Question:
Find the mean and compare it with the median. Find the standard deviation and compare it with the interquartile range. Calculate s for the data 4, 1, 3, 10, 2.
Answer:
(a)
[tex]Mean = 4[/tex]
[tex]Median=3[/tex]
[tex]Mean > Median[/tex]
(b)
[tex]IQR = 2[/tex]
[tex]SD = 3.2[/tex]
[tex]SD> IQR[/tex]
Step-by-step explanation:
Given:
Data: 4, 1, 3, 10, 2.
Solving (a): The mean and the Median
The mean is calculated as follows:
[tex]Mean = \frac{1}{n} \sum x[/tex]
Where
[tex]n = 5[/tex] i.e 5 data
So, the expression becomes:
[tex]Mean = \frac{1}{5}(4 + 1+3+10+2)[/tex]
[tex]Mean = \frac{1}{5}(20)[/tex]
[tex]Mean = 4[/tex]
Calculating the Median:
First, arrange the order (ascending order):
[tex]Data: 1, 2,3,4,10[/tex]
Because n is odd
The median is represented as:
[tex]Median = (\frac{n+1}{2})th\ item[/tex]
[tex]Median = (\frac{5+1}{2})th\ item\\[/tex]
[tex]Median = (\frac{6}{2})th\ item[/tex]
[tex]Median = 3rd\ item[/tex]
From the arranged data, the 3rd item is 3.
Hence:
[tex]Median=3[/tex]
By comparison, the mean is greater than the median because [tex]4 > 3[/tex]
Solving (b): Standard Deviation and IQR
The standard deviation is calculated as follows:
[tex]SD= \sqrt{\frac{\sum (x_i - Mean)^2}{n}[/tex]
So, we have:
[tex]SD= \sqrt{\frac{(4 - 4)^2+(1 - 4)^2+(3 - 4)^2+(10 - 4)^2+(2 - 4)^2}{5}[/tex]
[tex]SD= \sqrt{\frac{(0)^2+(- 3)^2+(- 1)^2+(6)^2+(-2)^2}{5}[/tex]
[tex]SD= \sqrt{\frac{0+9+1+36+4}{5}[/tex]
[tex]SD= \sqrt{\frac{50}{5}[/tex]
[tex]SD= \sqrt{10}[/tex]
[tex]SD = 3.2[/tex]
Calculating IQR
[tex]IQR = Q_3 - Q_1[/tex]
[tex]Data: 1, 2,3,4,10[/tex]
In (a), we calculate the median as:
[tex]Median=3[/tex]
First, we calculate [tex]Q_1[/tex]
[tex]Q_1 = Median\ of\ the\ first\ half.[/tex]
The first half is:
[tex]First\ Half = 1,2,3[/tex]
So:
[tex]Q_1 = 2[/tex]
First, we calculate [tex]Q_3[/tex]
[tex]Q_3 = Median\ of\ the\ second\ half.[/tex]
[tex]Second\ Half = 3,4,10[/tex]
So:
[tex]Q_3 = 4[/tex]
Recall that:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 4 - 2[/tex]
[tex]IQR = 2[/tex]
So, we have:
[tex]IQR = 2[/tex]
[tex]SD = 3.2[/tex]
By comparison, the standard deviation is greater than the IQR because:
[tex]3.2 > 2[/tex]
So,
[tex]SD> IQR[/tex]
PLS HELP THIS IS A MATTER OF LIFE OR DEATH!!I NEED AN ANSWER QUICKLY
Answer:
Well they are all equal sides so it could really be anything that's an even number ranging from 10-20, hope this helped and good luck on your test! :D
Step-by-step explanation:
#9. Find the slope of the line in the graph.
Remaining Money
у
140
120
A 100
Money ($)
80
60
40
20
0 1 2 3 4 5 6 7 8 9
Number of Games
i need help its the triangle sum theorem
The alphabet has been playing us this whole time!
ABCDEFGHIJKLMNOPQRSTUVWXYZ
ABCDEFG-HI-JK-LMNO-PQRSTUVWXYZ
Hi! Jk! Lmno (Laughing my nose off!)
Answer:
ABCDEFGHIJKLMNOPQRSTUVWXYZ i get it
Step-by-step explanation:
wahahahahahhahaha....
that's so funny l m a o....
I never noticed this....ahahahahahaha
ima share this with my friend lol...
thanks for this....ahahaha
have a great day :)
seriously, that's funny!
ez question unit and proportions!!!!??
Answer: 262.6
Step-by-step explanation: Well if she sold 110 hamburgers on tuesday for $545 That is a simple division equation (545/110). After dividing the answer would be how much each hamburguer cost on its own ( 4.954545454545455), you would then multiply that by the number of hamburgers she sold (53) and get your answer. (262.5909090909091) I am not quite sure where she wants us to round the answer to. so I just did the tens place.
Wylie climbs steadily down a trail that is 1,500 feet above sea level for 40 minutes. Then he takes a 10-
minute lunch break. After lunch, Wylie climbs back up the trail for 5 minutes to take a picture. Finally, he
hikes for 15 minutes until he reaches sea level. Which graph best represents this description?
о А.
OB
fy
ТУ
15
15
Elevation (100 ft)
Elevation (100 ft)
x
0 20 40 60
Time (min)
X
0 20 40 60
Time (min)
fy У
15
y
15
Elevation (100 ft)
Elevation (100 ft)
X
0 20 40 60
Time (min)
Х
0
20 40 60
Time (min)
Answer:
C
Step-by-step explanation:
Long Divison : 3 divided by 2,284 = and don't forget the remainder of it all
2,284 divided by 3,what is the remainder??
Answer :2,284÷3=761 and remainer=1
Answer:
761 R1
Step-by-step explanation:
Here I need the lateral surface area
10 points and brainliest
Answer: D
Step-by-step explanation:
The stem and leaf diagram below gives information about the ages of people in
a bowling club.
3 3 5 8
4 1 2 5 5 6 9
5 3 4 6 6 8
Key: 3/3 represents 33 years old
6 2 8 8 8
Find the range of these ages.
Which expression represents (−21−−−−√5)6 in rational exponent form? (−21)6/5 −215/6 (65)−21 (56)−21
Answer:
[tex](-21)^\frac{6}{5}[/tex]
Step-by-step explanation:
Which expression represents [⁵√(−21)]⁶ in rational exponent form?
Solution:
Rational numbers are numbers which can be expressed as fractions in the form a / b, where a, b are integers and b is not equal to zero.
A rational exponent is an exponent that is a fraction. For example √2 = [tex]2^\frac{1}{2}[/tex].
When expressing a number in rational exponent form, the numerator of the fractional exponent refers to a normal power, but the denominator refers to the root.
[tex][\sqrt[5]{(-21)}]^6 = (-21)^\frac{6}{5}[/tex]
Number 3 need the answer
Answer:
8
Step-by-step explanation:
one negative* one negative = always positive
If ΔABC is an equilateral triangle with, AB = 2x + 17, BC = 6x - 19, AC = 4x-1, find x and the measure of each side
Answer:
[tex]x=9, AB=BC=AC=35[/tex]
Step-by-step explanation:
Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that [tex]AB=BC=AC[/tex]. We are given the lengths of all 3 sides in terms of [tex]x[/tex], but we only need to set two of them equal to each other to solve for [tex]x[/tex]. Let's use [tex]AB[/tex] and [tex]BC[/tex] to solve for [tex]x[/tex]. We know that [tex]AB=BC[/tex], [tex]AB=2x+17[/tex], and [tex]BC=6x-19[/tex]. Therefore, we can write the following equation to solve for
[tex]AB=BC\\2x+17=6x-19[/tex] (Substitute given values into equation)
Solving for [tex]x[/tex], we get:
[tex]2x+17=6x-19\\2x+17-17=6x-19-17[/tex] (Subtract [tex]17[/tex] from both sides of the equation to isolate constants)
[tex]2x=6x-36[/tex] (Simplify)
[tex]2x-6x=6x-36-6x[/tex] (Subtract [tex]6x[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]-4x=-36[/tex] (Simplify)
[tex]\frac{-4x}{-4}=\frac{-36}{-4}[/tex] (Divide both sides of the equation by [tex]-4[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=9[/tex] (Simplify)
Therefore, [tex]AB=2x+17=2*9+17=18+17=35[/tex], and [tex]AB=BC=AC=35[/tex]. Hope this helps!
How many 3/4 cup servings are in a 6 cup container milk?
Answer:
There are 8 3/4-cup servings.
Step-by-step explanation:
What we know:
There is a 6-cup container of milk.
What we don't know:
How many 3/4-cup servings are there?
What we should do:
Divide 6 by 3/4.
6 / 3/4
This is the same as 6 times 4/3.
6 * 4/3
24/3
There are 8 3/4-cup servings in a 6-cup container of milk.
Adriano runs a website that helps writers write better stories. Every month, Adriano receives a subscription fee of \$5$5dollar sign, 5 from each of the subscribers to his website. The website had 200200200 subscribers last month. This month 404040 new members joined the website and 101010 members cancelled their subscription.
How much money will Adriano’s online business earn this month?
\$
Answer:
5$
Step-by-step explanation:
Max's shop sells stuffed teddy bears. Today, Max sold 7 teddy bears for a total of $122.50. Which equation can be used to find b, the cost of each bear?
Answer: 17.50
Step-by-step explanation:
(6x - 3) - (-3x + 2)
Answer:
Step-by-step explanation:
Simplifying
6x + -3 = (3x + -2)
Reorder the terms:
-3 + 6x = (3x + -2)
Reorder the terms:
-3 + 6x = (-2 + 3x)
Remove parenthesis around (-2 + 3x)
-3 + 6x = -2 + 3x
Solving
-3 + 6x = -2 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-3 + 6x + -3x = -2 + 3x + -3x
Combine like terms: 6x + -3x = 3x
-3 + 3x = -2 + 3x + -3x
Combine like terms: 3x + -3x = 0
-3 + 3x = -2 + 0
-3 + 3x = -2
Add '3' to each side of the equation.
-3 + 3 + 3x = -2 + 3
Combine like terms: -3 + 3 = 0
0 + 3x = -2 + 3
3x = -2 + 3
Combine like terms: -2 + 3 = 1
3x = 1
Divide each side by '3'.
x = 0.3333333333
Simplifying
x = 0.3333333333
I need help ASAP. Is it A B C or D???
- 5/6 m = -60
dude im so sorry but i reallyyy dont get why they put letters in math
Answer:
m = -72
Step-by-step explanation:
- 5/6m = -60
multiply both sides by - 6/5
m = -72
Hope This Helps!!!
Answer: m=72
Step-by-step explanation: look at the picture it have the explain & hope this help
PLS HELP MEEEEEEE IM CRYING RN IM GONNA FAIL
Write and graph an equation in two variables that shows the relationship between the time and the distance.
Moves 15 meters in 1 second.
Answer:
The relation between the time and the distance will be:
y = 15x
The graph of the equation y = 15x is attached below.
Step-by-step explanation:
We know that the equation of linear function in two variables in the slope-intercept form is
y = mx+b
where
m is the rate of change or slope b is the y-interceptLet y be the distance
Let t be the time
Given that the object moves 15 meters in 1 second.
Thus, the rate of change or slope = m = 15
As there is no initial condition in our case.
Thus the y-intercept b = 0
Now, substituting m = 15 and b = 0 in the linear function
y = mx+b
y = 15x + 0
y = 15x
Therefore, the relation between the time and the distance will be:
y = 15x
The graph of the equation y = 15x is attached below.
Examples:
Calculate the distance in 1 second
put x = 1 in the equation
y = 15(1) = 15 meters
Calculate the distance in 10 second
put x = 10 in the equation
y = 15(10) = 150 meters
please someone help
The point (0, 5) is the midpoint between (-18, -10) and what other point?
A. (18, 20)
B. (18, 15)
C. (20, 18)
D. (20, 20)
Answer:
The coordinates of the other point are:
(x₂, y₂) = (18, 20)
Hence, option A is correct.
Step-by-step explanation:
Given
The midpoint (x, y) = (0, 5)The first point (x₁, y₁) = (-18, -10)To determine
The second point (x₂, y₂) = ?Using the Mid-point formula between (x₁, y₁) and (x₂, y₂)
[tex]\left(x,\:y\right)=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
Here:
(x, y) is the midpoint between (x₁, y₁) and (x₂, y₂)
substituting (x, y) = (0, 5) and (x₁, y₁) = (-18, -10) in the formula
[tex]\left(0,\:5\right)=\:\left(\frac{x_2+\left(-18\right)}{2},\:\:\frac{y_2+\left(-10\right)}{2}\right)[/tex]
equating
[tex]0=\frac{x_2+\left(-18\right)}{2}[/tex]
[tex]x_2-18=0[/tex]
Add 18 to both sides
[tex]x_2-18+18=0+18[/tex]
[tex]x_2=18[/tex]
also
[tex]5=\frac{y_2+\left(-10\right)}{2}[/tex]
[tex]10=y_2+\left(-10\right)[/tex]
[tex]10=y_2-10[/tex]
[tex]10+10=y_2[/tex]
[tex]10+10=y_2[/tex]
[tex]y_2=20[/tex]
Therefore, the coordinates of the other point are:
(x₂, y₂) = (18, 20)
Hence, option A is correct.
Answer:
(x₂, y₂) = (18, 20)
Step-by-step explanation:
I hope this helps (✿◡‿◡)
Which transformation was performed on PQRS to form P'QʻR'S'? (1 point)
1) A dilation factor of 2
2) A dilation factor of 4
3) A dilation factor of 1/2
4) A dilation factor of 1/4
Given:
A transformation was performed on PQRS to form P'QʻR'S'.
To find:
The transformation.
Solution:
The given graph shows two similar polygons. It means, dilation was performed.
From the given graph it is clear that,
[tex]PS=2[/tex] units
[tex]P'S'=1[/tex] units
Now,
[tex]\text{Scale factor}=\dfrac{P'S'}{PS}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{2}[/tex]
A dilation factor of [tex]\dfrac{1}{2}[/tex] was performed on PQRS to form P'QʻR'S'.
Therefore, the correct option is (3).
Find the common difference of the arithmetic
sequence 13,9,5,
Answer: -4
Step-by-step explanation:
13 - 9 = 4
9 - 5 = 4
so, we can see that it is decreasing by 4 each time.
Answer:
common difference is -4
Step-by-step explanation:
The common difference is the amount we add between terms
13 + d = 9
Subtract 13 from each side
13+d-13 = 9-13
d = -4
Check
9+d = 5
9 + -4 = 5
5= 5
This is true so the common difference is -4
The doctor recommended that Matt decrease the number of calories he consumed from 3,000 to 2,400. By what percent did the number of calories decrease?
thanks.
Answer:
28%
Step-by-step explanation:
Answer: 28%
Step-by-step explanation:
1800/2500 = 0.72
0.72 = 72%
100% - 72% = 28%
A student incorrectly solved an exponential equation looking at the work shown, what mistake did the student make
Answer:
i have made it in pic above
a recipe uses 1 1/4 cups of milk to make 10 servings. if the same amount of milk is used for each serving how mant servings can be made using one gallon.
Answer:
I believe its 36
Step-by-step explanation:
so what i id is a took apart the answer, if 1 1/4 if 10 cups the 1/4 1/4 1/4 1/4 1/4 would also be 10 cups, so now i know that 1/4 = 2 servings
eso i took 3. 1/4 and that gave me 6 and now add the previous which is 10 so its 16 and i have 2 cups left
from here i knew 1 cup and 1/4 is 10 so subtract 1/4 which is -2 servings and you have 8 and 8+8 is 16 so
then i added
16+16= 36
which leads to my final answer of 36
Im so sorry if im wronge but if its right please give brainlest
The price of an item yesterday was $160 today price fell $136 find the percentage decrease
Answer:
15%
Step-by-step explanation:
you just subtract it and convert it to percentPrice-club sells a 12-ounce box of crackers for $2.59 and Shop Mart sells a 1-pound box of crackers for $4.68. The unit price at Price-Club is $ per ounce, and the unit price at Shop Mart is $ per ounce.
Answer:
$0.216 and $0.293
Step-by-step explanation:
Given,
Price club sells 12 ounce box = $2.59
Shop mart sells a 1 pound box = $ 4.68.
We have to find the unit price at Price club and Shop mart.
We know that 1 Pound = 16 ounce
Unit price at Price-club = [tex]\dfrac{2.59}{12}[/tex]
= $0.216
Unit price at Shop Mart= [tex]\dfrac{4.68}{16}[/tex]
= $0.293
because I got this question too. On odysse.yware.
Answer:
0.21 and 0.19
Step-by-step explanation:
It's simple, just divide it.
Divide 2.59 by 12 and divide 4.68. Then round the answers to the closest number in the choices. That's your answer buddy!
What do I divide by 5 to get 9
Step-by-step explanation:
Divide 45 / 5 to get 9
As 5 * 9 = 45