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
Anarel [89]
3 years ago
9

Suppose that the data for analysis includes the attributeage. Theagevalues for the datatuples are (in increasing order) 13, 15,

16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.(a) What is themeanof the data? What is themedian?(b) What is themodeof the data? Comment on the data’s modality (i.e., bimodal,trimodal, etc.).(c) What is themidrangeof the data?(d) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data?(e) Give thefive-number summaryof the data.(f ) Show aboxplotof the data.(g) How is aquantile–quantile plotdifferent from aquantile plot? g

Mathematics
1 answer:
Bas_tet [7]3 years ago
6 0

Answer:

a) \bar X = \frac{\sum_{i=1}^{27} X_i }{27}= \frac{809}{27}=29.96

Median = 25

b) Mode = 25, 35

Since 25 and 35 are repeated 4 times, so then the distribution would be bimodal.

c) Midrange = \frac{70+13}{3}=41.5

d) Q_1 = \frac{20+21}{2} =20.5

Q_3 =\frac{35+35}{2}=35

e) Min = 13 , Q1 = 20.5, Median=25, Q3= 35, Max = 70

f) Figura attached.

g) When we use a quantile plot is because we want to show the percentage or the fraction of values below or equal to an specified value for the distribution of the data.

By the other hand the quantile-quantile plot shows the quantiles of the distribution values against other selected distribution (specified, for example the normal distribution). If the points are on a straight line we assume that the data values fit very well to the hypothetical distribution selected.

Step-by-step explanation:

For this case w ehave the following dataset given:

13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.

Part a

The mean is calculated with the following formula:

\bar X = \frac{\sum_{i=1}^{27} X_i }{27}= \frac{809}{27}=29.96

The median on this case since we have 27 observations and that represent an even number would be the 14 position in the dataset ordered and we got:

Median = 25

Part b

The mode is the most repeated value on the dataset on this case would be:

Mode = 25, 35

Since 25 and 35 are repeated 4 times, so then the distribution would be bimodal.

Part c

The midrange is defined as:

Midrange = \frac{Max+Min}{2}

And if we replace we got:

Midrange = \frac{70+13}{3}=41.5

Part d

For the first quartile we need to work with the first 14 observations

13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25

And the Q1 would be the average between the position 7 and 8 from these values, and we got:

Q_1 = \frac{20+21}{2} =20.5

And for the third quartile Q3 we need to use the last 14 observations:

25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70

And the Q3 would be the average between the position 7 and 8 from these values, and we got:

Q_3 =\frac{35+35}{2}=35

Part e

The five number summary for this case are:

Min = 13 , Q1 = 20.5, Median=25, Q3= 35, Max = 70

Part f

For this case we can use the following R code:

> x<-c(13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70)

> boxplot(x,main="boxplot for the Data")

And the result is on the figure attached. We see that the dsitribution seems to be assymetric. Right skewed with the Median<Mean

Part g

When we use a quantile plot is because we want to show the percentage or the fraction of values below or equal to an specified value for the distribution of the data.

By the other hand the quantile-quantile plot shows the quantiles of the distribution values against other selected distribution (specified, for example the normal distribution). If the points are on a straight line we assume that the data values fit very well to the hypothetical distribution selected.

You might be interested in
At times, it is necessary to make plans even when all of the facts are not there. Bernard is currently facing such a dilemma. Be
Taya2010 [7]
A. Let us assume the width of the pool = x
Then
Length of the pool = 3x + 3
Depth of the pool = 2(3x + 3) - 7
                            = 6x + 6 - 7
                            = 6x - 1
B. Area of the land space = Width * length
                                          = x * (3x + 3)
                                          = 3x^2 + 3x
C. Volume of the pool = (6x - 1) * (3x^2 + 3x)
                                    = 18x^3 + 18x^2 - 3x^2 - 3x
                                    =  18x^3 + 15x^2 - 3x
 D. The highest degree is actually 3 and the number of terms that we get is also 3.                
7 0
3 years ago
Please answer these questions and have the work shown:
ahrayia [7]

Answer:

number one 50 I think and 3 is 75 not positive but I hope it helps

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Write 0.15151515 as a fraction
leonid [27]

Answer:

5/33

Step-by-step explanation:

4 0
3 years ago
What is the slope of the line through the points (1,5) and (-2,-4)?
olasank [31]

Answer:

slope = 3

Step-by-step explanation:

Use the coordinates of the points to determine the slope.

3 0
3 years ago
What is the value of x?
Dafna1 [17]

Answer:

3x = 12x - 81(vertically opposite angles)

→3x - 12x =  - 81

→- 9x =  - 81

→x =  \frac{ - 81}{ - 9}

→x =  \frac{81}{9}

→x = 9

hope it helped you:)

5 0
3 years ago
Other questions:
  • Y-0.6=-1.8 i don't understand this so plz help
    5·2 answers
  • When I double my number, add three, subtract my number, and subtract one, I get my number plus two.
    10·1 answer
  • ALL GREETINGS TO THE WORLD I AWAIT YOUR ASSISTANCE PRETTY PLEASE
    9·1 answer
  • The first one asks for the value of x. I need help on both. I am struggling to understand how to do this, please help
    13·1 answer
  • According to a sample study of a high school population only 46% of high school seniors can solve problems using fractions. We c
    8·1 answer
  • To find the quotient of 156.38 and 100, move the decimal point in 156.38 (two four three five) places to the (left,right)
    8·2 answers
  • What are the x-values of the quadratic equation (x-2)^2-9=0?
    6·1 answer
  • How is an ammeter used in a circuit?
    8·2 answers
  • How would you write one million as a power of 10? Thank you appreciate your help!
    13·2 answers
  • James fenced in his backyard. The perimeter of his fence is 20 feet, and the width of his yard is 2 feet wide. Use the perimeter
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!