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
Ann [662]
3 years ago
12

A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is

Mathematics
1 answer:
Svetllana [295]3 years ago
6 0

Answer:

Option D.

Step-by-step explanation:

Suppose that we have a set of N values:

{x₁, x₂, ..., xₙ}

The median is the value in the middle, and the mean is calculated as:

M = \frac{(x_1 + x_2 + x_3 ... + x_n)}{N}

Because here we have "the median" then we will assume that N is odd, and there is only one median, the value "k"  (if N was even, the median would be the mean of the two middle values, that case is really similar to the case where N is odd, so solving only one of the cases is enough)

Now we add 7 to all the values greater than the median

We subtract 7 to all values smaller than the median.

Then the median remains unchanged (because we did not add nor subtract anything to the median).

The new mean will be:

M' = \frac{(x_1 - 7) + (x_2 - 7) + ... + (x_{k}) + ... + (x_n + 7)}{N} = \frac{(x_1 + x_2 + ... + x_n) + (-7)*(n/2 - 0.5) + 7*(n/2 - 0.5)}{N}  = \frac{(x_1 + x_2 + ... + x_n)}{N} = M

So the mean does not change.

Because the mean is computed as the sum of the numbers divided by N, and the mean does not change, and N does not change, then the sum of the numbers does not change.

Finally, the standard deviation is computed as:

SD = \sqrt{\frac{(x_1 - M)^2 + ... + (xn - M)^2}{N} }

Because M does not change, if we add or subtract numbers to some of the values, the standard deviation will change (Because all the terms are squared, so the added and subtracted sevens don't cancel like in the previous cases)

Then the only value that does not have the same value in both the original and new data sets is the standard deviation.

You might be interested in
The population of a city is expected to
Furkat [3]

\huge\boxed{1.0925p}

Since the population is going to increase by a certain percentage, we have to add 100\% to the percentage to keep the original population.

9.25\%+100\%=109.25\%

Now, convert the percentage into a decimal. You can do this by moving the decimal place two places to the left.

109.25\longrightarrow 1.0925

Now, just multiply that by p.

\large\boxed{1.0925p}

8 0
3 years ago
What is the distributive property of 2 times 8
malfutka [58]
2*8 using <span>distributive property
= 2(3+5)
= 6+ 10
= 16</span>
5 0
3 years ago
Select all ratios equivalent to 30:6
Korolek [52]

Answer:

60 : 12

90 : 18

120 : 24

150 : 30

3 0
3 years ago
Which statement is true?
Oksi-84 [34.3K]

Answer:

C.

Step-by-step explanation:

A. 39 = 3 × 13; not prime

B. 33 = 3 × 11; not prime

C. 43 = 1 × 43; prime

D. 51 = 3 × 17; not prime

Answer: C.

5 0
2 years ago
Two accounts earn simple interest. The balance yy (in dollars) of Account A after xx years can be modeled by y=10x+500y=10x+500.
GrogVix [38]
1)
A has a greater principal

2) 
Principal of A is $500, the principal of B is $400, so A's principal is greater by $100

3)
Annual interest rate of A:
10/500 x 100
interest rate of A = 2%
The interest rate of B is higher.

4)
B's annual interest rate is 5% and A's annual interest rate is 2%, so B's is higher by 3%.
6 0
3 years ago
Other questions:
  • What values of data might affect the statistical measures of spread and center
    12·1 answer
  • Perimeter and area for these 2 please! Give explanation! BIG POINTS
    15·1 answer
  • You are adding two rational numbers with different signs. How can you tell if the sum will be positive negative or zero
    9·1 answer
  • Connor was given a box of asstorted chocolates for his birthday. Each night, Connor treated himself to some chocolates. There we
    5·1 answer
  • If f(x) = 3x-2, then f (8) - f (-5) =​
    13·2 answers
  • Estimate the product by rounding<br> 2×6254
    14·2 answers
  • The most which number has the same value as 20 tens
    12·1 answer
  • one number is four times as large as another if the numbers are added together the result is six less than seven times the small
    8·1 answer
  • Select the equation(s), where 9 is a solution.
    10·1 answer
  • question : fine the location of points a after a translation of 9 units up? Can someone please help me ?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!