The following data points represent the number of classes that each teacher at Broxin High School teaches.
Sort the data from least to greatest.
Find the interquartile range (IQR) of the data set.
57511945346
Answers
Answer:
IQR= 3
Step-by-step explanation:
Hello!
The data represents the number of classes taught by each teacher at Broxin High School.
To calculate the IQR you have to do the following steps:
1) Arrange the data from least to greatest:
Raw data: 5, 7, 5, 1, 1, 9, 4, 5, 3, 4, 6
Arranged: 1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
2) Calculate the 1st Quartile (Q₁):
The first quartile divides the bottom 25% of the data from the top 75%, to know which value of the data set corresponds to it you have to calculate its position:
PosQ₁= (n+1)/4= (11+1)/4= 3
This means that the 1st quartile corresponds to the 3rth observation:
1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
Q₁= 3
3) Calculate the 3rd Quartile (Q₃)
The third quartile divides the bottom 75% of the data from the top 25%, as before, you have to calculate its position and then identify the value in the data set.
PosQ₃= (n+1)*(3/4)= (11+1)*(3/4)= 9
The third quartile corresponds to the 9th observation:
1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
Q₃= 6
4) Interquartile range (IQR)
The IQR shows you the distance where the middle 50% of the data set is.
IQR= Q₃-Q₁= 6-3 = 3
I hope this helps!
Related Questions
Dove for x in the diagram below.
Answers
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for fraction bar(s)
f(x) {____if -1_< x _<1
____if 3_< x _<5
Answers
Answer: f(x) = 4 if -1 ≤x ≤ 1
f(x) = x - 1 if 3≤ x ≤ 5
Step-by-step explanation:
if -1 ≤x ≤ 1
We can see that in this range the function is constant, f(x) = 4
if 3≤ x ≤ 5
In this region we can see a linear relationship, with the points (3, 2) and (5, 4)
as the extremes, we can find the slope of this linear equation as:
s = (4 - 2)/(5 - 3) = 2/2 = 1
So our equation is
f(x) = 1*x + b
to find the value of b we can evaluate our function in the first point, we know that when x = 3, y = 2, so we have:
2 = 1*3 + b
b = 2- 3 = -1
then f(x) = 1*x - 1
Then we have:
f(x) = 4 if -1 ≤x ≤ 1
f(x) = x - 1 if 3≤ x ≤ 5
Which of the following represents a function?
Answers
Answer:
see below
Step-by-step explanation:
A graph is a function if any vertical line intersects points on the graph only once. The graph of A is a function.
__
Ordered pairs represent a function if no x-value is repeated. In the list of B, the x-value -1 shows up twice. The list of B is not a function.
__
As with ordered pairs, a table represents a function if no x-value is repeated. In the table of C, the x-value 3 shows up twice. The table of C is not a function.
__
A mapping diagram represents a function if each x-value is only mapped to one y-value. In the map of D, the x-value 3 is mapped to two different y-values. The map of D is not a function.
Answer:D
Step-by-step explanation:
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply.
Answers
Answer:
-2 & 1/3
Step-by-step explanation:
When you set the two equations equal to each other, they form to parallel, vertical lines. They cross the x-axis at -2 and 1/3. Hope this helps.
What’s the correct answer for this?
Answers
Answer:
A
Step-by-step explanation:
Cosine X= adjacent /hypotenuse
where adjacent=5 and hyp=13
Cos X=5/13
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answers
Answer:
19.5 in²
Step-by-step explanation:
Area of rhombus tile = side × height
Area = 3 × 6.5
Area = 19.5 in²
A rhombus, like any parallelogram, has area equal to base times height,
that's 3×6.5 = 19.5 square inches
Answer: 19.5
At 3:30 P.M., the water level in a pool is 14 inches. At 4:00 P.M., the water level is 20 inches. At 5:00 P.M., the water level is 32 inches. What is the constant rate of change?
Answers
Answer: Per 1/2 an hour it is changes by 5 so the constanT rate would be: 5 inches per 1/2 an hour
Which sequence of transformations produces an image that is not congruent to the original figure?
A. A reflection across the x axis followed by a rotation of 180 counterclockwise
B. A translation of 6 units to the left followed by a reflection across the x-axis
C. A rotation of 90° clockwise followed by a translation of 4 units to the left
D. A translation of 4 units to the left followed by a dilation of a factor of 3
Answers
Answer:
D. A translation of 4 units to the left followed by a dilation of a factor of 3
Step-by-step explanation:
Of the transformations, rotation, reflection, translation, dilation, the first three (rotation, reflection, translation) are known as "rigid" transformations. They do not change the shape or size of the object. Any result of a rigid transformation is congruent to the original.
Dilation, by its nature, changes the size of the object, so the result is NOT congruent to the original.
Choice D includes dilation, so the image is not congruent to the original.
What is the axis of symmetry for the graph of y – 4x = 7 – x2 ?
Answers
Answer:
x = 2
Step-by-step explanation:
A graph shows the axis of symmetry easily. It is the x-coordinate of the vertex.
x = 2
__
You can rearrange the equation to ...
y -7 = 4x -x^2
y -7 = x(4 -x)
The axis of symmetry is halfway between x-values that give the same y-value. Here, y=7 for x=0 and for x=4. That is, the right side of this equation is zero at those x-values. The axis of symmetry is halfway between, at x = (0+4)/2 = 2
The axis of symmetry is x=2.
_____
Alternate solutions
In standard form,
ax^2 +bx +c = y
the axis of symmetry is ...
x = -b/(2a)
Putting this equation into that form, we have ...
-x^2 +4x +7 = y
x = -(4)/(2(-1))
x = 2 . . . . axis of symmetry
__
We can rearrange the equation to vertex form.
y -7 = -x^2 +4x
y -7 -4 = -(x^2 -4x +4) . . . . . add the square of half the x-coefficient inside parentheses. Add an equal amount to the other side of the equation.
y -11 = -(x -2)^2
This tells us the vertex of the graph is (2, 11), so the axis of symmetry is x=2.
Mr. Khan went for a trip in his car, which travels 14.5km/h on 1 liter petrol. The
reading of a speedometer was 19034.0 km when he started his journey and read
19396.5 km after he had completed his journey. How many liters of petrol are
consumed?
Answers
Answer:
25L
Step-by-step explanation:
19396.5 km - 19034.0 km = 362.5 km travled
362.5 km / 14.5 km/L = 25L
9 inches of ribbon are needed for wrapping each present. How many presents can be wrapped with 6 yards of ribbon?
Answers
Answer:
a total of 24 presents can be wrapped
Step-by-step explanation:
6 x 3 = 18 feet of ribbon
18 x 12 = 216 inches of ribbon
216/9 = 24 presents can be wrapped
The daily exchange rates for the five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.832 in currency A (to currency B) and standard deviation 0.044 in currency A. Given this model, and using the 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely, complete parts (a) through (d). a) What would the cutoff rate be that would separate the highest 2.5% of currency A/currency B rates?
Answers
Answer:
The cutoff rate that would separate the highest 2.5% of currency A/currency B rates is 1.92.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 1.832
Standard deviation = 0.044
Top 2.5%
95% of the measures are within 2 standard deviation of the mean.
Since the normal distribution is symmetric, this 95% goes from the 50 - 95/2 = 2.5th percentile to the 50 + 95/2 = 97.5th percentile.
The 97.5th percentile is the cutoff for the highest 2.5% of currency A/currency B rates, and it is 2 standard deviations above the mean.
1.832 + 2*0.044 = 1.92
The cutoff rate that would separate the highest 2.5% of currency A/currency B rates is 1.92.
What is the area of the triangle
Answers
Answer:
A. 6 inchesssssssss
Answer:
6
Step-by-step explanation:
Determine whether the equation is always sometimes or never true 2/3x+4=2x
Answers
Answer:
true
Step-by-step explanation:
x=3
The value of the variable x is 3. Then the equation is always true.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
(2/3)x + 4 = 2x
Simplify the equation, then the value of x will be
2x + 12 = 6x
4x = 12
x = 3
The value of the variable x is 3. Then the equation is always true.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
The graph of a function is shown below.
D
Which statement best describes section D of the graph?
0 А.
linear and increasing
О В.
linear and decreasing
Ос.
nonlinear and increasing
OD
nonlinear and decreasing
Answers
A television show tests the abilities of alleged psychics by presenting contestants with a set of
4
44 cards placed upside down,
1
11 of which has a star printed on it. Each contestant attempts to identify which card has the star on it for a series of
50
5050 trials.
Assuming that the contestants are purely guessing, what are the mean and standard deviation of the number of trials where the contestant guesses correctly?
Answers
Answer:
The mean and standard deviation of the number of trials where the contestant guesses correctly are 12.50 and 3.062.
Step-by-step explanation:
Total number of cards presented to the contestants, N = 4.
Number of cards that has a star printed on it is, x = 1.
The probability of selecting the correct card is:
[tex]P(X)=\frac{x}{N}=\frac{1}{4}=0.25[/tex]
It is provided that each contestant attempts to identify which card has the star on it for a series of n = 50 trials.
Each trial's outcome is independent of other outcomes.
The success of each trial is denoted by the correct selection of the card with a star.
The random variable X can be explained by the Binomial distribution.
So, X follows a Binomial distribution with parameters n = 50 and p = 0.25.
The mean and standard deviation of a Binomial distribution are:
[tex]\text{Mean}=np\\\\\text{SD}=\sqrt{np(1-p)}[/tex]
Compute the mean and standard deviation of the number of trials where the contestant guesses correctly as follows:
[tex]\text{Mean}=np=50\times 0.25=12.50\\\\\text{SD}=\sqrt{np(1-p)}=\sqrt{50\times 0.25\times (1-0.25)}=3.062[/tex]
Thus, the mean and standard deviation of the number of trials where the contestant guesses correctly are 12.50 and 3.062.
[tex]N = 4[/tex] is the overall number of points distributed to the contestant, [tex]x = 1[/tex] reflects the number of decks with a star on them. The probability of selecting the correct card is as follows:
[tex]\to P(X)=\frac{x}{N}=\frac{1}{4}=0.25[/tex]
For a total of n = 50 trials, each competitor must determine whichever card has the star on it.The result of each trial is different from the results of the others.A proper selection of a card with such a star shows the success of each trial.The Binomial distributions can account for such a random value of x, As a result, X has a binomial distribution having values [tex]n = 50[/tex] and [tex]p = 0.25[/tex].The Binomial distribution does have the following mean and standard deviation:[tex]\to \text{Mean =np}\\\\\to \text{SD}=\sqrt{np(1-p)}\\\\[/tex]
Determine the mean difference of the number of tests where the contender correctly guesses:[tex]\to \text{Mean =np}= 50 \times 0.25= 12.5\\\\[/tex]
[tex]\to SD=\sqrt{np(1-p)}[/tex]
[tex]=\sqrt{50 \times 0.25 \times (1-0.25)}\\\\=\sqrt{50 \times 0.25 \times (0.75)}\\\\= \sqrt{12.5 \times 0.75}\\\\=\sqrt{9.375}\\\\=3.061[/tex]
As just a result, the standard deviation of the number most right guesses by the competitor are [tex]12.50 \ \ and\ \ 3.061[/tex], correspondingly.
Learn more about the contestant guesses:
brainly.com/question/1302166
se x vale 3 quanto vale 2x
Answers
Answer:
6
Step-by-step explanation:
x=3
2x = 2(3) = 6
1/3 of 3 feet equals how many inches
Answers
Answer:
12 inches
Step-by-step explanation:
1/3 of 3 feet = 1 foot
12 inches make 1 foot
so the answer is 12
The number of inches in 1/3 of 3 feet will be 12 inches.
What is the length?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
1/3 of 3 feet
Then the number of feet is given as,
⇒ (1/3) x 3
⇒ 1 foot
We know that in 1 foot, there are 12 inches. Then we have
⇒ 1 x 12 inches
⇒ 12 inches
The number of inches in 1/3 of 3 feet will be 12 inches.
More about the distance link is given below.
https://brainly.com/question/26711747
#SPJ2
The digit in the ten's place of a two digit number is one less than the digit in the one's place. If we add this number to the number obtained by reversing its digits, the result is 55, find the number.
Answers
Answer:
23
Step-by-step explanation:
55 = 23 + 32
14 and 41 came into my d, but 1 and 4 are 3 apart from each other
(would really appreciate the brainliest)
Can anyone help me with this?
Answers
Answer:
35 yards
Step-by-step explanation:
20yd+15yd
you add 20yd and the 15yd and that is your area.
Find cos(a) in the triangle.
Choose 1 answer
Answers
Answer:
the correct answer is 35 / 37
Im a parent for a 5th grader and don't remember this, plz help?
Again,
Josh wants to make 5 airplane propellers. he needs 18 centimeters of wood for each propeller. how many centimeters of wood will he use? How can I help him understand this problem.
Answers
Answer:
90 cm.
Step-by-step explanation:
One airplane propeller needs 18 centimetres of wood.
Josh wants to make 5 of them.
So, we would have to take the '18' centimetres of wood and multiply by 5 to get the total for all 5 pieces.
[tex]\text{Number of Propellers} * 18 \text{ Centimetres}[/tex]
[tex]5 * 18 = 90[/tex]
Josh should need 90 centimetres of wood total to make 5 airplane propellers.
Answer=90
Consider the estimated equation from Example 4.3, which can be used to study the effects of skipping class on college GPA: 2 colGPA 1.39 .412 hsGPA .015 ACT .083 skipped (.33) (.094) (.011) (.026) n 141, R2 .234. (i) Using the standard normal approximation, find the 95% confidence interval for hsGPA. (ii) Can you reject the hypothesis H0: hsGPA .4 against the two-sided alternative at the 5% level
Answers
Answer:
Step-by-step explanation:
1) The confidence interval is calculated as the following
[tex]CI = ( \bar x-1.96 \sigma ,\bar x=1.96 \sigmam)[/tex]
[tex]= (0.412-1.96 \times 0.094, 0.412 = 1.96 \times 0.094)\\\\= (0.22776, 0.59624)[/tex]
Hence, the confidence interval is [tex]0.22776 \leq \beta_G_P_A \leq 0.59624)[/tex]
11) Under two sid t-tailed test, the null hypothesis
[tex]H_0; \beta_{GPA}=0.4[/tex]
Against the alternative hypothesis
[tex]H_1 ; \beta _{GPA} \neq 0.4[/tex]
Under null hypothesis
[tex]t = \frac{\hat \beta _1 - \beta _1}{Se( \beta _1)} \\\\ =\frac{0.412-0.4}{0.094} \\\\=0.12766[/tex]
The degree of freedom is n - 1 = 140
From the t - table at 5% level of significance under two - tail is 1.96
Since , calculated value is lowe than the tabulated value, we do not reject the null hypothesis.
A researcher is interested in whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. He classifies participants into three transportation groups (those who: bike/walk, take public transit or drive) and asks them how they typically feel on a normal Monday morning: happy/excited, angry/irritated, or sleepy. Data from his survey on 200 participants are presented below.
Happy Angry sleepy Total
Bike/Walk 20 7 13 40
Public transit 13 5 42 7
Drive 17 18 65 100
Total 50 30 120 200
You would like to test his question of whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. Calculate a two variable chi-square test using an alpha (α) level of 0.01.
You will use the information above to complete the question parts below for a two variable chi-square test.
Part A: Which of the following represents the appropriate null hypothesis(H0), given your research question of interest?
Part B: Which of the following represents the appropriate alternative hypothesis (H1), given your research question of interest?
Part C: What is your degrees of freedom (df)?
Part D: What is the critical chi-square value (from the Chi-square table) appropriate for your test, testing at an alpha level (α) of 0.01?
Part E: What is your calculated chi-square statistic?
Part F: What is your decision about the null hypothesis based on your test results?
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
How large is the largest button in the jar ? , is this an statistical question ?
Answers
Let P(-6,4) be a point on a rectangle PQRS. What are the coordinates of P if the rectangle is dilated by a scale factor of 3/8?
Answers
Answer:
(-2.25, 1.5)
Step-by-step explanation:
If dilation is about the origin, each of the coordinates is multiplied by the dilation factor:
P' = (3/8)P = 3/8(-6, 4) = (-18/8, 12/8)
P' = (-2.25, 1.5)
Ivan needs gas for his truck. He knows his truck holds 20 gallons of gas. His gas can does not measure gallons, though. It measures pints. How many times will he have to fill up his gas can to get his truck full of gas?
Answers
Answer: 160 times
Step-by-step explanation:
Welcome hope it worked
Which of the following explains the cause of the seasons changing on Earth?
The rotation of the Earth and sun.
The tilt of the axis of Earth and orbit of Earth around the sun.
The orbit of the Earth around the sun and rotation of the Earth.
The orbit of the Earth around the sun and rotation of the sun.
Answers
Answer:
The tilt of the axis of Earth and orbit of Earth around the sun.
Step-by-step explanation:
Answer options
The rotation of the Earth and sun.
IncorrectThe tilt of the axis of Earth and orbit of Earth around the sun.
Correct, seasons change because Earth tilts on its axis, and the angle of tilt causes the Northern and Southern Hemispheres to trade places throughout the year in receiving the sun's light and warmth most directlyThe orbit of the Earth around the sun and rotation of the Earth.
IncorrectThe orbit of the Earth around the sun and rotation of the sun.
IncorrectAnswer:
C - The orbit of the Earth around the sun and rotation of the Earth.
Step-by-step explanation:
Select two ratios that are equivalent to 7: 10.
Choose 2 answers:
Answers
Answer:
I hope this helps. Have a great rest of your day!
Do you mind showing the answer choices? I just realized you had "Choose 2 answers".
esearchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is 0 versus the alternative that the slope is greater than 0 yielded a p-value of 0.04.
Which statement is an appropriate conclusion for the test?
(A)The p-value of 0.04 indicates that 4% ofthe variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass.
(B) The p-value of0.04 indicates that 16% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass.
(C)The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that college athletes with higher lean body mass tend to have higher maximal oxygen uptake.
(D)The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes.
(E) A p-value less than 0.05 indicates that the relationship displayed in the scatterplot is likely due to chance, and that there is no statistical evidence ofa relationship between lean body mass and maximal oxygen uptake for college athletes.
Answers
Answer:
The correct option is (D).
Step-by-step explanation:
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard H₀.
A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.
The hypothesis is defined as follows:
H₀: The slope of the regression line is 0, i.e. β = 0.
Hₐ: The slope of the regression line is greater than 0, i.e. β > 0.
A scatter-plot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables; lean body mass and maximal oxygen uptake.
The significance level of the test is, α = 0.05.
The p-value of the test is, p-value = 0.04
As the p-value = 0.04 < α = 0.05, we reject the null hypothesis.
So, it can be concluded that there is a statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes.
Since the scatter-plot shows a strong positive linear relationship, it implies that as the an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes.
Thus, the correct option is (D).
