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
Bond [772]
2 years ago
7

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and

standard deviation (to a maximum of 2 decimals, if decimals are necessary).
Mathematics
1 answer:
Valentin [98]2 years ago
6 0

So we have a set of integers,

X=\{15,20,25,25,27,28,30,34\}

And we need to compute some stats.

First the range,

The range of data set is difference between the maximum and the minimum of the data set.

So the minimum is 15 and maximum is 34 therefore the range is 34 - 15 = 19.

Second the interquartile range,

The interquartile range of data set is the difference of the first and third quartiles.

First quartile is the value separating the lower quarter and higher three - quarters of the set. The first quartile is computed by taking median of the lower half of the sorted set. This is 15, 20, 25, 25 and it's median is 22.5

Third quartile is therefore the median of 27, 28, 30, 34 which is 29.

Next up, variance.

The variance of set measures how much data is spread out. For data set x_1,\dots, x_n with an average a,

\mathsf{var}(X)=\Sigma_{i=1}^{n}\dfrac{(x_i-a)^2}{n-1}

So first compute the average value which is actually a mean,

a=\dfrac{1}{2}\Sigma_{i=1}^{n}a_i

The sum \Sigma_{i=1}^{n}a_i of numbers in set is 204.

Divide this by number of elements in the set (8).

a=\dfrac{204}{8}=25.5

Then compute the variance,

\mathsf{var}(X)=\dfrac{\Sigma_{i=1}^{n}(x_i-a)^2}{n-1}\approx\boxed{34.57}

And finally standard deviation,

Since have computed variance the standard deviation is nothing too hard. It's defined as a square root of variance,

\mathsf{sde}(X)=\sqrt{\dfrac{\Sigma_{i=1}^{n}(x_i-a)^2}{n-1}}=\sqrt{34.57}\approx\boxed{5.88}

Hope this helps.

r3t40

You might be interested in
What's the slope of (-5, -3) and (5,3)
MAVERICK [17]

Answer:

10/6

Step-by-step explanation:

all you have to do is divide x2 or 5 in this case - x2 or -5 with y2 or 3 - y1 or 3 so it would be

(5--5)/(3--3)

and 2 negatives are a positive so it would turn to

5+5/3+3   or    10/6

please rate 5 stars i would really appreciate it

8 0
3 years ago
What is the slope of the line below?
g100num [7]

Answer:

D. Negative.

Step-by-step explanation:

In truth, when given the graph you don't really need to use the points, but if needed it you would use the formula:

y-y₁=m(x-x₁)

Plug in your information and solve.

-1 - 5 = m (2 - (-1))

-6 = m (3)

-6 = 3m

m = -6 / 3

m = -2

(m = slope)

Also, when shown on the graph =

If the slope is going:

up from left to right: it's positive

down from left to right: it's negative

straight up and down (vertical): it's undefined

straight left to right (horizontal): it's zero.

8 0
3 years ago
How do you answer (2a)³ ?
s2008m [1.1K]
(2a)^{3}
Can be rewritten as;
2a*2a*2a
=8a^{3}
5 0
3 years ago
Read 2 more answers
Sonny has $75 to spend. The purchase he wants to make requires $93. If he borrows extra money that he needs, how much does he ne
xz_007 [3.2K]

he needs to borrow 18$


4 0
2 years ago
Read 2 more answers
two long books containing a total of 2400 pages have a ratio of 3 pages to 5 pages. how may pages are in each book?
Olegator [25]

Answer:

Here you go.

STAY SAFE, GOD BLESS YOU :)

7 0
3 years ago
Other questions:
  • Beverages inc. sells espresso for 8.50 per pound and roasted coffee for 10.25 per pound. the following equations represent a rec
    6·2 answers
  • The area of circle Z is 64πft². <br> What is the value of r? <br> r=__ ft
    13·1 answer
  • Can someone please help me. It's for the elimination method.
    11·1 answer
  • What is the answer?<br> Please and thanks
    9·2 answers
  • * PLEASE HELP WILL GIVE BRAINIEST* Your portfolio must include a minimum of the following five types of equations and solutions:
    10·1 answer
  • Answer these true or false questions:
    7·1 answer
  • Answer please thank ​
    10·1 answer
  • Helpppppppppppppppppppppppp
    9·2 answers
  • I’m getting brainlest
    7·1 answer
  • Am i correct pls help
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!