Absolute value means take the non-negative number of what is between the bars
|97|
Since 97 is already positive, the absolute value of 97 is 97
Ethan is measuring the lengths of various distances for a science project using feet. He is using the following formula to convert the distances to yards.
A. Proportional
B. Non- Proportional
C. Both Proportional and Non-Proportional
D. Neither Proportional nor Non-Proportional
-5-What is the intercept of function gif 9(r) = -4/(r) + 127
The parent function is given to be:
[tex]f(x)=10^x[/tex]The new function is given to be:
[tex]g(x)=-4f(x)+12[/tex]Therefore, the function will be:
[tex]g(x)=-4(10)^x+12[/tex]The y-intercept is the value of y when x = 0. Therefore, we have:
[tex]\begin{gathered} y=-4(10)^0+12 \\ y=-4+12 \\ y=8 \end{gathered}[/tex]Therefore, the y-intercept is:
[tex]\mathrm{Y\:Intercepts}:\:\left(0,\:8\right)[/tex]Given g(x)=x^2-5x, find the equation of the secant line passing through (-3,g(-3)) and (4g(4)). Write your answer in form of y=mx+b
Given:
[tex]g(x)=x^2-5x\text{ ; (}-3,g(-3)),(4,g(4))[/tex][tex]g(-3)=(-3)^2-5(-3)[/tex][tex]g(-3)=9+15[/tex][tex]g(-3)=24[/tex][tex]g(4)=4^2-5(4)[/tex][tex]g(4)=16-20[/tex][tex]g(4)=-4[/tex]Equation of line with the points (-3,24) and (4,-4)
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex][tex]\frac{y-24_{}}{-4_{}-24_{}}=\frac{x+3_{}}{4_{}+3_{}}[/tex][tex]\frac{y-24_{}}{-28_{}}=\frac{x+3_{}}{7_{}}[/tex][tex]\frac{y-24_{}}{-4_{}}=\frac{x+3_{}}{1_{}}[/tex][tex]y-24_{}_{}=-4(x+3)_{}_{}[/tex][tex]y_{}=-4x-12+24[/tex][tex]y=-4x+12[/tex]The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 4 minutes and a standard deviation of 3 minutes.
Find the probability that it takes at least 6 minutes to find a parking space. (Round your answer to four decimal places.)
The probability that it takes at least 6 minutes to find a parking space is given as: 0.1587. See the explanation below.
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
The working of the above solution is given as follows:
Given:
Mean = 4 minutes
Standard deviation = 3 minutes
P(X < A) = P(Z < (A - mean) /standard deviation)
P(at least 6 minutes) = P(X≥6)
= 1 - P(X < 6)
= 1 - P(Z < (6 - 4)/2)
= 1 - P(Z < 1)
= 1 - 0.8413
P = 0.1587
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if you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years you get the age of president Clinton when he was first inaugurated. how old was president G H.W. Bush when he was inaugurated?Age of first president Bush 54Age of Clinton 46
Let's call x the age of the first president bush, then:
Taking into account the sentence, "if you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years you get the age of president Clinton when he was first inaugurated", we can write the following equation:
x/2 + 14 = 46
So, solving for x, we get:
x/2 = 46 - 14
x/2 = 32
x = 32*2
x = 64
Answer: The first president Bush was 64 years old when he was inaugurated.
A computer consultant charges $50 plus $40 for each hour she works. The consultant charged $650 for one job. This can be represented by the equation below, where h represents the number of hours worked. How many hours did the consultant work?
Answer:
15
Step-by-step explanation:
from the equation 50+40h=650
solving for h which is the number of hours worked.
40h=650-50
40h=600
h=600÷40
h=15
Hi someone please help me and thanks have a great day. Hi someone please help me and thanks have a great day Question number 5Hi someone please help me and thanks have a great day.
Answer
a) Angle L = 36.9°
Angle N = 53.1°
b) For the relationship between them, we can see that
Angle L + Angle N = 36.9° + 53.1° = 90°
Hence, they both sum up to give 90° and are thus complementary angles.
Explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For this question, we first use Angle L as the non-right-angle angle
Hypotenuse = LN = 5
Opposite = NM = ?
Adjacent = LM = 4
Angle = L
Trignometric ratios allow us to interprete CAH as
Cos L = (Adj/Hyp)
Cos L = (4/5)
Cos L = 0.8
L = Cos⁻¹ (0.8)
L = 36.9°
Now, using Angle N as the non-right-angle angle,
Hypotenuse = LN = 5
Opposite = LM = 4
Adjacent = NM = ?
Angle = N
Trignometric ratios allow us to interprete SOH as
Sin N = (Opp/Hyp)
Sin N = (4/5)
Sin N = 0.8
N = Sin⁻¹ (0.8)
N = 53.1°
b) For the relationship between them, we can see that
Angle L + Angle N = 36.9° + 53.1° = 90°
Hence, they both sum up to give 90° and are thus complementary angles.
Hope this Helps!!!
Shelia is making a cake. She
needs 1/3 of a cup of oil. She
has 1/4 of a cup. How much
more does she need
She need 1/12 cup of oil. A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
What is meant by fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. fraction, A number expressed as a quotient in arithmetic, in which a numerator is divided by a denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator. A fraction is a portion of a whole number and a method of dividing a number into equal parts.How to find how much cup she want?She needs 1/3 cup of oil She have 1/4 cup of oilTo find how much need to obtain 1/3 of cup
we need to subtract what we have from what we need.
so , we have 1/4 and need 1/3
= 1/3 - 1/4
= [tex]\frac{1 * 4}{3 * 4} - \frac{1 * 3}{4 * 3}[/tex]
= 1/12
she need 1/12 cup of oil more to make cake.
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Can anyone explain this for #30?
Q.29 Variance is S² = 17.33
Q.30 Variance is S² = 46.67
What is Variance ?
Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.
S² = ∑(x - x(bar) )² / (n - 1 )
S² = sample Variance
x = the value of the one observation
x(bar) = the mean value of all observation
n = the number of observation
Q.29 | x | (x -x(bar)) | (x - x(bar) )² |
| -------------------------------------- |
| 2 | -5 | 25 |
| 6 | -1 | 1 |
| 8 | 1 | 1 |
| 12 | 5 | 25 |
-------------------------------------------
| 28 | 0 | 52 |
----------------------------------------------
x(bar) means, x mean = ∑x
∑x = (2 + 6 + 8 + 12) / 4
= 28/4
= 7
Now, put the values in variance formula,
S² = ∑(x - x(bar) )² / (n - 1 )
= 52 / (4 -1)
= 52/ 3
= 17.33
Q.30 | x | (x -x(bar)) | (x - x(bar) )² |
| -------------------------------------- |
| 10 | -7 | 49 |
| 14 | -3 | 9 |
| 18 | 1 | 1 |
| 26 | 9 | 81 |
-------------------------------------------
| 68 | 0 | 140 |
----------------------------------------------
x(bar) means, x mean = ∑x
∑x = (10 + 14 + 18 + 26)/4
= 68/4
= 17
Now, put the values in variance formula,
S² = ∑(x - x(bar) )² / (n - 1 )
= 140 / (4 -1)
= 140 / 3
= 46.67
Therefore, the Variance of Q.29 is S² = 17.33
and, for Q.30 Variance is S² = 46.67
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Customers return 14% of their gifts during the holiday season. How many gifts were returned during the holiday season if 500 gifts were purchased?
Given:
Customers return 14% of their gifts during the holiday season.
The total number of gifts = 500
So, the returned gifts = 14% of 500 = 0.14 x 500 = 70 gifts
So, the number of gifts were returned during the holiday season = 70 gifts
The diameter of a circle is 20 inches. What is the radius, in inches, of the circle?
Given:
The diameter of a circle is 20 inches.
So, d = 20 inches
We will find the radius of the circle (r)
The diameter is two times the radius
Or, we can say, the radius is half of the diameter
so, r = d/2 = 20/2 = 10 inches
so, the answer will be The radius = 10 inches
Add or subtract the monomials. (Simplify your answer compl
2a²+6²-8a² + x²y - 3x + 9xy²
After simplification of the given monomial 2a²+6²-8a² + x²y - 3x + 9xy², the result is -6a²- 3x + x²y + 9xy² + 12.
What are monomials?A monomial in mathematics is essentially a polynomial with only one term. There are two possible definitions of a monomial: A monomial, also known as a power product, is a product of variables, possibly with repetitions, and powers of variables with nonnegative integer exponents. A polynomial with only one term is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also have multiple variables and a higher degree. When 9 is the coefficient, x, y, and z are the variables, and 3 is the degree of the monomial, for instance, 9x³yz is a single term.So, 2a²+6²-8a² + x²y - 3x + 9xy²:
Now, simplify as follows:
2a²+6²-8a² + x²y - 3x + 9xy²2a²-8a²- 3x + x²y + 9xy² + 6²-6a²- 3x + x²y + 9xy² + 12Therefore, after simplification of the given monomial 2a²+6²-8a² + x²y - 3x + 9xy², the result is -6a²- 3x + x²y + 9xy² + 12.
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Youngs rule to calculate a child medicine dosage is c=na/n+12 where c is the child's dosage in mL, n is the child's age and A is the adult's dosage in mLA nurse gave an 8-year-old child a dose of 6 mL of medicine. What would be the adult equivalent of this dosage
1) Given that rule, we can write out the following for this case:
[tex]\begin{gathered} C=\frac{nA}{n+12}= \\ \end{gathered}[/tex]2) So let's plug into that the data:
[tex]\begin{gathered} 6=\frac{8A}{8+12} \\ 8A=20\times6 \\ 8A=120 \\ \frac{8A}{8}=\frac{120}{8} \\ A=15 \end{gathered}[/tex]Note that we have cross multiplied and then divided both sides by 8. So the dosage of an adult, according to this rule would be 15 ml
I quite do t understand will I be now to help mrunderstand
From the given inequality graph
6. The solution shown by the graph is
[tex]\begin{gathered} x<0,or,x\ge4 \\ x<0\cong0>x \\ So, \\ 0>x\ge4 \end{gathered}[/tex]7. The solution shown by the graph is
[tex]x<-6,or,x>-3[/tex][tex]\begin{gathered} x<-6\cong-6>x \\ So, \\ -6>x>-3 \end{gathered}[/tex]8.
The graph of k ≤ -1 is
The graph of k > 4 is
The graph of k ≤ -1, or, k > 4 is
Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible.(-1,3); y = 1
we have that
The equation of the given line is
y=1
this equation represents a horizontal line
so
the slope is zero (m=0)
Remember that, if two lines are parallel, then their slopes are equal
that means
the slope of the parallel line is m=0 too
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=0
point (-1,3)
the equation is
y=3The pentagonal prism below has a cross-sectional area of
27 cm² and a length of 3 cm.
Calculate the volume of the prism.
Give your answer in cm³.
Answer:
volume=27 multiply 3 =81
you want to buy some beans a 6 oz package cost $2.10 a 14 oz package cost $5.04 a 20 oz package cost $6.60
QUESTION:
you want to buy some beans a 6 oz package cost $2.10 a 14 oz package cost $5.04 a 20 oz package cost $6.60. Which package is the best to buy?
ANSWER
We will first find the unit price.
6 0z = $2.10
1 oz = $2.10/6 = $0.35
a 14 oz package that cost $5.04
14 0z = $5.04
1 oz = $5.04 / 10 = $0.504
a 20 oz package that cost $6.60
20 oz = $6.60
1 oz = $6.60 / 2 =$3.30
Comparing the three prices, the 6 oz package that cost $2.30 has the lowest price. This implies that it is the best to buy.
Pete Size read the following partial advertisement: Price $20,999; down payment $1,000 cash or trade; $390.85 per month for 60 months. Calculate (A) the total finance charge and (B) the APR. (to the nearest percent).
The total finance charge is $3452 and the APR will be 6.45%.
How to calculate the value?The total finance charge will be:
Price = $20999
Down payment = $1000
Loan amount = $20999 - $1000 = $19999
Total repayment = $390.85 × 60 = $23451
Total finance charge = $23451 - $19999 = $3452
It should be noted that the APR will be:
= Rate(nper, pmt, -pv) × 12
where nper = 60
PMT = $390.85.
pv = 19999
APR = 6.45%
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In the triangle shown we can find the angle as follows.A153936(a) = sin-X(b) 0 - cos(C) 0 = tan-10
We need to calculate the three trigonometrics relations on the right triangle. They are as follow:
[tex]\begin{gathered} \sin \theta=\frac{36}{39}=0.92 \\ \cos \theta=\frac{15}{39}=0.38 \\ \tan \theta=\frac{36}{15}=2.4 \end{gathered}[/tex]We need to use this values on each option. The "sin^-1" is the inverse of the sine, the "cos^-1" is the inverse of the cosine and the "tan^-1" is the inverse of the tangent. If we use these values on the functions we will find the value of theta.
[tex]\sin ^{-1}0.92=\text{ 66.93}[/tex]The angle is equal to 66.93 degrees
The Chandlers are moving across the countryMr. Chandler leaves 5 hours before Mrs. Chandlerhe averages 40 mph and she averages 80 mphhow many hours will it take Mrs. Chandler to catch up to Mr. Chandler?
From the information provided, we know that Mr Chandler travels at a speed of 40 miles per hour (40mph). He also left 5 hours before Mrs Chandler.
Therefore, we can tell that for 5 hours he has travelled
[tex]\begin{gathered} Dis\tan ce=speed\cdot time \\ \text{Distance}=40\times5 \\ \text{Distance}=200 \end{gathered}[/tex]We shall now label the total distance covered as d, and the number of hours taken (time) as t.
We now have for Mr Chandler;
[tex]d=40t+200---(1)[/tex]For Mrs Chandler, we would have;
[tex]d=80t---(2)[/tex]We would now solve the system of equations as follows;
[tex]\begin{gathered} d=40t+200---(1) \\ d=80t---(2) \\ \text{Substitute for the value of d into equation (1)} \\ We\text{ now have;} \\ 80t=40t+200 \\ \text{Collect all like terms;} \\ 80t-40t=200 \\ 40t=200 \\ \text{Divide both sides by 40} \\ t=5 \end{gathered}[/tex]This result shows that, travelling at the speed given for both Mr and Mrs Chandler, it would take her 5 hours to catch up with him.
ANSWER:
5 hours
PART B
If Mr Reeds leaves 3.5 hours ahead of Mrs Reeds and he travels at the speed of 55 miles per hour (55 mph), then his distance would be;
[tex]\begin{gathered} \text{Distance}=\text{spee}d\times\text{time} \\ \text{Distance}=55\times3.5 \\ \text{Distance}=192.5 \end{gathered}[/tex]If the total distance covered is given as d, then for Mr Reeds the total distance would be;
[tex]d=55t+192.5---(1)[/tex]For Mrs Reeds, we would have;
[tex]d=90t---(2)[/tex]Note that d represents the total distance covered and t represents the time taken (in hours).
We shall now solve the system of equations, as follows;
[tex]\begin{gathered} d=55t+192.5---(1) \\ d=90t---(2) \end{gathered}[/tex]We shall substitute for the value of d into equation two. Note that d = d, which means equation (1) equals equation (2). We now have;
[tex]\begin{gathered} 55t+192.5=90t \\ \text{Collect all like terms;} \\ 192.5=90t-55t \\ 192.5=35t \\ \text{Divide both sides by 35} \\ \frac{192.5}{35}=\frac{35t}{35} \\ 5.5=t \end{gathered}[/tex]The calculations here shows that travelling at the speeds given for both of them, it would take Mrs Reeds 5.5 hours to catch up with Mr Reeds.
ANSWER:
5.5 hours
Hi, can you help me to solve this problem, please!!!
Given:
The equation of a parabola is given as,
[tex]y=x^2-5[/tex]The objective is to find the axis of symmetry of the parabola.
Explanation:
The general formula to find the axis of symmetry of a parabolic equation is,
[tex]x=-\frac{b}{2a}\text{ .. . . . . (1)}[/tex]From the given equation,
[tex]\begin{gathered} a=1 \\ b=0 \\ c=-5 \end{gathered}[/tex]On plugging the obtained values in equation (1),
[tex]\begin{gathered} x=-\frac{0}{2(1)} \\ x=0 \end{gathered}[/tex]Hence, the axis of symmetry of the parabola is at x = 0.
4(3x-6) + (x + 22) how do I simplify it?
Answer:
13x - 2
Step-by-step explanation:
First Were going to do the distributive property:
So, 4(3x) + 4(-6) = 12x + -24
Now we have :
12x - 24 + x + 22
Now we have to add like terms together:
So, 12x + x = 13x
and 22-24 = -2
So in the end we have 13x -2
Round 3,204 to the nearest thousand
to round to the nearest thousand, we have to look at the hundreds place. In this case, there is a 2 in the hundreds place, which is less than 5. Then, the 3 in the thousands place must be kept. In conclusion, 3,204 rounded to the nearest thousand is 3,000
Answer:
3,000
Step-by-step explanation:
the thousands place is where the 3 is and we look at the number next to it if it is 5 or over we round up or if it’s under 5 we round down and since 2 is under 5 we round down to 3,000
Simplify the following expression.-5a - 10(-a - 10) + 1 - 2a
Step 1
break the parenthesis
[tex]\begin{gathered} -5a-10(-a-10)+1-2a \\ -5a+10a+100+1-2a \\ \end{gathered}[/tex]Add similar terms
[tex]\begin{gathered} -5a+10a+100+1-2a \\ 3a+101 \end{gathered}[/tex]so, the answer is 3a+101
Select all of the expressions that are less than 10 2/3.A.10 2/3×9/10B.1×10 2/3C.10 2/3×2 1/3D.1/8×10 2/3E.10 2/3×3/5
Given:
[tex]10\frac{2}{3}[/tex]To Determine: All expressions that are less than 10 2/3
Verify for each of the options
OPTION A
[tex]\begin{gathered} 10\frac{2}{3}\times\frac{9}{10} \\ =\frac{32}{3}\times\frac{9}{10} \\ =\frac{96}{10}=9\frac{6}{10} \end{gathered}[/tex]OPTION B
[tex]1\times10\frac{2}{3}=10\frac{2}{3}[/tex]OPTION C
[tex]undefined[/tex]Given F(x) = x2 + 4x − 9, evaluate. F(−4)
pls guys need a quick hep
Factorise 2x³+9x²+7x-6=0
The most appropriate choice for factorization will be given by-
(x +2)(x + 3)(2x - 1) is the factorization of f(x) = 2x³+9x²+7x-6
x = -2, -3, [tex]\frac{1}{2}[/tex] are the solutions of f(x) = 0
What is factorization?
Factorization is the process of breaking down of an algebraic expression into product of algebraic expressions of smaller degree.
Each algebraic expression of smaller degree are called factors
Here,
Vanishing method will be used
f(x) = 2x³+9x²+7x-6
[tex]f(-2) = 2(-2)^3 + 9(-2)^2 + 7(-2) -6\\= -16 + 36 -14 -6\\ = 0[/tex]
(x + 2) is a factor of f(x)
[tex]f(x)[/tex] [tex]= 2x^2(x + 2) + 5x(x + 2) - 3(x + 2)[/tex]
[tex]= (x + 2)(2x^2 + 5x - 3) \\ = (x + 2)(2x^2 + 6x - x - 3) \\ = (x + 2)[2x(x + 3) - 1(x + 3)] \\ = (x + 2)(x + 3)(2x - 1)[/tex]
For solving f(x) = 0
x +2 = 0 or x + 3 = 0 or 2x - 1 = 0
x = -2 or x = -3 or x = [tex]\frac{1}{2}[/tex] are the solutions of f(x) = 0
This is the required factorization of f(x)
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What is 2/3 divided by -5/7
[tex] = \frac{2}{3} \div - \frac{5}{7} \\ = \frac{2}{3} \times - \frac{7}{5} \\ = - \frac{14}{15} [/tex]
ATTACHED IS THE SOLUTION.
NOTE WHEN WE ARE DIVIDING WE CHANGE THE DIVISION SIGN TO A MULTIPLICATION SIGN TO AND SWAP THE FOLLOWING FRACTION .
Answer:
-0.019047619
That’s the Answer Hope this helps:)
Which model(s) below could represent the solution to the problem 45 X 15?
Circle the letter for all that apply.
675 is product by using multiplication's commutative property.
What does multiplication's commutative property mean ?
According to the multiplication's commutative property, you can multiply numbers in any sequence, and the result will always be the same. The amount of seeds is the same even though your gardens differ in appearance (one is longer and one is taller). Whether you multiply 3 by 8 or 8 by 3 is irrelevant.Examples of Commutative Multiplication Property
1 × 2 = 2 × 1 = 2.
3 × 8 = 8 × 3 = 24.
12 × 5 = 5 × 12 = 60.
45 X 15
= 675
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1. Create a box plot using this data: A large school summarizes the number of
teachers at 51 schools in the area. Here is some of the information:
25 25 30 35 40 44 47 52 56
60
64
70
71
75 82 95 110
20
58
H 10
0
20
Explain.
110
40
60
teachers per school
80 100 120
Hint use a straight edge for box
What measure of center would you use to describe the typical value for this data?
me
hotween 2 do
Answer:Display data graphically and interpret graphs: stemplots, histograms, and box plots.
Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.
Box plots (also called box-and-whisker plots or box-whisker plots) give a good graphical image of the concentration of the data. They also show how far the extreme values are from most of the data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them.
To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks one end of the box and the third quartile marks the other end of the box. Approximately the middle
50
percent of the data fall inside the box. The “whiskers” extend from the ends of the box to the smallest and largest data values. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both. The box plot gives a good, quick picture of the data.
NOTE
You may encounter box-and-whisker plots that have dots marking outlier values. In those cases, the whiskers are not extending to the minimum and maximum values.
Consider, again, this dataset.
1
,
1
,
2
,
2
,
4
,
6
,
6.8
,
7.2
,
8
,
8.3
,
9
,
10
,
10
,
11.5
The first quartile is two, the median is seven, and the third quartile is nine. The smallest value is one, and the largest value is
11.5
. The following image shows the constructed box plot.
NOTE
See the calculator instructions on the TI web site.
Horizontal boxplot's first whisker extends from the smallest value, 1, to the first quartile, 2, the box begins at the first quartile and extends to the third quartile, 9, a vertical dashed line is drawn at the median, 7, and the second whisker extends from the third quartile to the largest value of 11.5.
The two whiskers extend from the first quartile to the smallest value and from the third quartile to the largest value. The median is shown with a dashed line.
NOTE
It is important to start a box plot with a scaled number line. Otherwise the box plot may not be useful.
EXAMPLE
The following data are the heights of
40
students in a statistics class.
59
;
60
;
61
;
62
;
62
;
63
;
63
;
64
;
64
;
64
;
65
;
65
;
65
;
65
;
65
;
65
;
65
;
65
;
65
;
66
;
66
;
67
;
67
;
68
;
68
;
69
;
70
;
70
;
70
;
70
;
70
;
71
;
71
;
72
;
72
;
73
;
74
;
74
;
75
;
77
Construct a box plot with the following properties; the calculator instructions for the minimum and maximum values as well as the quartiles follow the example.
Minimum value =
59
Maximum value =
77
Q1: First quartile =
64.5
Q2: Second quartile or median=
66
Q3: Third quartile =
70
Horizontal boxplot with first whisker extending from smallest value, 59, to Q1, 64.5, box beginning from Q1 to Q3, 70, median dashed line at Q2, 66, and second whisker extending from Q3 to largest value, 77.
Each quarter has approximately
25
% of the data.
The spreads of the four quarters are
64.5
–
59
=
5.5
(first quarter),
66
–
64.5
=
1.5
(second quarter),
70
–
66
=
4
(third quarter), and
77
–
70
=
7
(fourth quarter). So, the second quarter has the smallest spread and the fourth quarter has the largest spread.
Range = maximum value – the minimum value = 77 – 59 = 18
Interquartile Range:
I
Q
R
=
Q
3
–
Q
1
=
70
–
64.5
=
5.5
.
The interval
59
–
65
has more than
25
% of the data so it has more data in it than the interval
66
through
70
which has
25
% of the data.
The middle
50
% (middle half) of the data has a range of
5.5
inches.
USING THE TI-83, 83+, 84, 84+ CALCULATOR
To find the minimum, maximum, and quartiles:
Enter data into the list editor (Pres STAT 1:EDIT). If you need to clear the list, arrow up to the name L1, press CLEAR, and then arrow down.
Put the data values into the list L1.
Press STAT and arrow to CALC. Press 1:1-VarStats. Enter L1.
Press ENTER.
Use the down and up arrow keys to scroll.
Smallest value =
59
.
Largest value =
77
.
Q
1
: First quartile =
64.5
.
Q
2
: Second quartile or median =
66
.
Q
3
: Third quartile =
70
.
To construct the box plot:
Press 4:Plotsoff. Press ENTER.
Arrow down and then use the right arrow key to go to the fifth picture, which is the box plot. Press ENTER.
Arrow down to Xlist: Press 2nd 1 for L1
Arrow down to Freq: Press ALPHA. Press 1.
Press Zoom. Press 9: ZoomStat.
Press TRACE, and use the arrow keys to examine the box plot.
Step-by-step explanation:
