Dannette and Alphonso work for a computer repair company. They must include the time it takes to complete each repair in their repair log book. The dot plots show the number of hours each of their last 12 repairs took. Part a. Calculate the median, mean, IQR, and standard deviation of each data set. Part b. Which measure of central tendency and spread should you use to compare the two data sets? Explain your reasoning. Part c. Determine whether there are any outliers in either data set. Dannette's Repair Times х х X X X X Х Х + 9 + 1 0 Relations 2 3 4 8 10 12 5 6 7 Repair Time (hours) Geometry Alphonso's Repair Times Groups X Trigonometry X Х X X X х X х Statistics 7 X + 3 10 9 0 4 12 Series 8 1 2 5 7 Repair Time (hours) Greek
PLZ HELP
Answers
Answer:
(a):
Dannette Alphonso
[tex]\bar x_D = 4.33[/tex] [tex]\bar x_A = 5.17[/tex]
[tex]M_D = 2.5[/tex] [tex]M_A = 5[/tex]
[tex]\sigma_D = 3.350[/tex] [tex]\sigma_A = 1.951[/tex]
[tex]IQR_D = 7[/tex] [tex]IQR_A = 1.5[/tex]
(b):
Measure of center: Median
Measure of spread: Interquartile range
(c):
There are no outliers in Dannette's dataset
There are outliers in Alphonso's dataset
Step-by-step explanation:
Given
See attachment for the appropriate data presentation
Solving (a): Mean, Median, Standard deviation and IQR of each
From the attached plots, we have:
IQR_A = 1.5 ---- Dannette
[tex]A = \{3,4,4,4,4,5,5,5,5,6,6,11\}[/tex] ---- Alphonso
n = 12 --- number of dataset
Mean
The mean is calculated
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_D = \frac{1+1+1+1+2+2+3+7+8+8+9+9}{12}[/tex]
[tex]\bar x_D = \frac{52}{12}[/tex]
[tex]\bar x_D = 4.33[/tex] --- Dannette
[tex]\bar x_A = \frac{3+4+4+4+4+5+5+5+5+6+6+11}{12}[/tex]
[tex]\bar x_A = \frac{62}{12}[/tex]
[tex]\bar x_A = 5.17[/tex] --- Alphonso
Median
The median is calculated as:
[tex]M = \frac{n + 1}{2}th[/tex]
[tex]M = \frac{12 + 1}{2}th[/tex]
[tex]M = \frac{13}{2}th[/tex]
[tex]M = 6.5th[/tex]
This implies that the median is the mean of the 6th and the 7th item.
So, we have:
[tex]M_D = \frac{2+3}{2}[/tex]
[tex]M_D = \frac{5}{2}[/tex]
[tex]M_D = 2.5[/tex] ---- Dannette
[tex]M_A = \frac{5+5}{2}[/tex]
[tex]M_A = \frac{10}{2}[/tex]
[tex]M_A = 5[/tex] ---- Alphonso
Standard Deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma_D = \sqrt{\frac{(1 - 4.33)^2 +.............+(9- 4.33)^2}{12}}[/tex]
[tex]\sigma_D = \sqrt{\frac{134.6668}{12}}[/tex]
[tex]\sigma_D = 3.350[/tex] ---- Dannette
[tex]\sigma_A = \sqrt{\frac{(3-5.17)^2+............+(11-5.17)^2}{12}}[/tex]
[tex]\sigma_A = \sqrt{\frac{45.6668}{12}}[/tex]
[tex]\sigma_A = 1.951[/tex] --- Alphonso
The Interquartile Range (IQR)
This is calculated as:
[tex]IQR =Q_3 - Q_1[/tex]
Where
[tex]Q_3 \to[/tex] Upper Quartile and [tex]Q_1 \to[/tex] Lower Quartile
[tex]Q_3[/tex] is calculated as:
[tex]Q_3 = \frac{3}{4}*({n + 1})th[/tex]
[tex]Q_3 = \frac{3}{4}*(12 + 1})th[/tex]
[tex]Q_3 = \frac{3}{4}*13th[/tex]
[tex]Q_3 = 9.75th[/tex]
This means that [tex]Q_3[/tex] is the mean of the 9th and 7th item. So, we have:
[tex]Q_3 = \frac{1}{2} * (8+8) = \frac{1}{2} * 16[/tex] [tex]Q_3 = \frac{1}{2} * (5+6) = \frac{1}{2} * 11[/tex]
[tex]Q_3 = 8[/tex] ---- Dannette [tex]Q_3 = 5.5[/tex] --- Alphonso
[tex]Q_1[/tex] is calculated as:
[tex]Q_1 = \frac{1}{4}*({n + 1})th[/tex]
[tex]Q_1 = \frac{1}{4}*({12 + 1})th[/tex]
[tex]Q_1 = \frac{1}{4}*13th[/tex]
[tex]Q_1 = 3.25th[/tex]
This means that [tex]Q_1[/tex] is the mean of the 3rd and 4th item. So, we have:
[tex]Q_1 = \frac{1}{2}(1+1) = \frac{1}{2} * 2[/tex] [tex]Q_1 = \frac{1}{2}(4+4) = \frac{1}{2} * 8[/tex]
[tex]Q_1 = 1[/tex] --- Dannette [tex]Q_1 = 4[/tex] ---- Alphonso
So, the IQR is:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR_D = 8 - 1[/tex] [tex]IQR_A = 5.5 - 4[/tex]
[tex]IQR_D = 7[/tex] --- Dannette [tex]IQR_A = 1.5[/tex] --- Alphonso
Solving (b): The measures to compare
Measure of center
By observation, we can see that there are outliers is the plot of Alphonso (because 11 is far from the other dataset) while there are no outliers in Dannette plot (as all data are close).
Since, the above is the case; we simply compare the median of both because it is not affected by outliers
Measure of spread
Compare the interquartile range of both, as it is arguably the best measure of spread, because it is also not affected by outliers.
Solving (c): Check for outlier
To check for outlier, we make use of the following formulas:
[tex]Lower =Q_1 - 1.5 * IQR[/tex]
[tex]Upper =Q_3 + 1.5 * IQR[/tex]
For Dannette:
[tex]Lower = 1 - 1.5 * 7 = -9.5[/tex]
[tex]Upper = 8 + 1.5 * 7 = 18.5[/tex]
Since, the dataset are all positive, we change the lower outlier to 0.
So, the valid data range are:
[tex]Valid = 0 \to 18.5[/tex]
From the question, the range of Dannette's dataset is: 1 to 9. Hence, there are no outliers in Dannette's dataset
For Alphonso:
[tex]Lower = 4 - 1.5 * 1.5 =1.75[/tex]
[tex]Upper = 5.5 + 1.5 * 1.5 =7.75[/tex]
So, the valid data range are:
[tex]Valid = 1.75\to 7.75[/tex]
From the question, the range of Alphonso's dataset is: 3 to 11. Hence, there are outliers in Alphonso's dataset
Related Questions
Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?
x less-than negative 5
x greater-than negative 5
x greater-than negative 1
x less-than negative 1
Answers
Answer:
B
Step-by-step explanation:
Let the number = x
2/5 (x - 1)
<
3/5 (x + 1)
2/5 (x - 1 ) < 3/5(x+ 1) Multiply both sides by 5
2(x - 1) < 3 ( x + 1) Remove the brackets.
2x - 2 < 3x + 3 Add 2 to both sides
2x < 3x + 5 Subtract 3x from both sides
2x - 3x < 5
- x < 5 Here's the tricky part . Divide by - 1
x > -5 Notice what happened. The < become > That happens because you have divided (or multiplied) by a negative number.
The original question 2/5 (x - 1 ) < 3/5(x+ 1) was graphed. The red part is every value that satisfies the inequality. You should be using a y and x together to find a more suitable answer using this program. But if you just look along the x axis, you will see that the < has been turned around.
B The second one from the top.
Expand & simplify ( 3 x − 2 ) ( 3 x - 2 ) + ( x + 6 ) ( x − 8 )
Answers
Answer:
x=2,92 or x=_1.51
Step-by-step explanation:
factories out all the brackets first
(3x_3)(3x_2)+(x+6)(x_8)
9x^2_6x_6x+4+x^2_8x+6x_48
add and sutract only like terms
10x^2_14x_44
solve the equation using the quadratic fomula
x =2.91 and x= _1.51
In psychology, aptitude tests are designed to measure the ability to learn. Questions are designed to be age appropriate so as not to be biased toward age due to knowledge acquired. In this study, an aptitude test is given on the skills necessary to use apps on a smart phone. An aptitude test with a maximum score of 150 is given to measure the ability to learn how to use apps on a smartphone.
The regression line for the predicted value of aptitude given age is as follows:
Aptitude = 111.3 - 1.13*Age
Find the expected aptitude test score for a person whose age is 15 years. Your answer should be rounded to the nearest whole number.
Answers
Answer:
The expected aptitude test score for a person whose age is 15 years is 94.
Step-by-step explanation:
Aptitude formula in function of age:
The aptitude A in function of age a is given by:
[tex]A(a) = 111.3 - 1.13a[/tex]
Find the expected aptitude test score for a person whose age is 15 years.
This is A when a = 15. Thus, finding the numeric value of the function:
[tex]A(a) = 111.3 - 1.13a[/tex]
[tex]A(15) = 111.3 - 1.13(15) = 94.35[/tex]
Rounding to the nearest whole number, 94.
In this question, we first explain the expected aptitude test after that we calculate its value.
The test of aptitude allows employers to assess the skills of a candidate via a variety of test formats. Required to test your ability to do things and react to working circumstances is tested. It includes, among others, problem-solving, prioritization as well as numeracy skills.When a score of 100% again for a perfect aptitude test, as well as a score of 80% or greater is considered a good person with the minimum acceptable score is deemed to be between 70% and 80%.Given:
[tex]\to \bold{Aptitude = 111.3 - 1.13*Age}[/tex]
[tex]\to \bold{Age= 15 \ years}\\\\[/tex]
Putting the age value into the Aptitude equation to calculate its value:
[tex]\bold{= 111.3 - 1.13*(15)}\\\\\bold{= 111.3 - 16.95}\\\\\bold{=94.35 \approx 94} \\\\[/tex]
Therefore, For a person 15 years of age 94, the anticipated test score for aptitude.
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Avery's piggy bank has 300 nickels
Answers
Answer:
Step-by-step explanation:
?
Solve mentally. See the image below.
Answers
Answer:
7.5 is 37.5% of 20.
Step-by-step explanation:
Solve for %
We know that ; % = given no. ÷ total no. × 100
Where, we've
Given number = 7.5and Total number = 20plug the values
[tex] \small \sf \frac{7.5}{20} \times 100 \\ [/tex]
canceling 100 by 20 to get
7.5 × 5
multiply the numbers
37. 5 %
From the information given, (a) construct the indicated sample space and (b) answer the probability question.
a. A couple planning to have three children.
b. Find the probability of having exactly one girl.
Answers
Answer:
(a) 3 (b) 1/3
Step-by-step explanation:
The probability is defined as the ratio of number of elements in event to the number of elements in sample space.
(a) As the total number of child is 3, so the number of elements in sample space = 3
(b) The sample space is { boy, boy, girl}
So, the probability is 1/3.
In a Louisiana chili cook-off, 18 of the 40 chilis included two types of beans.
A photo of multiple crock pots on a long table is shown. The caption says chili cook-off.
What percentage of the chilis did not include two types of beans?
Enter the correct answer in the box.
Answers
Answer:
55%
Step-by-step explanation:
18 out of 40 include chili.
So 22 has no chili
22/40 = 0.55 or 55%
24.
What is the value of x to the nearest tenth?
A. 4.8
B. 9.2
C. 7.2
D. 12.0
Answers
I'm not sure it its prob D
Student researchers investigated whether balsa wood is less elastic after it has been immersed in water. They took 60 pieces of balsa wood and randomly assigned half to be immersed in water and the other half not to be. They measured the elasticity by seeing how far (in inches) the piece of wood would project a dime into the air.
Required:
​Does the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation-based method (p < 0.0001)?
Answers
Yes, they are quite similar. the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation - based method (p < 0.0001)
P- value is the probability of obtaining a value of test statistic more extreme in the direction of alternative hypothesis than the observed one. In easy words if p -value < level of significance we reject H0 in favor of H1.
Here:
p-value < 0.0001 => we reject H0.
If the statistical software renders a p value of 0.000 it means that the value is very low, with many "0" before any other digit.
So the interpretation would be that the results are significant, same as in the case of other values below the selected threshold for significance.
Therefore, yes they are quite similar.
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Incomplete Question:
Student researchers investigated whether balsa wood is less elastic after it has been immersed in water. They took 60 pieces of balsa wood and randomly assigned half to be immersed in water and the other half not to be. They measured the elasticity by seeing how far (in inches) the piece of wood would project a dime into the air.
Does the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation-based method (p < 0.0001)?
A. No, they are different.
B. Yes, they are quite similar.
which of the following exponential functions represents the graph below?
[tex] a.\: \: \: \: \: \: f(x) = 5 • ( \frac{1}{4}) {}^{x} [/tex]
[tex] b. \: \: \: \: \: \: \: \: \: \: \ f(x)5•4 {}^{x} [/tex]
[tex]c .\: \: \: \: \: \: f(x) = 4• ( \frac{1}{5}) {}^{x} [/tex]
[tex]d. \: \: \: \: f(x)=4•5 {}^{x} [/tex]
Answers
Step-by-step explanation:
the answer is not a and b because when we accept 0 from x and look at graphic you can see 4
Balance m - 16=35 image attached
Answers
Answer:
B
Step-by-step explanation:
You're trying to isolate the m so add 16 to both sides to cancel the -16
What is the length of leg s of the triangle below?
459
872
90+
45
A. 8
B. v
C. 8-12
D. 4.2
E. 1
F. 2
Answers
Answer:
option A
Step-by-step explanation:
take 45 degree as reference angle
using sin rule
sin 45 = opposite / hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] = s/[tex]8\sqrt{2}[/tex]
[tex]\frac{1}{\sqrt{2} } *8\sqrt{2}[/tex] = s
root 2 and root 2 gets cancel
8 = s
What is the answer for this one
Answers
Answer: 2617 centimeters cubed
Step-by-step explanation:
The formula for finding volume of a cylinder is [tex]V=\pi r^2h[/tex]
The radius is half of the diamerter which will be 7 for this figure.
The height is marked 17
[tex]\pi 7^2(17)\\\pi (49)(17)\\833\pi \\[/tex]
833π is about 2616.95
Rounded to the nearest whole number it is 2617
As percents of the whole, how big are the following?
Answers
Answer:
A= 1%
B=10%
C= 32%
Step-by-step explanation:
There are 100 total squares, which makes this easy because a percent is out of 100%. All you have to do is count the number of squares and put it out of 100
The probability distribution for a random variable x is given in the table X: -5,-3,-2,0,2,3 Probability: .17,.13,.33,.16,.11,.10 Find the probability that -2<_x<_2
Answers
Answer:
0.6 probability that [tex]-2 \leq x \leq 2[/tex]
Step-by-step explanation:
The probability distribution is given in the table.
Probability that x is between -2 and 2.
Between -2 and 2, inclusive, we have -2, 0 and 2. So
[tex]P(-2 \leq x \leq 2) = P(X = -2) + P(X = 0) + P(X = 2)[/tex]
From the table:
[tex]P(X = -2) = 0.33, P(X = 0) = 0.16, P(X = 2) = 0.11[/tex]. So
[tex]P(-2 \leq x \leq 2) = P(X = -2) + P(X = 0) + P(X = 2) = 0.33 + 0.16 + 0.11 = 0.60[/tex]
0.6 probability that [tex]-2 \leq x \leq 2[/tex]
work out the value of 6.8x10^2 x 1.3x10^-3
Answers
Answer:
0.884
Step-by-step explanation:
just use a calculator
Please help, What equation is always true?
Answers
Answer:
4. m<7 = m<3 + m<2
Step-by-step explanation:
Recall: the exterior angle theorem of a triangle states that an exterior angle is equal to the sum of the two opposite interior angles of a triangle.
❌Option 1 CANNOT be true
Rationale:
m<1 is an exterior angle of triangle ∆ABC and ∆EBC, so based on the exterior angle theorem of a triangle, m<1 = m<3 + m<4 or m<1 = m<ABC + m<5
❌Option 2 CANNOT be true.
Rationale:
m<5 ≠ m<3 - m<2
❌Option 3 CANNOT be true.
Rationale:
m<6 ≠ m<3 - m<2
✅Option 4 is CORRECT.
Rationale:
Based on the external angle theorem of a triangle,
m<7 = m<3 + m<2
Jasmine bought a game system
that cost $299 before tax. The total
including sales tax was 1.07 times
the price. A discount was then
applied by multiplying the total price
by 0.90. What was the total cost of
the game system including the sales
tax and discount?
Answers
9514 1404 393
Answer:
$287.94
Step-by-step explanation:
The final cost is found by multiplying the cost by the various factors:
$299 × 1.07 × 0.90 ≈ $287.94
whenever a,x,y are positive integers, which of the following expressions is equivalent to x^ay^a
Answers
Answer:
[tex]{(xy)}^{a} [/tex]
Step-by-step explanation:
when the exponent is equal, we can put the x and y together in a bracket and a as the Exponent of xy.
Hope I get your question~
HELP HELP HELP HELP solve this
Answers
Answer:
77
Step-by-step explanation:
When the variable is on both sides of the inequality it must be isolated on one side and it doesn’t matter which side
Answers
Answer:
True
Step-by-step explanation:
Answer:
Isolate the variable and then use substitution to solve the system of equations.
Step-by-step explanation:
.
Calculate the number of vertices in a full 5-ary tree with 35 internal vertices.
Also, find out the number of leaves
Answers
Answer:
Step-by-step explanation:
With 35 internal nodes, there are 5*35=175 vertices out of which are 175-35=140 leaves.
The number of vertices in a full 5-ary tree is 175.
The number of leaves is 140.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of full trees = 5
Number of internal vertices = 35
Now,
The number of vertices.
= 5 x 35
= 175
Now,
The number of leaves.
= 175 - 35
= 140
Thus,
Number of vertices is 175.
Number of leaves is 140.
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A random sample of 10 subjects have weights with a standard deviation of 12.7363 kg. What is the variance of their weights?
Answers
Answer:
Variance, V = 162.2133 kg²
Step-by-step explanation:
Given the following data;
Standard deviation = 12.7363 kg.
To find the the variance of their weights?
Mathematically, standard deviation is equal to the square root of variance.
[tex]Sd = \sqrt{V}[/tex]
Where;
Sd is the standard deviation of the sample.
V is the variance of the sample.
Substituting into the formula, we have;
[tex]12.7363 = \sqrt{V}[/tex]
Taking the square of both sides, we have;
[tex]12.7363^{2} = V [/tex]
Variance, V = 162.2133 kg²
La temperatura exterior era de 8 grados a la medianoche. La temperatura bajó 5 grados durante cada una de las siguientes 3 horas. ¿Cuál era la temperatura a las 3 a.m.?
Answers
Answer:
A las 3 AM la temperatura era de -7 grados.
Step-by-step explanation:
Dado que la temperatura exterior era de 8 grados a la medianoche, y la temperatura bajó 5 grados durante cada una de las siguientes 3 horas, para determinar cuál era la temperatura a las 3 a.m. se debe realizar el siguiente cálculo:
8 - (3 x 5) = X
8 - 15 = X
-7 = X
Por lo tanto, a las 3 AM la temperatura era de -7 grados.
b.) The number of boys and girls in a class are in the ratio 9:3. The number of boys is 16 more
than the numbers of girls. What is the total class strength
Answers
Answer:
9/3::16x/X
Step-by-step explanation:
do in this way the answer will come
Answer:
32 students
Step-by-step explanation:
9 : 3
9 - 3 = 6
6 : 16
9 + 3 = 12
12 : y
[tex]\frac{6}{16} :\frac{12}{y}[/tex]
y · 6 = 12 · 16
6y = 192
6y ÷ 6 = 192 ÷ 6
y = 32
can someone tell me what the diffrence of 8 through 5 is
Answers
Answer:
The answer is 3.
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
Answer:
3
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
What is the unit rate for 297 miles on 11 gallons of gas?
Answers
Answer:
27 miles per gallons
Step-by-step explanation:
Take the number of miles and divide by the number of gallons
297 miles / 11 gallons
27 miles per gallons
Find the measure of angle X. The horizontal lines are parallel. HINT: The sum
of all interior angles in a triangle is 180 degrees.
Answers
===========================================================
Explanation:
The angle adjacent and supplementary to the 107 degree angle is 73 degrees because 107+73 = 180.
Or you could say 180 - 107 = 73.
The base angles of the upper isosceles triangle are 73 degrees each, which means the third remaining angle (let's call it y for now) is
73+73+y = 180
146+y = 180
y = 180-146
y = 34
Refer to the diagram below. Notice how the 34 degree angle shows up twice because we have vertical angles. Consequently, the base angles of the bottom isosceles triangle are y = 34 degrees each
We can now solve for x
y+y+x = 180
34+34+x = 180
68+x = 180
x = 180-68
x = 112, so the answer is choice D
Zagia is taking a bicycling trip across the United States. Her destination is 3, 150
miles away. If Zagia travels 90 miles per day, how far does she have left to travel
after 20 days of bicycling?
The distance left after 20 days is
miles.
Answers
Answer: The distance left after 20 days is 1350 miles
Step-by-step explanation:
To calculate the distance, we use the formula:
[tex]s=\frac{d}{t}[/tex]
where,
s = speed of the bicycle = 90 miles/day
t = time taken = 20 days
d = distance travelled = ? miles
Putting values in above equation, we get:
[tex]d=(90miles/day\times 20days)=1800 miles[/tex]
Total distance to the destination = 3150 miles
Distance travalled in 20 days = 1800 miles
Distance left after 20 days = [3150 - 1800] = 1350 miles
Hence, the distance left after 20 days is 1350 miles
There are 12 people in an office with 3 different phone lines. If all the lines begin to ring at once, how many groups of 3 people can answer these lines
Answers
Answer: the required answer is 1320
Step-by-step explanation:
Total people = 12
Different phone lines = 3
We will choose the person to answer the first phone in 12 ways.
Then choose the second person in 11 ways. (11 people left)
Then choose the third person in 10 ways. ( 10 people left)
The number of groups of 3 people can answer these lines[tex]12 \times11\times10=1320[/tex]
Hence, the required answer is 1320