Answers
Answer:
36°
Step-by-step explanation:
x+27+27+90=180
x=36°
Related Questions
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answers
The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 14, with an IQR of 6.
How to solveTo obtain measures of spread, we can use the dot plot to visualize the frequency of each observation in the data-set, and then calculate the interquartile range (IQR).
For a group of 15 students, we can find the quartiles as follows:
The first quartile (Q1) is the median of the first half of the data-set, which consists of the first seven students.
Looking at the dot plot, the fourth dot represents the median of the first half. For Bus 14, Q1 = 12. For Bus 18, Q1 = 9.
The third quartile (Q3) is the median of the second half of the data-set, which consists of the last seven students. Looking at the dot plot, the eleventh dot represents the median of the second half. For Bus 14, Q3 = 18.
For Bus 18, Q3 = 16.
We can then calculate the IQR as the difference between Q3 and Q1:
For Bus 14, IQR = Q3 - Q1 = 18 - 12 = 6.
For Bus 18, IQR = Q3 - Q1 = 16 - 9 = 7.
Based on the IQR values, we can conclude that Bus 14 is more consistent than Bus 18, as it has a lower IQR.
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Write a polynomial function in standard form with real coefficients whose zeros include 1,4i, and -4i
Answers
(x - 1)(x - 4i)(x + 4i)
To write this polynomial in standard form, we need to multiply out the factors and simplify:
(x - 1)(x - 4i)(x + 4i)
= (x - 1)(x^2 - (4i)^2)
= (x - 1)(x^2 - 16i^2)
= (x - 1)(x^2 + 16)
Expanding the product, we get:
x^3 + 16x - x^2 - 16
So the polynomial function with real coefficients whose zeros include 1, 4i, and -4i is:
f(x) = x^3 - x^2 + 16x - 16
:))
Answer:
f(x) = x^3 - x^2 + 16x - 16
Step-by-step explanation:
If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.
To find the polynomial, we can multiply these factors together:
(x - 1)(x - 4i)(x + 4i)
= (x - 1)(x^2 - (4i)^2)
= (x - 1)(x^2 + 16)
= x^3 + 16x - x^2 - 16
So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:
f(x) = x^3 - x^2 + 16x - 16
Find cordinates of point of inter section
7x+4y=23
8x-10y=19
Answers
Answer:
To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.
First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:
- 70x + 40y = 230
- 32x - 40y = 76
Adding these two equations, we get:
- 102x = 306
Dividing both sides by 102, we get:
- x = 3
Now we can substitute this value of x into either equation to find the value of y. Using the first equation:
- 7(3) + 4y = 23
- 21 + 4y = 23
- 4y = 2
- y = 1/2
Therefore, the point of intersection is (3, 1/2).
Answer:
Step-by-step explanation:
Pythagorean theorem - Missing sides
Pls help me I need your help to my homework
If you help me, I help you too I promise
Answers
C is the hypotenuse, and a and b are the other sides of the triangle. You can identify the hypotenuse of the triangle as it being the longest side, and the one opposite the right angle.
I see you have done Question 1 and Question 2 correctly, so I’ll start with Question 3.
(But with question 1, you did the working out slightly wrong but still managed to get the right answer?! That confuses me, but well done!)
Question 3:
The hypotenuse is 4 and the other side length is 3. You can tell the side length that’s 4 is the hypotenuse because it’s the longest side, and the one opposite the right angle.
a^2+b^2=c^2 (c is the hypotenuse)
a^2+3^2=4^2
So: a^2=4^2-3^2
a^2=16-9
a^2= 7
a= root of 7, or 2.6 to one decimal place.
Answer: 2.6 (to one decimal place)
Question 5:
12 is the hypotenuse and 5 is another side length.
a^2+b^2= c^2
a^2+5^2=12^2
So: a^2= 12^2-5^2
a^2= 144-25
a^2= 119
a= root of 119, or 10.9 to one decimal place
Answer: 10.9 (to one decimal place)
I’ll skip question 5, and cover question 6:
Question 6:
This time the side lengths are 5 and 2, and the hypotenuse is missing.
a^2+b^2=c^2
5^2+2^2=c^2
25+4=c^2
29=c^2
c= root of 29, or 5.4 to one decimal place
Answer: 5.4 (to one decimal place)
Try to do the rest of the homework by yourself, with this to help you! (Unless someone else finishes the rest for you)
If you want to get better at something, you have to practice lots, which is why I’m not doing all of it.
(sorry if I’m wrong on any!!)
:)
what is 5w–4w–w+6w simplified
Answers
The value of the expression 5w–4w–w+6w is 6w
What is simplification of expression?When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
For example, 2( 3a+5) can be simplified by using 2 to multiply both 3a and 5. This will give 6a+10. This means that the simplification of 2(3a+5) = 6a+10.
Similar , 5w-4w-w+6w can be simplified into:
5w+6w-4w-w
= 11w-5w
= 6w.
Therefore,the value of the expression 5w–4w–w+6w is 6w
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4% is equivalent to what fraction
Answers
the value of 4% as a fraction is 1/25
4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.
I have 2 questions
1. my final for one of my classes is 150 points and I need to score at least a 53.16% on the final exam, how many points of the overall 150 would I need to get correct.
2. for my other final it is worth 200 points and I need to score at least a 44.45% on the final exam, how many points of the overall 200 would I need to get correct.
Answers
2. You need to get around 89 points
3 1/2 be classified as integer
Answers
Answer:
False.
Step-by-step explanation:
A integer in math is defined as a whole number. Therefore, the presence of fractions (which, in this case, is 1/2) and decimals, would mean that the term is in fact, not a integer.
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Emilio puts $4,000.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 6 years?
Round your answer to the nearest cent.
Answers
Answer:
$10,359.73.
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money after the specified time
P = the principal amount (the initial amount of money)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have:
P = $4,000.00
r = 15% = 0.15
n = 1 (compounded annually)
t = 6 years
Substituting into the formula, we get:
A = 4000(1 + 0.15/1)^(1*6)
A = 4000(1.15)^6
A ≈ $10,359.73
Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the initial principal (or starting amount), which is $4,000.00 in this case
r = the annual interest rate as a decimal, which is 0.15 (since the interest rate is 15%)
n = the number of times the interest is compounded per year, which is 1 since the interest is compounded annually
t = the number of years, which is 6 in this case
Plugging in the values, we get:
A = 4000(1 + 0.15/1)^(1*6)
A = 4000(1.15)^6
A ≈ $9,432.44
Therefore, the amount in the account after 6 years is approximately $9,432.44.
A circle is represented by the equation (x + 6)2 + (y − 3)2= 121.
Which of the following statements is true?
Group of answer choices
The circle is centered at (−6, 3) and has a radius of 11.
The circle is centered at (−6, 3) and has a diameter of 11.
The circle is centered at (6, −3) and has a diameter of 11.
The circle is centered at (6, −3) and has a radius of 11.
Answers
The statement that is true about the given circle equation is:
Option A: The circle is centered at (−6, 3) and has a radius of 11.
How to find the equation of a circle?The standard form for finding the equation of a circle is given by the expression:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the coordinates of the center of circle
r represents the radius of the circle
We are given the equation of the circle as:
(x - 6)² + (y - 3)² = 121
Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:
(x - 6)² + (y - 3)² = 11²
Comparing with the standard form of equation of a circle gives:
Coordinates of center = (-6, 3)
Radius = 11
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Please see the attached
Answers
The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.
How to Write the equation of a Line in the Slope-intercept Form?The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:
m = slope of the line
b = the y-intercept
Given the following:
slope (m) = -2/5.
y-intercept (b) = -4
To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:
y = -2/5x - 4
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The number of meters a student swam this week are listed.
200, 450, 600, 650, 700, 800
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability and equals 600.
The IQR is the best measure of variability and equals 250.
The mean is the best measure of variability and equals about 567.
The median is the best measure of variability and equals 625.
Answers
The appropriate measure of variability for the data shown and its value is A. The range is the best measure of variability and equals 600.
What is the range?The range is one of the three measures of variability.
The range shows the difference between the highest value and the lowest value in a data set.
The other measures of variability are the IQR (Interquartile Range) and the the Standard Deviation.
Range:Highest value = 800 m
Lowest value = 200 m
The range = 600 m (800 - 200)
IQR = 400 (600 - 200)
Mean = 567 (3,400 ÷ 6)
Median = 625 [(650 + 600) ÷ 2]
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Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
-409-8
Click twice to plot each segment.
Click a segment to delete it.
Slope of the Line:
-3 -2 7
10
9
Submit Answer
5
4
7
9
10
Answers
The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.
What is the Slope of a Line?The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.
Slope of a line (m) = change in y / change in x = rise / run
The red line in the image below represents the rise of the line while the blue line represents the run of the line.
The rise = 3 units
The run = 4 units
Therefore, we have:
Slope (m) = rise/run = -3 units / 4 units
Slope (m) = -3/4.
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4. Which of the following has the best price per unit?
Brand A $5.00 for 2
Brand C $7.00 for 7
Brand B $6.00 for 3
Brand C $8.00 for 3
Answers
OAB is a minor sector of the circle below.
Calculate the length of the minor arc AB in terms of pi
Not drawn accurately
AWARDING BRAINLIEST TO FIRST ANSWER
Answers
The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.
How to Calculate the Length of an Arc?The length of an arc in a given circle can be calculated by applying the formula as expressed below:
Length of arc (s) = ∅/360 * 2πr, where:
Reference angle = ∅
Radius of the circle = r.
Given the parameters:
Radius (r) = 16 cm
Reference angle (∅) = 40 degrees.
Plug in the values:
Length of the arc (s) = 40/360 * 2 * π * 16
Length of the arc (s) = 3.6π cm
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Answer:
To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?
Step-by-step explanation:
College Level Trig Question Please Help!
Answers
The solution of the trigonometric problem is y = -3
How is this so ?Starting with the equation
3/2 cos^-1(y/6) = pi
First, we can simplify by dividing both sides by 3/2 ....
cos^-1(y/6) = pi / (3/2)
cos^- 1(y/6) = 2pi / 3
Next, we can take the cosine of both sides to get...
cos (cos^-1(y/6 ) )
= cos( 2pi/3)
y/6 = -1/2
y = -3
Therefore, the exact solution to the equation 3/2 cos^-1(y/6) = pi is y = -3.
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what is the graphed line of the equation 2x + 3y = -6
Answers
The graphed line of the equation is attached 2x + 3y = -6
What is linear equation?A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:
ax + b = 0
The given equation 2x + 3y = -6 can be rearranged to get
y = -2/3x - 2
The x variables is plugged in to solve for y and used for the table of values for the graph
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tamara plays video games for the same amount of time each day. in 4 days she played video games for 48 minutes in 9 days how many minutes did she play video games
Answers
Answer:
Step-by-step explanation:
Its simple, you need to find x
4 days the same amount of time (x) gives 48 min
4x = 48
x = 48/4
x = 12
then to get the amount of minutes in 9 days it would be:
9x=days
9(12)=108
the answer would be 108 min
Answer:
108 mins
Step-by-step explanation:
48 mins/4 days = x mins/9 days
4x= 432
x=108 mins
Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
Answers
we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .
what is equation ?
An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition
In the given question,
Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:
3 / 15 = 0.2 or 20%
Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.
So, the expected number of white horses among the next 20 horses that come to board is:
20 x 0.2 = 4
Therefore, we should expect 4 white horses among the next 20 horses that come to board.
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Shane has 2 white shirts, 2 blue ones and 1 red one, He has gray pants and black pants. He hung them all up on hangers in his closet, but one shirt and a pair of pants fell on the floor. The probability that a red shirt and black slacks are on the floor is
Answers
The probability that a red shirt and black slacks are on the floor is 1/10.
What is the probability?Probability is the odds that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.
Probability that a red shirt and black slacks are on the floor = (number of red shirts / total number of shirts) x (number of black slacks / total number of slacks)
Total number of shirts = 2 + 2 + 1 = 5
Total number of slacks = 1 + 1 = 2
(1/5) x (1/2) = 1 /1 0
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In a recent test cricket match, Steve made 286 runs in both innings which represented 37% of the team total. How many runs did the team make in the match
Answers
The team made approximately 773 runs in the match.
How to find How many runs did the team make in the matchLet's start by setting up an equation to represent the information given in the problem.
Let's call the total runs made by the team "T".
37% of T = 286
To solve for T, we can start by converting the percentage to a decimal:
37% = 0.37
0.37T = 286
Now we can solve for T by dividing both sides of the equation by 0.37:
T = 286 ÷ 0.37
T ≈ 773.0
Therefore, the team made approximately 773 runs in the match.
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Keyboard A Keyboard B Keyboard C
Person
Person Totals (P) Overall
M = 1 M = 5 M = 6 A 6 N = 15
SS = 8 SS = 22 SS = 10 B 9 G = 60
C 18
D 12 k = 3
E 15
n = 5
Complete all calculations for the ANOVA Summary Table:
SS total, SS within, SS between treatments, SS between subjects, and SS error
df total, df within, df between treatments, df between subjects, and df error
MS between treatments and MS error
the F ratio
Then:
Find critical value for F based on df between treatments and df error, and decide if F ratio is significant or not.
Tukey's HSD is 2.0. Determine which keyboards are significantly different from one another in the number of errors people make and summarize the results.
Answers
Keyboards A and B are significantly different from one another
How to explain the informationThe F ratio has been found to be 4.30, equating to the MS between treatments divided by MS error resulting in a value of 2082/484. In order to seek out the critical value for F at an alpha level of 0.05 within degrees of freedom between treatments (2) and degrees of freedom error (3), we must consult the F-table, revealing it to be 5.14.
We reach the conclusion that rejecting the null hypothesis would not prove necessary as there appears to be no great significance when it comes down to the number of errors made with the three concerned keyboards.
Tukey's HSD signifies 2.0, indicating any distinction of means exceeding such scores is considered noteworthy. Calculating pairwise comparisons can enlighten us as to which keyboards are significant from one another:
Comparing Keyboard A versus Keyboard B: The difference was calculated using |25-6| / ✓(484/6*(1/6+1/6)) = 3.03, determining its significance surpassing Tukey's HSD (2.0).
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Someone help i really need help with this
Answers
The cost of each admission tickets is 37.5 dollars.
How to find the cost in dollars of each admission ticket?Ms Boi spent a total of 175 dollars for 4 admission ticket and for parking at a baseball game. The cost of each admission ticket was the same amount, including tax. The cost of the parking was 25 dollars.
Therefore, the equation that can be use to determine the cost, i of each admission ticket can be represented as follows:
Therefore,
175 = 4i + 25
subtract 25 from both sides of the equation
175 = 4i + 25
175 - 25 = 4i + 25 - 25
150 = 4i
divide both sides by 4
i = 150 / 4
i = 37.5 dollars
Therefore,
cost of each admission ticket = 37.5 dollars
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natalie has $330mto send at the amusment park of this total amount 5% is soent on games, 5/11 is for food and drinks, and she spends $13 on parking. the rest of her budget is spent on buying a ticket for herself and a friend. what is the price of one ticket
Answers
Answer:
Step-by-step explanation:
This is a word problem involving percentages. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.
Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:
games+food and drinks+parking+tickets0.05×330+115×330+13+2x=total amount=330
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
16.5+150+13+2x2x2xxx=330=330−16.5−150−13=150.5=2150.5=75.25
Therefore, the price of one ticket is $75.25.
En un grupo de 60 alumnos, 12 sacaron 10 en el examen de matemáticas. ¿Cuál es el porcentaje de alumnos que sacaron 10?
Answers
We can see that the percentage is 20%, then 20 percent of the students got a 10.
Which percentage of the students got a 10?To find this, we need to use the formula:
Percentage = 100%(number of students with a 10)/(total number of students)
Here we know the that the revelant numbers are:
Number of students with a 10 = 12
total number of students in the class = 60
Replacing that in the formula we will get the percentage:
P = 100%*(12/60)
P = 20%
So 20% of the total number of students got a 10.
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Answer please!!! Will be very thankful
Answers
The estimate of the cost for a 20-ft cord is given as follows:
$74.66.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points in the context of the problem are given as follows:
(3, 12.75), (5, 16), (6, 25.99), (50, 185).
Inserting these points into a calculator, the regression equation is given as follows:
y = 3.6794x + 1.06462.
Hence the estimate of the cost for a 20-ft cord is given as follows:
y = 3.6794(20) + 1.06462
y = $74.66.
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years from 1970 through 2010. X a mathematical model p+ 2 =44
Answers
Given the above model, we can state that it's predictions were accurate.
How is this so?The model uses the variable x which represents no. of years from 1970 to 2010
2010 -1970 = 40
P + (x/2) = 44
P + 40/2 = 44
P + 20 = 44
P = 44 - 20
p = 24
The model, it predicted 24% of the population would be smoking in this city in the year 2010. Whereas the data from the graph tell us that
28 % of the adults actually smoked in the city in 2010. Hence the model is accurate .
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Full Question:
The mathematical model
p+ x/2 =44
Describes the percentage, p, of adults who smoked cigarettes x years after 1970
Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much?
Consider the bridge shown. Use the figure and the fact that AGC is congruent to EGC to complete parts (a) through (e). Round each answer to the nearest tenth
Answers
Therefore, the width of the bridge is approximately 5.9 feet. Therefore, the height of the bridge is approximately 8.4 feet. Therefore, the length of CH is approximately 36.9 feet. Therefore, the measure of angle BHC is approximately 189 degrees. Therefore, the answer to part (e) is no.
What is triangle?A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry, and is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and there are several types of triangles including equilateral, isosceles, and scalene.
Here,
To solve this problem, we will use the fact that AAGC is congruent to AEGC. This means that angle ACG is equal to angle AEC, and angle AGC is equal to angle AEG.
(a) To determine the width AE of the bridge, we can use the tangent function. We have:
tan(27°) = AE/12
Solving for AE, we get:
AE = 12 tan(27°) ≈ 5.9 ft
(b) To determine the height CG of the bridge, we can use the same approach. We have:
tan(36°) = CG/12
Solving for CG, we get:
CG = 12 tan(36°) ≈ 8.4 ft
(c) To determine the length of CH, we can use the Pythagorean theorem. We have:
CH² = CG² + GH²
Substituting the values we found earlier, we get:
CH² = (8.4 ft)² + (40 ft - 5.9 ft)²
CH² = 70.56 ft² + 1288.41 ft²
CH² = 1358.97 ft²
Taking the square root, we get:
CH ≈ 36.9 ft
(d) To determine the measure of angle BHC, we can use the fact that angles AGC and AEG are congruent. We have:
angle BHC = 180° - angle AHC - angle CHB
angle AHC = angle ACG - angle HCG = 27° - 36° = -9° (note that this is a negative angle because it is measured clockwise)
angle CHB = angle CGB - angle HCG = 36° - 36° = 0°
Substituting these values, we get:
angle BHC = 180° - (-9°) - 0°
angle BHC = 189°
(e) To determine whether CH bisects angle ZACG, we need to show that angle CAH is congruent to angle CAG. We have:
angle CAH = 180° - angle HCG - angle ACG
= 180° - 36° - 27°
= 117°
angle CAG = 180° - angle ACG - angle AGC
= 180° - 27° - 27°
= 126°
Since angle CAH is not congruent to angle CAG, we can conclude that CH does not bisect angle ZACG.
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What is the definition of perpendicular lines?
1.two lines that intersect in a way that forms right angles
2.two lines that intersect in a way that cuts both lines in half
3.two lines that intersect in a way that they share more than one common point
4.two lines that intersect in a way that forms two congruent angles
Answers
Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
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Smart Kitchen sells chocolate nonpareils in 8 oz. containers. Because the candy pieces are not uniform, the weight of each individual container varies slightly. A random sample of nine containers was weighed on a precision scale and the results are shown below:
8.09
8.20
8.03
7.86
7.87
8.06
8.43
7.99
8.08
Determine the interquartile range for this sample. Are there any outliers in this data set?
Answers
The interquartile range of the data will be 0.215.
How to calculate the valueThe lower half is:
7.86, 7.87, 7.99, 8.03
The median of the lower half is:
(Q1) = (7.87 + 7.99) / 2 = 7.93
The upper half is:
8.06, 8.08, 8.09, 8.20, 8.43
The median of the upper half is:
(Q3) = (8.09 + 8.20) / 2 = 8.145
The IQR is the difference between the third and first quartiles:
IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215
Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955
Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795
None of the data points fall outside these thresholds, so there are no outliers in this data set.
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