, 15, 18
The lower half of the numbers is: 3, 4, 8, 8, 8
Find the median of the lower half: (8 + 8) / 2 = 8
So, the first quartile (Q1) is 8.
3. To find the third quartile (Q3), you need to find the median of the upper half of the numbers. This means you arrange the numbers in ascending order and find the median of the numbers above the median.
For example:
Arrange the numbers in ascending order: 3, 4, 8, 8, 8, 11, 13, 14, 15, 18
The upper half of the numbers is: 11, 13, 14, 15, 18
Find the median of the upper half: (14 + 15) / 2 = 14.5
So, the third quartile (Q3) is 14.5.
Therefore, the correct answer for the first and third quartiles (Q1 and Q3) of the set of numbers 14, 4, 13, 18, 8, 15, 8, 3, 11, 8 is:
C) 8; 14.5