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
Juliette [100K]
2 years ago
11

In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0

Mathematics
1 answer:
kolbaska11 [484]2 years ago
5 0

Answer:

Q_3 = 56.45 --- The third quartile

Var = 370.18 -- Variance

Step-by-step explanation:

Given

Q_1  =  30.8 -- First quartile

Q_2 =  48.5 --- Median

\bar x = 42 --- Mean

Skp = -0.38 --- Coefficient of skewness

Solving (9): The third quartile Q_3

This is calculated from

Skp =  \frac{Q_1   + Q_3  - 2Q_2}{Q_3 - Q_1}

So, we have:

-0.38 =  \frac{30.8 + Q_3- 2*48.5}{Q_3 - 30.8}

Cross Multiply

-0.38 (Q_3 - 30.8)=  30.8 + Q_3- 2*48.5

Open bracket

-0.38Q_3 + 11.704=  30.8 + Q_3- 97.0

Collect like terms

-0.38Q_3 -Q_3=  30.8 - 97.0- 11.704

-1.38Q_3=  -77.904

Divide both sides -1.38

Q_3 = \frac{-77.904}{-1.38}

Q_3 = 56.45 --- approximated

Solving (b): The variance

First, calculate the standard deviation from:

3IQR  = 4SD

IQR= Q_3 - Q_1

So:

3IQR  = 4SD

3(Q_3 - Q_1) = 4SD

Make SD the subject

SD = \frac{3}{4}(Q_3 - Q_1)

SD = \frac{3}{4}(56.45 - 30.8)

SD = \frac{3}{4}*25.65

SD = \frac{3*25.65}{4}

SD = \frac{76.95}{4}

SD = 19.24

So, the variance is:

Var = SD^2

Var = 19.24^2

Var = 370.18

You might be interested in
State if each triangle is a right triangle:<br><br>13 ft<br>5 ft<br>10 ft<br>​
Kaylis [27]

Answer:

Step-by-step explanation:

the longest length is always the hypotenuse

Use Pythagorean theorem

a^2+b^2=c^2

5^2+10^2=c^2

c=11.18

Note: if c=13 than it is a right triangle

since 11.18 not=13

not right triangle

4 0
2 years ago
Read 2 more answers
What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?
UkoKoshka [18]
Y = kx ⇒ k = y/x = 2/(-3) = -2/3

Answer: k = -2/3
8 0
3 years ago
3 + 2x ≥ -4 solutions
erik [133]

Answer:

x  ≥ -7/2

Step-by-step explanation:

3 + 2x ≥ -4

Subtract 3 from each side

3-3 + 2x ≥ -4-3

2x ≥ -7

Divide each side by 2

2x/2  ≥ -7/2

x  ≥ -7/2

6 0
3 years ago
Read 2 more answers
Barney made $50,000 last year. He increases amount by 8% this year how much does he make this year?
bekas [8.4K]

Answer:$54000

Step-by-step explanation:

8%of50000=4000

4000+50000=54000

3 0
2 years ago
An example of a rectangular Prism can be: A globe or ball O Fish tank o Bowl Can​
garik1379 [7]

Answer:

Fish Tank

Step-by-step explanation:

This of a rectangular prism as a cardboard box. It has rectangles on the top and the bottom. The fish tank is somewhat similar to this so it will be a rectangular prism.

3 0
3 years ago
Other questions:
  • Whats 5*4/2+3 pls help
    9·2 answers
  • What is 3x squared minus 3x
    14·1 answer
  • If a1=47 and d=-5 find a12
    6·1 answer
  • I really need help guys what is the verbal expression for these I made this question
    10·1 answer
  • Determine which variable is the independent variable and which variable is the dependent variable. Write an equation,
    12·2 answers
  • PLEASE HELP ME, I WILL THE CORRECT AWnSER BRAILIEST
    14·2 answers
  • How many times doe 56 go into 512
    10·2 answers
  • Complete the point-slope equation of the line through (3,6)(3,6)left parenthesis, 3, comma, 6, right parenthesis and (5,-8)(5,−8
    13·1 answer
  • Please help
    10·1 answer
  • Last year jo paid £245 for her car insurance. This year she paid£883 for her car insurance. What was the percentage increase
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!