Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.
Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.
Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.
To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.
If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.
The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.
These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.
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100 POINTS + BRAINLIEST !!!!!!!!
In a certain mathematics examination, the probability of being award a grade A is believed to be 0.3
For a group of 10 candidates, calculate:
i) the probability that at least half achieve grade A
The probability of being awarded a grade B is also 0.3
ii) Find the probability that all ten candidates achieve either grade A or grade B
Answer: (i) 15% (ii) 0.6%
Step-by-step explanation:
Given: P(A) = 0.3 ⇒ ~P(A) = 0.7
P(B) = 0.3 ⇒ ~P(B) = 0.7
P(A ∪ B) = 0.6 ⇒ ~P(A ∪ B) = 0.4
If you don't have a calculator function for the Binomial Formula, the equation is: [tex]P(X)=\dfrac{n!}{X!(n-X)!}\cdot p^X\cdot (1-p)^{n-X}[/tex] where
n is the number of trialsp is the probability of successX is the number of successes(i) Probability of at least 5 --> P(X ≥ 5) means P(5) + P(6) + P(7) + P(8) + P(9) + P(10)
P(5): n = 10, p = 0.3, X = 5 → P(5) = 0.1029
P(6): n = 10, p = 0.3, X = 6 → P(6) = 0.0368
P(7): n = 10, p = 0.3, X = 7 → P(7) = 0.0090
P(8): n = 10, p = 0.3, X = 8 → P(8) = 0.0014
P(9): n = 10, p = 0.3, X = 9 → P(9) = 0.0001
P(10): n = 10, p = 0.3, X = 10 → P(10) = 0.0000
TOTAL = 0.1502 → 15.02%
(ii) Probability of A or B = 10 --> P(X = 10)
P(10): n = 10, p = 0.6, X = 10 → P(10) = 0.0060 → 0.6%
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How many
2
5
cup servings are in
9
5
cups of ice cream? (in simplest fraction form)
There would be 5/2 cup servings
A parking garage charges $2 for the first hour and $3 for each additional hour. Fran must spend less than $20 for parking. What is the
greatest number of hours Fran can park? Let u , stand for hours parked.
Answer:
he can only stay for 6hr cause 7 hr would use his whole 20
Item New Price Price Change Decrease Bike $110 $96 Scooter $45 $56 Tennis Racket $79 Increase Skis $580 25% Decrease
Did it increase or decrease..?
Answer:
increase
Step-by-step explanation:
I apologize , but I still don’t get none of these questions , can I have help ?
Answer:
The measures of the angles: m∠1 = 51°, m∠2 = 39°
Step-by-step explanation:
In this type of question, you should substitute the measures of the angle by the given values and solve the equation to find x, then find the measure of each angle.
∵ m∠1 + m∠2 = 90°
∵ m∠1 = 3x°
∵ m∠2 = (x + 22)°
→ Substitute m∠1 by 3x° and m∠2 by (x + 22)° in the equation above
∴ 3x° + (x + 22)° = 90°
→ Add the like terms in the right side
∴ (3x + x) + 22 = 90
∴ 4x + 22 = 90
→ Subtract 22 from both sides
∴ 4x + 22 - 22 = 90 - 22
∴ 4x = 68
→ Divide both sides by 4 to find the value of x
∴ [tex]\frac{4x}{4}=\frac{68}{4}[/tex]
∴ x = 17
→ Now substitute the value of x in each angle to find them
∵ m∠1 = 3x°
∴ m∠1 = 3(17) = 51°
∵ m∠2 = (x + 22)°
∴ m∠2 = (17 + 22) = 39°
The measures of the angles: m∠1 = 51°, m∠2 = 39°
On a coordinate plane, a curved line with a minimum value of (1.5, negative 1) and a maximum value of (negative 1.5, 13), crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 6).
Which lists all of the x-intercepts of the graphed function?
0, 6)
(1, 0) and (2, 0)
(1, 0), (2, 0), and (–3, 0)
(1, 0), (2, 0), (–3, 0), and (0, 6)
Someone pls help me answer this is worth a lot of points on my test.
Answer:
(-3,0) and (1,0)
Answer
The answer is C, because those are the points that cross the x-axis.
Step-by-step explanation:
i worked it out on paper
(70 x 10^-4) x (60 x 10^6) =
Answer:
Step-by-step explanation:
(70 x 10^-4) x (60 x 10^6) = (70 x ([tex]\frac{1}{10}[/tex] x [tex]\frac{1}{10}[/tex] x [tex]\frac{1}{10}[/tex] x [tex]\frac{1}{10}[/tex])) x ( 60 x 1000000)
= 70 x [tex]\frac{1}{10000}[/tex] x 60000000 = 420000
Answer:
(70x10^-4) x (60 x 10^6) = 420000
so the answer would be
420000
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18
A.
symmetrical
B.
uniform
C.
skewed to the left
D.
skewed to the right
Answer:e
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
have a great day
fast plssss help me out !
Answer:
combine like terms
Step-by-step explanation:
7x and 4x were added together to get 11x. 35 and 20 were added together to get 55
Item 17 You have 13 gallons of lemonade to sell. You use cone-shaped cups that are 7 centimeters in diameter and 11 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
find the value of the x for the following 5x - 7 = 18
Answer:
x = 5
Step-by-step explanation:
Step 1: Write equation
5x - 7 = 18
Step 2: Solve for x
Add 7 to both sides: 5x = 25Divide both sides by 5: x = 5Step 3: Check
Plug in x to verify it's a solution.
5(5) - 7 = 18
25 - 7 = 18
18 = 18
Answer:
.x =5Step-by-step explanation:
5x - 7 = 185x = (18+7)5x = 25divide 5 both sides.
x = 5
Need help for one question for geometry !
A young sumo wrestler decided to go on a special diet to gain weight rapidly. WWW represents the wrestler's weight (in kilograms) after ttt months. W=80+5.4tW=80+5.4tW, equals, 80, plus, 5, point, 4, t What was the wrestler's weight before his special diet?
Answer:
80kg
Step-by-step explanation:
Given:
W = 80 + 5.4t
Where,
W = the wrestler's weight (in kilograms
t = number of months
What was the wrestler's weight before his special diet?
W = 80 + 5.4t
When t = 0 (that is before the weight gain)
W = 80 + 5.4t
= 80 + 5.4(0)
= 80kg
When t = 1 ( first month of the weight gain)
W = 80 + 5.4t
= 80 + 5.4(1)
= 80 + 5.4
= 85.4 kg
The wrestler's weight before his special diet is 80kg
ALTERNATIVELY
W = 80 + 5.4t
80 = the fixed weight
5.4 = weight gained per month
t = number of months
Therefore,
The fixed weight which is 80kg is the weight of the wrestler before the special diet.
Answer:
10.8
Step-by-step explanation:
This is correct on khan academy.
f(x) = 3x – 2 if f(x) =7
Answer:
19
Step-by-step explanation:
3(7)-2
21-2=19
this explanation needs to be more than 20 characters so that's why I'm typing this sentence
Answer: 19
Step-by-step explanation:
1. Substitute 7 for x
2. 3x7=21
3.21-2=19
What is the measure of ABD?
A 32
B 58
C 64
D 148
E 180
Answer: The answer is 148
Step-by-step explanation:
Angle CBA and ABD should add up to 180 degrees. So you just do 180-32=148
The measurement of the ∠ABD in the given figure is 148°.
Hence the correct option is D.
Given that are two lines AE and CD are intersecting at point B, making angle ∠ABC = 32°.
We need to find the measurement of the ∠ABD.
To find the measurement of the ∠ABD, we will use the concept of linear pair angles.
According to the figure, angles ABC and ABD are linear pair angles, that mean they are supplementary, or we can say their sum is 180°.
Therefore, setting up the equation.
∠ABC + ∠ABD = 180°
Plugging the value of angle ABC from the given information,
32° + ∠ABD = 180°
Subtracting 32 from both the sides,
∠ABD = 180° - 32°
∠ABD = 148°
Hence the angle ABD is equal to 148°.
Therefore, the correct option is D.
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Find f(0)
(-3
f(x) = {10+ x
(4-x
-55x<-1
0
Answer:
34o
Step-by-step explanation:
There is 1/8
of a pizza left to split between 2 of your friends. If you split the pizza equally, what fraction of the pizza will each of your friends get?
Answer:
youll get 1/16 each
Step-by-step explanation:
1/16 + 1/16 = 2/16 = 1/8
each person will get 1/16
answer please ? i don’t understand
Answer:
It is letter C
Step-by-step explanation:
Which product is negative?
−2⋅(−7)⋅12⋅(4)
4⋅(−9)⋅(−3)⋅(−1)
−6⋅(−7)⋅(−8)⋅0
−3⋅(−2)⋅(−4)⋅(−7) ( plz help me)
Answer:
The second product is negative.
Step-by-step explanation:
A negative times a positive is a negative.
Answer:
Step-by-step explanation:
4•(-9)•(-3)•(-1)
-36•(-3)•(-1)
108•(-1)
-108
What is the product of (-a+3)(a+4)
Answer:
[tex]-a^{2} -a+12[/tex]
Step-by-step explanation:
Use the FOIL method and multiply the equations into each other to get the final answer.
Make an equation to find the area of this figure.
Answer:
20x20=400
Step-by-step explanation:
My bad for the autocorrect
What is the answer :
2/34 = 5/Y ( criss cross algebra)
Answer:
85
Step-by-step explanation:
2 / 34 = 5 / Y
2 x Y = 34 x 5
2 x Y = 170
Y = 170 / 2
Y = 85
What is the multiplicative inverse of 1/5?
Answer:
5/1
Step-by-step explanation:
because the multiplicative invers is the number that makes it equal to zero
Pls awnser the question (I will name brainliest)
Answer:
Yes, the last digit i think its 10 is a outlier.
Step-by-step explanation:It is one because it just stick in the chart, like it fit in
Answer:10 foot is the outlier
Step-by-step explanation:it differs
from the rest
Can someone please help me asap I’ll mark brainlist!!?!?
Answer:
32/13
Step-by-step explanation:
2 6/13
2(13)=26
26+6=32
32/13
Answer:
32/13
Step-by-step explanation:
13x2=26
26+6=32
Denominator stays the same
16 + 8 to the power of 2 divided by 4 - 4, Add on set of parenthesis to make it undefined
Answer:
(16+8)²÷(4-4)
Evaluate the expression for x=5, y=-3 and z=7
(x2 – z) (22+5)
Answer:
81
Step-by-step explanation:
(Refer to image)
Plug in x and z and follow order of operations to simplify the expression
The function C(x) = 25x + 50 represents the labor cost (in dollars) for Certified Remodeling to build a deck, where x is
the number of hours of labor. The table shows sample labor costs from its main competitor, Master Remodeling.
Answer:
Master RemodelingStep-by-step explanation:
Original question is attached
Option 1C(x) = 25x + 50C(8) = 25*8 + 50 = $250Option 2As per table, the rate of change is $30 per 2 hours.So 8 hours will cost $190 + $30 = $220As we see the second option is cheaper so we should hire the Master Remodeling
Find the equation of the line containing (3,-2) and (6,3).
Express the equation in slope-intercept form,
Answer:
Y= 5/3x -7
Step-by-step explanation:
To find the slope with the given points you find the distance between the y values and the x values. (Rise/Run = Y/X). Once you find the pattern you can use it until you find the y intercept if you're using graph paper!
Hope this helps! :)
(Side Note: The distance for the y values from -2 and 3 is +5. The distance for the x values is +3 )
Write an equation to represent the following statement. j is 7times as large as 6 .
