An article in Technometrics (Vol. 19, 1977, p. 425) presents the following data on the motor fuel octane ratings of several blends of gasoline:

88.5 98.8 89.6 92.2 92.7 91.8 91.0 91.0 94.7 88.3 90.4 83.4 87.9 88.4 87.5 90.9 84.3
90.4 91.6 91.0 93.0 92.6 87.8 89.9 90.1 91.2 90.7 88.2 94.4 93.7 88.3 91.8 89.0 90.6
88.6 88.5 90.4 96.5 89.2 89.7 89.8 92.2 88.3 93.3 91.2 84.3 92.3 92.2 91.6 87.7 94.2
87.4 91.2 93.2 88.9 90.3 91.1 85.3 91.1 86.7 88.6 89.8 90.0 86.7 90.1 90.5 94.2 88.7
92.7 91.5 93.4 89.3 100.3 90.8 92.7 93.3 89.9 96.1 91.1 87.6 90.1 89.3 86.7

Required:
Construct a stem-and-leaf display for these data. Calculate the median and quartiles of these data.

Answer:

[tex]Median = 90.4[/tex]

[tex]Q_1 = 88.6[/tex]

[tex]Q_3 = 92.2[/tex]

Step-by-step explanation:

Given

The above data

Required

- A stem and leaf display

- The median

- The quartiles

First, determine the range of the data

[tex]Smallest = 83.4[/tex]

[tex]Highest = 100.3[/tex]

Next, group each dataset base on common whole numbers.

So, we have:

[tex]83.4[/tex]

[tex]84.3\ 84.3[/tex]

[tex]85.3[/tex]

[tex]86.7\ 86.7\ 86.7[/tex]

[tex]87.4\ 87.5\ 87.6\ 87.7\ 87.8\ 87.9[/tex]

[tex]88.2\ 88.3\ 88.3\ 88.3\ 88.4\ 88.5\ 88.5\ 88.6\ 88.6\ 88.7\ 88.9[/tex]

[tex]89.0\ 89.2\ 89.3\ 89.3\ 89.6\ 89.7\ 89.8\ 89.8\ 89.9\ 89.9[/tex]

[tex]90.0\ 90.1\ 90.1\ 90.1\ 90.3\ 90.4\ 90.4\ 90.4\ 90.5\ 90.6\ 90.7\ 90.8\ 90.9[/tex]

[tex]91.0\ 91.0\ 91.0\ 91.1\ 91.1\ 91.1\ 91.2\ 91.2\ 91.2\ \ 91.5\ 91.6\ 91.6\ 91.8\ 91.8[/tex]

[tex]92.2\ 92.2\ 92.2\ 92.3\ 92.6\ 92.7\ 92.7\ 92.7[/tex]

[tex]93.0\ 93.2\ 93.3\ 93.3\ 93.4\ 93.7[/tex]

[tex]94.2\ 94.2\ 94.4\ 94.7[/tex]

[tex]96.1\ 96.5[/tex]

[tex]98.8[/tex]

[tex]100.3[/tex]

Next, we construct the stem and leaf plot.

The whole numbers will be the stem while the decimal parts will be the leaf.

So, we have:

[tex]\begin{array}{ccc}{Stem} & {} & {Leaf} & {83} & {|} & {.4} & {84} & {|} & {.3\ .3} & {85} & {|} & {.3} & {86} & {|} & {.7\ .7\ .7} & {87} &{|} & {.4\ .5\ .6\ .7\ .8\ .9} & {88} & {|} & {.2\ .3\ .3\ .3\ .4\ .5\ .5\ .6\ .6\ .7\ .9} &{89} & {|} & {.0\ .2\ .3\ .3\ .6\ .7\ .8\ .8\ .9\ .9} & {90} & {|} &{.0\ .1\ .1\ .1\ .3\ .4\ .4\ .4\ .5\ .6\ .7\ .8\ .9} & {91} &{|}&{.0\ .0\ .0\ .1\ .1\ .1\ .2\ .2\ .2\ .5\ .6\ .6\ .8\ .8} &{92} &{|} &{.2\ .2\ .2\ .3\ .6\ .7\ .7\ .7} \ \end{array}[/tex]

  [tex]\begin{array}{ccc} {93} & {|} & {.0\ .2\ .3\ .3\ .4\ .7} & {94} &{|} & {.2\ .2\ .4\ .7} &{96} & {|} & {.1\ .5} & {98} & {|} & {.8} & {100} &{|} &{.3} \ \end{array}[/tex]

From the above plot,

[tex]n = 83[/tex]

The median is calculated as:

[tex]Median = \frac{n+1}{2}th[/tex]

[tex]Median = \frac{83+1}{2}th[/tex]

[tex]Median = \frac{84}{2}th[/tex]

[tex]Median = 42nd[/tex]

i.e. the median is at the 42nd position.

From the above stem and leaf plot.

The 42nd position is at stem 90 and the leaf  .4

So the median is:

[tex]Median = 90.4[/tex]

The lower quartile (Q) is calculated as:

[tex]Q_1 = \frac{n+1}{4}th[/tex]

[tex]Q_1 = \frac{83+1}{4}th[/tex]

[tex]Q_1 = \frac{84}{4}th[/tex]

[tex]Q_1 = 21st[/tex]

i.e. the lower quartile is at the 21st position.

From the above stem and leaf plot.

The 42nd position is at stem 88 and the leaf .6

So the lower quartile is:

[tex]Q_1 = 88.6[/tex]

The upper quartile (Q3) is calculated as:

[tex]Q_3 = 3 * \frac{n+1}{4}th[/tex]

[tex]Q_3 = 3 * \frac{83+1}{4}th[/tex]

[tex]Q_3 = 3 * \frac{84}{4}th[/tex]

[tex]Q_3 = 3 * 21th[/tex]

[tex]Q_3 = 63rd[/tex]

i.e. the upper quartile is at the 63rd position.

From the above stem and leaf plot.

The 63rd position is at stem 92 and the leaf .2

So the upper quartile is:

[tex]Q_3 = 92.2[/tex]

I need help with this please. I need to find the volume. For number 7

name a radius circle qrtps

.............................................

The figures in the picture are similar to each other. Find the value of x, rounded to the nearest whole number.

The solution to (-3.9) + 1.5 - 6.2 is -8.6.
Quick Nav
True
False

I am STRESSED. Please answer the following questions below that are HIGHLIGHTED.

Condense the logarithm

q log b + 3 log k

What is the mode out of these numbers?


63, 63, 76, 67, 75, 79, 65, 95, 68, 90

this is a nice question for 69 points (nice)
What's 34.5 x 2

A. 45
B. nice
C. 78
D. 50

Profit, P (x), is the difference between revenue, R (x), and cost C (x), so P (x) = R (x) - C (x), Which expression represents P (x), if R (x) = 2x^4 - 3x^3 + 2x - 1 and C (x) = x^4 - x^2 + 2x + 3?
A) x^4 - 3x^3 - x^2 + 4x +2
B) 3x^4 - 3x^3 - x^2 + 4x + 2
C) x^4 - 3x^3 + x^2 - 4
D) 2x^8 - 3x^3 + x^2 - 4

who was the first Democratic elected president of Nigeria

The Diagram below shows rectangle PLUM find the area of PLUM if entering answer as a decimal, round your final answer to the nearest hundredth. Please Help!

Find the angular size of a circular object with a 1-inch diameter viewed from a distance of 4 yards.
The angular size of the object is Iº.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)

Given a polynomial f(x), if (x + 7) is a factor, what else must be true

A All angles are acute and measure 60°. B One angle is a right angle that measures 90°. C One angle is an obtuse angle that measures more than 90°. D The sum of the three angles equals more than a straight angle. YOU WILL EARN 20 POINTS IT U ANSWER

The amount y of your​ friend's allowance if the amount she receives is ​$5 more than the amount x you receive.

Use the method of cylidrincal shells to find the volume of the solid generated by rotating the region bounded by the curves y=6x-2x^2 and y=x^2 about the y axis.

Maria had $3,500 and invested it into an account with an annual
interest rate of 1.2%. If her investment were compounded monthly,
write an eqaution to find the value of her investment after t years.

As reported in Trends in Television, the proportion of US households who have at least one VCR is 0.592. If 8 households are selected at random, without replacement, from all US households, what is the (approximate) probability that the number having at least one VCR is exactly 4. Be sure to use many decimal places in your calculations (at least 4), but report your answer to three decimal places.

What is the answer? Thank you!

In July, Jannat did yard work for a total of 26 hours. For
all the hours Jannat worked, she earned $234. How
much money did Jannat make per hour doing yard work?
$7/hr
B
$9/hr
$15/hr
D
$35/hr

What is the area of this triangle?
h = 5 in.

b =10 in.

Find the value of x in the triangle shown below.
a. x=80
b. x=48
c. x= 32
d. x=12

The table and graph below show the enrollment in Italian, Chinese, and German classes at two schools.





Which statement is NOT supported by the data distributions?
A.
There is a greater number of students in the Chinese and German classes combined at School B than at School A.
B.
There is a greater percentage of students in the Italian and German classes combined at School A than at School B.
C.
65% of the total enrollment at School A and School B combined are in the Italian class.
D.
There are 2 more students taking Italian at School A than are taking Chinese at School B.

Drag and drop the correct volume of the cylinder into the box to find the volume of the
figure. Use 3.14 for a.

A runner ran of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
How long did it take to run the entire race?
How many minutes did it take to run 1 kilometer? ​

sum of -4/5 and -5/12. please answer.​

(Need help ASAP, I’m taking a test) A researcher is 95% confident that the interval from 5.09 to 10.13 captures x = the true mean amount of
times models change clothes during a fashion shoot.
Is it plausible that the true mean number of times for all models to change clothes during a fashion shoot may
be 102
No, this is not a plausible value for the population mean, because 10 is within the 95% confidence interval
No, this is not a plausible value for the population mean, because 10 is not within the 9596 confidence
interval
Yes, this is a plausible value for the population mean, because 10 is within the 95% confidence interval
Yes, this is a plausible value for the population mean, because 10 is only a little bit above the upper
boundary of the 95% confidence interval.

A car which originally cost $3000000 when new decreases in value by 20% during the first year. what is the value of the car at the end of the first year.​ No Links please​

Does anybody know the answer to this question