1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zielflug [23.3K]
2 years ago
7

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

ds 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.
Mathematics
1 answer:
Slav-nsk [51]2 years ago
8 0

Answer:

Median = 90.4

Q_1 = 88.6

Q_3 = 92.2

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

Smallest = 83.4

Highest = 100.3

Next, group each dataset base on common whole numbers.

So, we have:

83.4

84.3\ 84.3

85.3

86.7\ 86.7\ 86.7

87.4\ 87.5\ 87.6\ 87.7\ 87.8\ 87.9

88.2\ 88.3\ 88.3\ 88.3\ 88.4\ 88.5\ 88.5\ 88.6\ 88.6\ 88.7\ 88.9

89.0\ 89.2\ 89.3\ 89.3\ 89.6\ 89.7\ 89.8\ 89.8\ 89.9\ 89.9

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

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

92.2\ 92.2\ 92.2\ 92.3\ 92.6\ 92.7\ 92.7\ 92.7

93.0\ 93.2\ 93.3\ 93.3\ 93.4\ 93.7

94.2\ 94.2\ 94.4\ 94.7

96.1\ 96.5

98.8

100.3

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:

\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}

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

From the above plot,

n = 83

The median is calculated as:

Median = \frac{n+1}{2}th

Median = \frac{83+1}{2}th

Median = \frac{84}{2}th

Median = 42nd

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:

Median = 90.4

The lower quartile (Q) is calculated as:

Q_1 = \frac{n+1}{4}th

Q_1 = \frac{83+1}{4}th

Q_1 = \frac{84}{4}th

Q_1 = 21st

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:

Q_1 = 88.6

The upper quartile (Q3) is calculated as:

Q_3 = 3 * \frac{n+1}{4}th

Q_3 = 3 * \frac{83+1}{4}th

Q_3 = 3 * \frac{84}{4}th

Q_3 = 3 * 21th

Q_3 = 63rd

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:

Q_3 = 92.2

You might be interested in
Math math math pls help
bearhunter [10]

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em><em> </em><em>⤴</em>

<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em>

8 0
3 years ago
Read 2 more answers
9. A blueprint of a house plan uses a scale in
nata0808 [166]

Answer:

The length on the blueprint for an actual length of 65 feet is 16\frac{1}{4}\ inches

Step-by-step explanation:

Given:

Scale of the blueprint is \frac{1}{4}\ in=1\ foot

Length of one side of the house is 65 feet.

Now, as per given data;

1 foot in actual = \frac{1}{4}\ in on the blueprint.

Therefore, using unitary method, we can find find the length on the blueprint for an actual length of 65 feet by multiplying 65 and \frac{1}{4}. Therefore,

Length on the blueprint for 65 feet is given as:

=\frac{1}{4}\times 65\\\\=\frac{65}{4}\\\\=16\frac{1}{4}\ inches

Therefore, the length on the blueprint for an actual length of 65 feet is 16\frac{1}{4}\ inches

5 0
3 years ago
Pls help me out and pls explain
LenKa [72]

Answer:

It is a function

Step-by-step explanation:

The x has only one y and that makes it a function

5 0
3 years ago
Mohamed decided to track the number of leaves on the tree in his backyard each year The first year there were 500 leaves Each ye
svetlana [45]

Answer:

The required recursive formula is

f(n)= 500\times(1.4)^{n-1}\\

Step-by-step explanation:

Mohamed decided to track the number of leaves on the tree in his backyard each year.

The first year there were 500 leaves

Year \: 1 = 500

Each year thereafter the number of leaves was 40% more than the year before so that means

Year \: 2 = 500(1+0.40) = 500\times 1.4\\

For the third year the number of leaves increase 40% than the year before so that means

Year \: 3 = 500\times 1.4(1+0.40) = 500 \times 1.4^{2}\\

Similarly for fourth year,

Year \: 4 = 500\times 1.4^{2}(1+0.40) = 500\times 1.4^{3}\\

So we can clearly see the pattern here

Let f(n) be the number of leaves on the tree in Mohameds back yard in the nth year since he started tracking it then general recursive formula is

f(n)= 500\times(1.4)^{n-1}\\

This is the required recursive formula to find the number of leaves for the nth year.

Bonus:

Lets find out the number of leaves in the 10th year,

f(10)= 500\times(1.4)^{10-1}\\\\f(10)= 500\times(1.4)^{9}\\\\f(10)= 500\times20.66\\\\f(10)= 10330

So there will be 10330 leaves in the 10th year.

3 0
3 years ago
Read 2 more answers
What are the solutions of 64x^3 - 1 = 0 by factoring​
fenix001 [56]

Answer:

x=1/4

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Trey has money saved for a school trip. He earns an additional $40 moving lawns to add to his savings. Trey's parents give him e
    14·1 answer
  • The length of a rectangle is 3 inches more than three times the width. the perimeter is 94 inches. find the length and width.
    8·1 answer
  • Sandy is working with a carpenter to frame a house
    15·1 answer
  • Which values are solutions to the inequailty below ? check all that apply x2 &lt; 25
    9·1 answer
  • In △ABD, DG=40 in.<br> What is the length of DF?<br><br> Enter your answer in the box.
    8·1 answer
  • .
    11·2 answers
  • Help pleas I will give brainliest
    10·2 answers
  • HELPPPP I WILL GIVE POINTS AND BRAINLIEST
    6·1 answer
  • The following set of random numbers represents 20 simulations of three daily
    5·1 answer
  • If $300 is invested at a rate of 6% per year and is compounded quarterly, how much will the investment be worth in 12 years?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!