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]

Urgent need help now

Does coordinate p or coordinate q represent a greater number?
PLEASE HELP!!

2
One type of redwood tree has an average height of 65 feet when it is 20 years old. If the tree is more than 20 years
old, the average height, h, can be modeled by the function h = 1.95(a - 20) + 65, where a is the age of the tree in
years. Which statement about this situation is true?
A Every additional 1.95 ft of length over 20 ft adds 45 years to the age of this type of redwood tree.
8. For this type of redwood tree, the average height increases by 1.95 ft per year throughout its lifetime.
c. Each additional year of age over 20 years adds 1.95 ft to the average height of this type of redwood tree.
D. For this type of redwood tree, the average height increases by 65 ft for every 20 years of growth.

Jillian wants to figure out how much water will fit inside the water tower that is by her house. So she wants to find the volume of the water tower. True False

The line plot shows the different lengths of nails in your toolbox. If you take all the nails
that are less than 2 inches long and lay them end to end, how far will they reach?

8 less than the quotient of 20 and 5

de una bolsa donde hay veinte bolas numeradas del 1 al 20 extraemos una, A: obtener un número par , B: obtener número primo, C: obtener un número tal que su suma de cifras sea 5,
a) comprobar que cumplan con las propiedades asociativa y distributiva en los sucesos, b) comprobar que se cumplan con las propiedades de las leyes de morgan entre los sucesos AyC , ByC, AyB , c) efectúa las siguientes operaciones en los sucesos unión entre AB, BC, AB, intersección entre AB,BC, AB, diferenciación entre AB, BA, CA, AC, ​

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm. He knows that the population standard deviation is 0.83 cm. Assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? State the null and alternative hypotheses for the test.

Write the number in 2 equivalent forms as a fraction, decimal, or percent.

start time 7:30 elapsed time 2 hours 20 minutes end time is

​

Which fraction represents the probability of getting at least 1 heads?
A.7/8
B.3/4
C.1/6
D.1/8

Help out plsss ...... ​

Colton's truck weighs 1 tons. Francine's
truck weighs 2 į tons. What is the difference
between the weights of their two trucks?

please help me with this !

THIS IS MY LAST QUETSION!!!! Please help!!!

2. Barnes and Noble bookstore is having a sale. Dr. Mumin's book sells for
$4 per copy. Dan Moyer's book sells for $1 per copy. Leannie spends $23
for 8 books'. How many copies of books from each author did she buy?

What shape is always classified as a rectangle?​

Lesson 13 Problem Set 5.4
2.
Draw rectangular fraction models of 3 >
f3x3 and
Compare multiplying a number by 3 and by 1 third.

Question in the image will give brainlyy

I need help with this

Is 3/4 closer to 0 or 1?

What’s the answer of this text question???

A number n is at most −110.

6,6,6,6,7,7,7,7,7,7,8,8,9,9,10
Select the statement that correctly describes the data,
O A. The typical value is 7 because it is an extreme value,
B. The typical value is 15 because that is the total number of bags,
C. The typical value is 7. Most values are close to 7, and there are no
extreme values
D. The typical value is 10 because it is the maximum,

an equilateral triangle has perimeter P. The length of one side is p/3 which expression is equivalent to the length of one side?
a.) 2/3p
b.) 3/4p
c.) 1/3p
d.) 3p​

Which statement is true?

24 – 15 × 4 – 3 × 2 = 30
24 – 15 × (4 – 3) × 2 = 30
(24 – 15) × 4 – 3 × 2 = 30
(24 – 15) × 4 – 3 × 2 = 66

Roger is standing next to a tree where his shadow is 3 feet long and the shadow of the tree is 18 feet long.
If Roger is 4.5 feet tall, what is the height of the tree?
O A. 12 ft
OB. 16.5 ft
O C. 19.5 ft
OD. 27 ft​

Maya plots the yards lost during a football game on a number line and labels it A. She plots Point B to the right of zero, a distance that is exactly as far from zero as Point A is. Which sentence is a correct statement about Point B?
The sum of the values of Point A and Point B is negative.
The sum of the values of Point A and Point B is zero.
Point B lies twice the distance from 0 as Point A.
Point B lies to the left of Point A on a number line.

How much money would Julie earn for working 16 hours? 15 hours is 180$ PLEASE HELP

I have several pages like this and do not understand it at all.​