Sample proportions of size ten were taken from a group of students. Students were asked if they wore glasses while watching TV. The proportion that wore glasses while watching TV was recorded. The standard deviation of the data is 0.19 The margin of error can be given by the formula Margin ferror = 2 * s/(sqrt(n)) where s is the standard deviation and n is the sample size . What is the margin of error for the data collected ?
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Margin of error:
[tex]ME=2\times\frac{s}{\sqrt{n}}[/tex]For the given data collected
[tex]\begin{gathered} s=0.19 \\ n=10 \\ \\ ME=2\times\frac{0.19}{\sqrt{10}}=\frac{0.38}{\sqrt{10}}=0.12 \end{gathered}[/tex]Then, the margin of error is 0.12Related Questions
ratio of number of boys to girl is 5 to 4 there are 60 girls in choir how many boys are there
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Since the ratio of boys to girls is 5:4 and there are 60 girls, let b be the number of boys and g be the number of girls. Then:
[tex]\begin{gathered} \frac{b}{g}=\frac{5}{4} \\ \Rightarrow\frac{b}{60}=\frac{5}{4} \\ \Rightarrow b=\frac{5}{4}\times60 \\ \Rightarrow B=75 \end{gathered}[/tex]Therefore, there are 75 boys in the choir.
For each of the following pairs of rational numbers, place a greater than symbol, >, a less than symbol, <, or an equality symbol, =, in the square to make the statement true.
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I chow you how to solve for (d) and (i) and you could do the rest by yourself:
The best way to solve this operations is convert the numbers to a one form and then compare.
For (d)
[tex]\begin{gathered} \frac{7}{3}=\frac{6+1}{3}=\frac{6}{3}+\frac{1}{3}=2+\frac{1}{3}=2\frac{1}{3}=2.333 \\ \frac{13}{5}=\frac{10+3}{5}=\frac{10}{5}+\frac{3}{5}=2+\frac{3}{5}=2\frac{3}{5}=2.6 \\ So, \\ \frac{7}{3}<\frac{13}{5} \end{gathered}[/tex]Now for (i), take into account that this numbers are negative:
[tex]\begin{gathered} -11.5=-11.5\cdot\frac{4}{4}=-\frac{11.5\cdot4}{4}=-\frac{46}{4} \\ So,\text{ } \\ -\frac{46}{4}<-\frac{31}{4} \end{gathered}[/tex]Note that 46/4 is greater than 31/4, but -46/4 is lower than -31/4.
Also note that in this example I find to equalize the denominator of the numbers adn then you can compare the numerators.
Match each solid cone to it’s surface area. Answers are rounded to the nearest square unit
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The surface area of a cone is given by the formula below:
[tex]S=\pi r^2+\pi rs[/tex]Where r is the base radius and s is the slant height.
So, calculating the surface area of first cone, we have:
[tex]\begin{gathered} s^2=21^2+6^2\\ \\ s^2=441+36\\ \\ s^2=477\\ \\ s=21.84\\ \\ S=\pi\cdot6^2+\pi\cdot6\cdot21.84\\ \\ S=525 \end{gathered}[/tex]The surface area of the second cone is:
[tex]\begin{gathered} s^2=8^2+12^2\\ \\ s^2=64+144\\ \\ s^2=208\\ \\ s=14.42\\ \\ S=\pi\cdot12^2+\pi\cdot12\cdot14.42\\ \\ S=996 \end{gathered}[/tex]The surface area of the third cone is:
[tex]\begin{gathered} s^2=15^2+8^2\\ \\ s^2=225+64\\ \\ s^2=289\\ \\ s=17\\ \\ S=\pi\cdot8^2+\pi\cdot8\cdot17\\ \\ S=628 \end{gathered}[/tex]And the surface area of the fourth cone is:
[tex]\begin{gathered} s^2=10^2+10^2\\ \\ s^2=100+100\\ \\ s^2=200\\ \\ s=14.14\\ \\ S=\pi\cdot10^2+\pi\cdot10\cdot14.14\\ \\ S=758 \end{gathered}[/tex]If there are six servings in a 2/3 pound package of peanut which fraction of a pound is in each serving.
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We will have the following:
If there are 6 servings in a 2/3 pound package, we will divide the pounds by the number of servings, that is:
[tex]\frac{(\frac{2}{3})}{6}=\frac{(\frac{2}{3})}{(\frac{6}{1})}=\frac{2\cdot1}{3\cdot6}=\frac{2}{18}[/tex][tex]=\frac{1}{9}[/tex]So, each serving has 1/9 of a pound.
***Explanation***
Since we have 6 servings and then the total value of pounds the package represents we will have that the weigth (in pounds) for each serving is given to us by dividing the total weight by the number of servings.
Now, in order to apply the division of a fraction by another fraction we rewrite the integer 6 as a fraction, and we know that 6 / 1 = 6 so, that is the fraction from for this number (At least the less complicated one) and we proceed with the "ear" opeation.
Translate the sentence into an equation Three times the sum of a number and 2 is equal to 9 Use the variable y for the unknown number
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Three times
multiply a value by 3
[tex]3\times()[/tex]The sum of a number and 2
We named the number "Y", then inside the parenthesis be the sum of x and 2
[tex]3\times(y+2)[/tex]Is equal to 9
we equal the equation to 9
[tex]3\times(y+2)=9[/tex]Sondra is going rock climbing. She starts at 12.25 yards above sea level. She ascends 38.381yards before lunch. She then descends 15.25 yards after lunch. What is Sondra's finalheight relative to sea level?
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What we need to do is follow up with Sondra.
Starts at 12.15 yd
Ascendes 38.281, therefore:
[tex]12.15+38.5=50.65[/tex]A total 50.65 yd
Then, descends 15.25, therefore:
[tex]50.65-12.25=38.5[/tex]This means that the relative 38.5 - (15.25 - 12.25) = 38.5 - 3 = 35.5, it is means 35 1/2
The answer is 35 1/2
Which statement is true?123.466 > 132.4659.07 > 9.00850.1 < 5.013.37 < 3.368
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In the given decimal inequality statements we can infer that only
9.07 > 9.008 is true.
The given statements are :
123.466 > 132.465
9.07 > 9.008
50.1 < 5.01
3.37 < 3.368
Let us take each statement and find out if it is true or false.
Statement 1: 123.466 > 132.465
Using the properties of decimals we see that 231<132 hence the statement is false.
Statement 2:
9.07 > 9.008
Here the second digit after decimal are 7 and 0. Since the first two significant digits are same , and 7>0 therefore 9.07>9.008 so it is true.
Statement 3:
50.1 < 5.01
Here 50 > 5 so the statement is false
Statement 4:
3.37 < 3.368
Here the first two significant digits are same. Again the digit in the hundredths place are 7 and 6, as 7>6, hence the statement is false.
to learn more about decimal visit:
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If the number 659, 983 is rounded to the nearest hundred, how many zeros does the rounded number have?The solution is
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We will have the following:
*For 569:
For this number we would round to 600, thus the number of zeros the rounded number would be 2.
*For 983:
For this number, we would round to 1000, thus the number of zeros the rounded number would be 3.
For the following line, name the slope and y-intercept. Then write the equation of the line in slope-interceptform.Slope= y - intercept = (0,_ ) Equation: y =
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Given:
A line that passes the through the points (4, 0) and (0,-3).
Required:
Slope, y-intercept, and the equation of the given line.
Explanation:
As the line passes through the points (4, 0) and (0,-3), the slope is calculated as,
[tex]\begin{gathered} Slope\text{ = }\frac{y_2-y_1}{x_2-\text{ x}_1} \\ Slope\text{ = }\frac{-3\text{ - 0}}{0\text{ - 4}} \\ Slope\text{ = }\frac{-3\text{ }}{-4} \\ Slope\text{ = }\frac{3}{4} \end{gathered}[/tex]The y-intercept of the given line is the point through which the given line passes on the y-axis which is -3. Therefore the intercept of the given line is -3.
The equation of line in slope point form is given as,
[tex]y\text{ = mx + c}[/tex]Where m is the slope and c is the y-intercept. Therefore the equation of the line is given as,
[tex]y\text{ = }\frac{3}{4}x\text{ - 3}[/tex]Answer:
Thus the required equation of line is
[tex]y\text{ }=\text{ }\frac{3}{4}\text{x{\text{ - 3}}}[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 8". Find P(A). Outcome Probability 1 0.01 2 0.04 3 0.4 4 0.01 5 0.08 6 0.07 7 0.21 8 0.07 9 0.11
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For divisor of 8:
A be the event "the outcome is a divisor of 8".
Then P(A):
[tex]\begin{gathered} P(A)=P(1)+P(2)+P(4)+P(8) \\ P(A)=0.01+0.04+0.01+0.07 \\ P(A)=0.13 \end{gathered}[/tex]Consider the following measures shown in the diagram with the circle centered at point A. Determine the arc length of CB.
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Answer:
[tex]\frac{4}{3}\pi\; cm[/tex]Explanation:
If an arc of a circle radius, r is subtended by a central angle, θ, then:
[tex]\text{Arc Length}=\frac{\theta}{360\degree}\times2\pi r[/tex]In Circle A:
• The central angle, θ = 40 degrees
,• Radius = 6cm
Therefore, the length of arc CB:
[tex]\begin{gathered} =\frac{40}{360}\times2\times6\times\pi \\ =\frac{4}{3}\pi\; cm \end{gathered}[/tex]The correct choice is C.
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 44 and a standard deviation of 4. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 36 and 52?
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The empirical rule is an approximation that can be used sometimes if we have data in a normal distribution. If we know the mean and standard deviation, we can use the rule to approximate the percentage of the data that is 1, 2, and 3 standard deviations from the mean. The rules is:
In this case, the mean is 44. The receptionist who answered less than 44 phone calls are to the left of the mean, and to the right are the ones who answered more. Since we want to know the percentage of phone calls numbering between 36 and 52, we know that:
[tex]\begin{gathered} 44+4=48 \\ . \\ 48+4=52 \end{gathered}[/tex][tex]\begin{gathered} 44-4=40 \\ . \\ 40-4=36 \end{gathered}[/tex]Thus, the lower bound is two standard deviations from the mean, and the upper bond is also 2 standard deviations from the mean.
Using the chart above, we can see that this corresponds to approximately 95% of the data.
The answer is approximately 95% of the data is numbering between 36 and 52
Two Column Proof. If you could write it on a piece of paper and send a picture, that would be great.
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Let's suppose
∠1 =∠5 and ∠2 = ∠4
then
180° - ∠1 - ∠2 = ∠3
180° - ∠1 - ∠2 =
Ava solved the compound inequality +7
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Tell me if the inequalities are correct
x/4 + 7 < -1 2x - 1 >= 9
x/4 < -1 - 7 2x >= 9 + 1
x/4 < -8 2x >= 10
x < -32 x >= 10/2
x >= 5
The second option is the correct one
Dilate f (x) = (x+4)(x+2) by x
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Given:
[tex]f(x)=(x+4)(x+2)[/tex]Dilate of function is:
[tex]\begin{gathered} f(x)=(x+4)(x+2) \\ =x(x+2)+4(x+2) \\ =x^2+2x+4x+8 \\ =x^2+6x+8 \end{gathered}[/tex]On a map, the scale shown is1 inch : 5 miles. If a park is75 square miles, what is thearea of the park on the map?The park's area issquarelinches on the map.
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We have the relationship between inches and miles is:
1 inch to 5 miles.
The park has an actual area of:
[tex]75mi^2[/tex]Now, to make the conversion to inches, we need to consider that 1 inch represent 5 miles. Thus:
[tex]\begin{gathered} 1in=5mi \\ 1in^2=25mi^2 \end{gathered}[/tex]We squared this amounts, if 1 inch is 5 miles, 1 inch squared will be equal to 5 squared which is 25.
Now we divide 75 miles squared by 25, to know how many inches squared will the park represent on the map:
[tex]\frac{75}{25}=3in^2[/tex]Answer: the area of the park on the map will be 3 inches squared.
Suzie has cards in numbers 9-21 in a bag. What is the probability she will pull a card lower than 17?
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She has cards that go from 9 to 21.
We assume she has one card with each number that goes from 9 to 21:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
If we want to calculate the probability she pulls a card lower than 17, we have to count how many cards are lower than 17 and then divide this number by the total amount of cards.
NOTE: each card is a possible event. We will calculate the probability as the quotient between the number of successful events (cards lower than 17) and the total possible events (number of cards available).
We have 17-9 = 8 cards that are lower than 17.
The total number is 22-9 = 13 cards (all the cards lower than 22).
Then, we can calculate the probability as:
[tex]P(C<17)=\frac{8}{13}[/tex]Answer: The probabilty she pull a card lower than 17 is P=8/13
2,047÷41=sloveadd expression
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The given expression is,
[tex]\frac{2047}{41}[/tex]On solving, we have,
[tex]\frac{2047}{41}=49\frac{38}{41}=49.93[/tex]Thus, 2,047÷41=49.93.
500 books were sold the first day it went on sale. 150 books were sold each day after that. Write an equation to represent the total number of books sold. How many books were sold after 50 days?
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Let x represent the number of days after release and y represent the number of books sold.
The first day there were 500 books sold, after that, 150 books were solf each passing day.
This means that for the first day y=500 ann each passing day 150 books were added, the equation is:
y=500+150x
Using this equation you have to calculate the number of books solf after x=50 days.
To do so replace in the equation above:
y=500+150*50
y=8000
After 50 days 8000 books were sold
Compute the common and natural logarithms using the properties of logarithms and a calculator.Type the correct answer in each box. Round your answers to two decimal places.
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(b)
[tex]\log _{}3.26[/tex]Using the calculator to compute the logarithm, we have;
[tex]\begin{gathered} \log \text{ 3.26 = 0.5132} \\ \log \text{ 3.26 = 0.51 (Round to two decimal places)} \end{gathered}[/tex](c)
[tex]\begin{gathered} \log \text{ 10000} \\ =\log _{10}10^4 \\ =4\log _{10}10 \\ =4\times1 \\ \log \text{ 10000}=4.00\text{ (Round to two decimal places)} \end{gathered}[/tex](d)
[tex]\begin{gathered} \ln 22=3.0910 \\ \ln 22=3.09\text{ (Round to two decimal places)} \end{gathered}[/tex]Complete the tables using the formula. Then, identify the starting amount and the amount you change by. These are linear, so the table should go up or go down by a constant amount.Y = 5x + 8
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Part A
x= 0 y=8
x=1 y=13
x=2 y=18
x=3 y=23
y=4 y=28
x=5 y=33
y=6 y=28
y=7 y=43
Part B
Starting point (y-intercept) = 8
Part C.
slope is 5.
STEP - BY - STEP EXPLANATION
What to find?
• The values of y at x=0,1,2,3,4,5, 6 and 7
,• Slope
,• Y- intercept.
Given:
y=5x + 8
To determine the values of y at each point of x, substitute into the formula given and simplify.
That is;
At x = 0
[tex]\begin{gathered} y=5(0)\text{ +8} \\ y=0+8 \\ y=8 \end{gathered}[/tex]At x = 1
[tex]\begin{gathered} y=5(1)+8 \\ =5+8 \\ =13 \end{gathered}[/tex]At x = 2
[tex]\begin{gathered} y=5(2)+8 \\ =10+8 \\ =18 \end{gathered}[/tex]At x = 3
[tex]\begin{gathered} y=5(3)+8 \\ =15+8 \\ =23 \end{gathered}[/tex]At x = 4
[tex]\begin{gathered} y=5(4)+8 \\ =20+8 \\ =28 \end{gathered}[/tex]At x = 5
[tex]\begin{gathered} y=5(5)+8 \\ =25+8 \\ =33 \end{gathered}[/tex]At x = 6
[tex]\begin{gathered} y=5(6)+8 \\ =30+8 \\ =38 \end{gathered}[/tex]At x=7
[tex]\begin{gathered} y=5(7)+8 \\ =43 \end{gathered}[/tex]Hence,
x= 0 y=8
x=1 y=13
x=2 y=18
x=3 y=23
y=4 y=28
x=5 y=33
y=6 y=28
y=7 y=43
Part B
Starting point( y-intercept).
The y-intercept is the point at which x =0
Hence, from the values above, at x=0, y=8
Hence, the starting point (y-intercept) = 8
Part C
The changes in slope.
The slope is the changes in y-intercept, the y -values kept increasing by 5.
Hence, the slope is 5.
Graph the parabola.Y = -2x^2 - 16x - 34Plat five points on a parable the vertex ,two points to the left of the vertex ,and two points to the right of the vertex . then click on the graph a function button.
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The graph is shown below:
• The point (-4, -2) is the vertex
,• The points to the left are (-5, -4) and (-6, -10)
,• The points to the right are (-3, -4) and (-2, -10)
what is the y- intercept in the following equationy=-4x-5
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..Sam works 40 hours in one week and is paid $610. How much does Samearn per hour?
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Answer:
Sam earns $15.25 per hour.
Explanation:
Sam works 40 hours in one week, and is paid $610
To know how much Sam earns per hour, we divide the amount earned by the number of hours worked.
This is:
[tex]\frac{610}{40}=15.25[/tex]Therefore, Sam earns $15.25 per hour.
In the diagram below the larger angle is four times bigger than the smaller angle find the larger angle
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Answer:
Given that,
In the diagram below the larger angle is four times bigger than the smaller angle
To find the larger angle.
Let x be smaller angle.
Then we get,
Larger angle is,
[tex]4x[/tex]Larger angle and smaller angle are a linear pair.
Therefore we get,
[tex]x+4x=180[/tex][tex]5x=180[/tex][tex]x=36\degree[/tex]Larger angle is,
[tex]4x=4\times36=144[/tex]The larger angle is 144 degrees.
Given:• AJKL is an equilateral triangle.• N is the midpoint of JK.• JL 24.What is the length of NL?L24JKNO 12O 8V3O 12V2O 1213
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Answer:
12√3
Explanation:
First, we know that JL = 24.
Then, the triangle JKL is equilateral. It means that all the sides are equal, so JK is also equal to 24.
Finally, N is the midpoint of segment JK, so it divides the segment JK into two equal parts. Therefore, JN = 12.
Now, we have a right triangle JLN, where JL = 24 and JN = 12.
Then, we can use the Pythagorean theorem to find the third side of the triangle, so NL is equal to:
[tex]\begin{gathered} NL=\sqrt[]{(JL)^2-(JN)^2} \\ NL=\sqrt[]{24^2-12^2} \end{gathered}[/tex]Because JL is the hypotenuse of the triangle and JN and NL are the legs.
So, solving for NL, we get:
[tex]\begin{gathered} NL=\sqrt[]{576-144} \\ NL=\sqrt[]{432} \\ NL=\sqrt[]{144(3)} \\ NL=\sqrt[]{144}\cdot\sqrt[]{3} \\ NL=12\sqrt[]{3} \end{gathered}[/tex]Therefore, the length of NL is 12√3
What is 6 hundred thousand in hundreds
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600,000 (Six hundred thousand)
1) If we divide 600,000 by 100 we'll have 6000
So 600,000 is equal to 6000 hundreds.
2.) Which equation represents the balance scale shown? 3x = 7 X-3 = 7 x/3 = 7 x + 3 = 7
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As you can see from the figure,
There are 7 dots on the right side of the scale.
On the left side of the scale, there are 3 dots + x
So, we write these numbers on the left and the right side of the equality sign.
[tex]x+3=7[/tex]Therefore, the equation x + 3 = 7 represents the balance scale shown in the figure.
If ABCD is dilated by a factor of 1/2coordinate of d' would be
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Answer the statistical measures and create a box and whiskers plot for the following set of data.1, 1, 2, 2, 5, 6, 11, 11, 12, 13, 14, 16, 17, 19
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DEFINITIONS
A boxplot is a way to show the spread and centers of a data set.
The box and whiskers chart shows you how your data is spread out. Five pieces of information (the “five-number summary“) are generally included in the chart:
1) The minimum (the smallest number in the data set). The minimum is shown at the far left of the chart, at the end of the left “whisker.”
2) First quartile, Q1, is the far left of the box (or the far right of the left whisker).
3) The median is shown as a line in the center of the box.
4) Third quartile, Q3, shown at the far right of the box (at the far left of the right whisker).
5) The maximum (the largest number in the data set), is shown at the far right of the box.
SOLUTION
From the data set given, we have the following information:
1) Minimum Value: 1
2) First Quartile: The position for the first quartile is given by the formula
[tex]\Rightarrow\frac{n+1}{4}[/tex]where n is the number of data.
In the problem, there are 14 data values. Therefore, the position is:
[tex]\Rightarrow\frac{14+1}{4}=3.75th\text{ position}[/tex]Using the 3.75th position, we have
[tex]\begin{gathered} 3rd\Rightarrow2 \\ 4th\Rightarrow2 \\ \therefore \\ Q1=2 \end{gathered}[/tex]3) Median: The median position is given by the formula
[tex]\Rightarrow\frac{n+1}{2}[/tex]Therefore, the median position will be:
[tex]\Rightarrow\frac{14+1}{2}=\frac{15}{2}=7.5th\text{ position}[/tex]The 7.5th position will give:
[tex]\begin{gathered} 7th\Rightarrow11 \\ 8th\Rightarrow11 \\ \therefore \\ Med=11 \end{gathered}[/tex]4) Third Quartile: The third quartile's position is gotten using the formula:
[tex]\Rightarrow\frac{3}{4}(n+1)_{}[/tex]Therefore, the Q3 position will be:
[tex]\Rightarrow\frac{3}{4}\times15=11.25th\text{ position}[/tex]Therefore, the 11.25th position will give:
[tex]\begin{gathered} 11th\Rightarrow14 \\ 12th\Rightarrow16 \\ \therefore \\ Q3=14(0.75)+16(0.25)=14.5 \end{gathered}[/tex]5) Maximum: 19
Therefore, the boxplot is shown below: