In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. c
1 answer:
The standard deviation of both the data are the same which is 3.67 and adding the same constant c to each data value results in the standard deviation remaining the same.
<h3>What is the standard deviation?</h3>It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have a data set:
8, 16, 14, 8, 16
As we know the formula for standard deviation is:
Here σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observation in data set.
X = (8+16+14+8+16)/5 = 12.4
n = 5
After calculating the standard deviation will be:
σ = 3.67
Add 8 to each data value to get the new data set 16, 24, 22, 16, 24.
New standard deviation:
σ(new) = 3.67
The standard deviation of both the data are same we can say the standard deviation does not change when we add a constant to each data value.
Adding the same constant c to each data value results in the standard deviation remaining the same.
Thus, the standard deviation of both the data are the same which is 3.67 and adding the same constant c to each data value results in the standard deviation remaining the same.
Learn more about the standard deviation here:
#SPJ1
You might be interested in
Answer:
The measure of the angles of a parallelogram are ∠A = 120°, ∠B = 60°, ∠C = 120° and ∠D = 60°.
Step-by-step explanation:
The consecutive angles of a parallelogram are supplementary, i.e. they sum up to 180°.
Consider the parallelogram ABCD.
∠A and ∠D and ∠B and ∠C are consecutive angles.
In a parallelogram opposite angles are equal.
That is: ∠A = ∠C and ∠B = ∠D.
Using the provided information, suppose ∠A = 2 × ∠D.
Compute the value of ∠A and ∠D as follows:
∠A + ∠D = 180°
2∠D + ∠D = 180°
3∠D = 180°
∠D = 60°
Then the measure of ∠A is:
∠A = 2∠D
= 2 × 60°
= 120°
Now the measure of ∠B and ∠C are:
∠C = ∠A = 120°
∠B = ∠D = 60°
Thus, the measure of the angles of a parallelogram are ∠A = 120°, ∠B = 60°, ∠C = 120° and ∠D = 60°.
Answer:
0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they will develop the flu after getting the shot, or they will not. The probability of a person developing the flu after getting the shot is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The probability that a person will develop the flu after getting a flu shot is 0.04.
This means that
Random sample of 100 people:
This means that
What is the probability that 5 or more of the 100 people will get the flu?
This is:
In which
So
Then
0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu