25. Approximate the sample variance and standard deviation given the following frequency distribution: Class Frequency 0–9 13 10–19 7 20–29 10 30–39 9 40–49 11
Answers
Sample variance = 228.408
Standard deviation = 15.113
Step-by-step explanation:The well formatted frequency table has been attached to this response.
To calculate the sample variance and standard deviation of the given grouped data, follow these steps:
i. Find the midpoint (m) of the class interval.
This is done by adding the lower bounds and upper bounds of the class intervals and dividing the result by 2. i.e
For class 0 - 9, we have
m = (0 + 9) / 2 = 4.5
For class 10 - 19, we have
m = (10 + 19) / 2 = 14.5
For class 20 - 29, we have
m = (20 + 29) / 2 = 24.5
For class 30 - 39, we have
m = (30 + 39) / 2 = 34.5
For class 40 - 49, we have
m = (40 + 49) / 2 = 44.5
This is shown in the third column of the attached table.
ii. Find the product of each of the frequencies of the class intervals and their corresponding midpoints. i.e
For class 0 - 9, we have
frequency (f) = 13
midpoint (m) = 4.5
=> f x m = 13 x 4.5 = 58.5
For class 10 - 19, we have
frequency (f) = 7
midpoint (m) = 14.5
=> f x m = 7 x 14.5 = 101.5
For class 20 - 29, we have
frequency (f) = 10
midpoint (m) = 24.5
=> f x m = 10 x 24.5 = 245
For class 30 - 39, we have
frequency (f) = 9
midpoint (m) = 34.5
=> f x m = 9 x 34.5 = 310.5
For class 40 - 49, we have
frequency (f) = 11
midpoint (m) = 44.5
=> f x m = 11 x 44.5 = 489.5
This is shown in the fourth column of the attached table.
iii. Calculate the mean (x) of the distribution i.e
This is done by finding the sum of all the results in (ii) above and dividing the outcome by the sum of the frequencies. i.e
x = ∑(f x m) ÷ ∑f
Where;
∑(f x m) = 58.5 + 101.5 + 245 + 310.5 + 489.5 = 1205
∑f = 13 + 7 + 10 + 9 + 11 = 50
=> x = 1205 ÷ 50
=> x = 24.1
Therefore, the mean is 24.1
This is shown on the fifth column of the attached table.
iv. Calculate the deviation of the midpoints from the mean.
This is done by finding the difference between the midpoints and the mean. i.e m - x where x = mean = 24.1 and m = midpoint
For class 0 - 9, we have
midpoint (m) = 4.5
=> m - x = 4.5 - 24.1 = -19.6
For class 10 - 19, we have
midpoint (m) = 14.5
=> m - x = 14.5 - 24.1 = -9.6
For class 20 - 29, we have
midpoint (m) = 24.5
=> m - x = 24.5 - 24.1 = 0.4
For class 30 - 39, we have
midpoint (m) = 34.5
=> m - x = 34.5 - 24.1 = 10.4
For class 40 - 49, we have
midpoint (m) = 44.5
=> m - x = 44.5 - 24.1 = 20.4
This is shown on the sixth column of the attached table.
v. Find the square of each of the results in (iv) above.
This is done by finding (m-x)²
For class 0 - 9, we have
=> (m - x)² = (-19.6)² = 384.16
For class 10 - 19, we have
=> (m - x)² = (-9.6)² = 92.16
For class 20 - 29, we have
=> (m - x)² = (0.4)² = 0.16
For class 30 - 39, we have
=> (m - x)² = (10.4)² = 108.16
For class 40 - 49, we have
=> (m - x)² = (20.4)² = 416.16
This is shown on the seventh column of the attached table.
vi. Multiply each of the results in (v) above by their corresponding frequencies.
This is done by finding f(m-x)²
For class 0 - 9, we have
=> f(m - x)² = 13 x 384.16 = 4994.08
For class 10 - 19, we have
=> f(m - x)² = 7 x 92.16 = 645.12
For class 20 - 29, we have
=> f(m - x)² = 10 x 0.16 = 1.6
For class 30 - 39, we have
=> f(m - x)² = 9 x 108.16 = 973.44
For class 40 - 49, we have
=> f(m - x)² = 11 x 416.16 = 4577.76
This is shown on the eighth column of the attached table.
vi. Calculate the sample variance.
Variance σ², is calculated by using the following relation;
σ² = ∑f(m-x)² ÷ (∑f - 1)
This means the variance is found by finding the sum of the results in (vi) above and then dividing the result by one less than the sum of all the frequencies.
∑f(m-x)² = sum of the results in (vi)
∑f(m-x)² = 4994.08 + 645.12 + 1.6 + 973.44 + 4577.76 = 11192
∑f - 1 = 50 - 1 = 49 {Remember that ∑f was calculated in (iii) above}
∴ σ² = 11192 ÷ 49 = 228.408
Therefore, the variance is 228.408
vii. Calculate the standard deviation
Standard deviation σ, is calculated by using the following relation;
σ =√ [ ∑f(m-x)² ÷ (∑f - 1) ]
This is done by taking the square root of the variance calculated above.
σ = [tex]\sqrt{228.408}[/tex]
σ = 15.113
Therefore, the standard deviation is 15.113
Related Questions
A restaurant charges large parties an amount that depends on the number of people
that are eating. The restaurant charges $650 for 25 people and $1,850 for 80 people.
What is the restaurant charging per person (unit rate)?
Answers
Answer:
$26 per person or $23.125 per person for the bigger group
Step-by-step explanation:
Savannah needs to buy a bag of dog food that will last for 2 weeks (14 days). She
estimates that a 20 lb bag will be enough. Is she correct?
Answers
Answer:
if it is a chihuahua, then it will be just fine with 20lb
solve the following
2(x-2)=8
Answers
Answer:
2
Step-by-step explanation:
2 (x-2)=8 equal to 2x-4=8, put -4 to the other side by subtracting 4 on both sides once you do you get 2x=4 so 4 divided by 2 equals 2.
Answer:
x = 6
Step-by-step explanation:
2(x - 2) = 8
2x - 4 = 8
2x = 12
x = 6
anyone help me, let's prove
Answers
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
Quadrilateral
N
V
D
I
NVDI can be mapped onto Quadrilateral
F
L
S
W
FLSW by a reflection. If
m
∠
V
=
2
3
∘
m∠V=23
∘
and
m
∠
D
=
8
1
∘
m∠D=81
∘
, find
m
∠
S
m∠S.
Answers
9514 1404 393
Answer:
∠S = 81°
Step-by-step explanation:
Reflection does not change the angle measures.
The quadrilateral names tell you angle D corresponds with angle S. So, angle S has the same measure.
∠S = ∠D = 81°
There are 4 teams. Each team plays each other team once. How many games are played?
A 3
B 4
C. 6
D. 12
E 16
Answers
Answer:
E) 16
Step-by-step explanation:
4 * 4 = 16
Hope this helps
The solution is Option C.
The number of games played by 4 teams if they play each other only once is given by combinations and is 6 games
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the total number of teams be n = 4 teams
Each team plays the other team only once , so x = 2
The number of games played by 4 teams if they play each other only once is given by Combination
ⁿCₓ = n! / ( ( n - x )! x! )
Substituting the values in the equation , we get
⁴C₂ = ( 4! ) / 2! x 2!
On simplifying the equation , we get
⁴C₂ = ( 4 x 3 ) / 2 x 1
⁴C₂ = 2 x 3
⁴C₂ = 6 games
Therefore , the value of ⁴C₂ =6
Hence , the number of games is 6 games
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At a real estate agency, an agent sold a house for $367,000 The commission rate is
6.5% for the real estate agency and the commission rate for the agent is 25 % of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made $___ on the house.
Answers
Answer:
The agency makes 23855
The agent makes 5963.75
Step-by-step explanation:
First find the commission for the agency
367000 * 6.5%
367000*.065
23855
Now the agent gets 25% of this amount
23855 *25%
23855 *.25
5963.75
Answer:
Step-by-step explanation:
The agency made $24,440.00
The Agent made $6,110.00
To test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are:_________
a. 14 and 255.
b. 255 and 14.
c. 13 and 240.
d. 14 and 240.
Answers
Answer:
d). 14 and 240
Step-by-step explanation:
According to the Question,
Given that, The regression model involving 14 independent variables and 255 observationsWe need to find out the numerator and denominator freedom degrees ,
k = 14 regression variable
= n - k - 1
= 255 - 14 - 1
= 240 residuals
df=14,240
Now The degree of freedom for F-critical isF_{k,n-k-1}=F_{14,240}
So, The df of the numerator is 14 and df of the denominator is 240
Simplify:......................................................
Answers
Answer:
...
Step-by-step explanation:...
What are the zeros of the function y = 2x2 + 5x + 2?
A. x =
- 3x =
x = -2
B. X =
1
2
.X = 2
C. X =
3.x=-2
O D. x=-1.x = 2
Answers
Answer: not sure
but I need points
Step-by-step explanation:
JUST KIDDING It’s A I did this in school before and got it correct :)
Marcus likes to go for a run each morning before school. He recorded the number of minutes he spends running and the distance he covers. The scatter plot represents the data he collected
Answers
Answer:
D. 0.85
Step-by-step explanation:
The data points in the scatter plot are closer to each other along the line of best fit, this means that there is a strong positive association between minutes and distance and therefore, the correlation coefficient would be relatively closer to 1.
The correlation is positive since both variables tend to increase together in the same direction.
Therefore, the best estimate of the correlation coefficient out of the given options would be 0.85
The mean height of women in a country (ages 20-29) is 64 4 inches A random sample of 50 women in this age group is selected What is the probability that the mean height for the sample is greater than 65 inches? Assume o = 2.91 The probability that the mean height for the sample is greater than 65 inches is
Answers
Answer:
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 64.4 inches, standard deviation of 2.91
This means that [tex]\mu = 64.4, \sigma = 2.91[/tex]
Sample of 50 women
This means that [tex]n = 50, s = \frac{2.91}{\sqrt{50}}[/tex]
What is the probability that the mean height for the sample is greater than 65 inches?
This is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 64.4}{\frac{2.91}{\sqrt{50}}}[/tex]
[tex]Z = 1.46[/tex]
[tex]Z = 1.46[/tex] has a p-value of 0.9279
1 - 0.9279 = 0.0721
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
The rate of inflation measures the percentage increase in the price of consumer goods. The rate of inflation in the year 2014 was 2% per year. To get a sense of what this rate would mean in the long run, let's suppose that it persists through 2034.
What would be the cost in 2034 of an item that costs $100 in 2014? (Round your answer to the nearest cent.)
$
Answers
Answer:
148.59
Step-by-step explanation:
Inflation is kind of similar to interest and with that bieng said we can (kind of ) use the same formula
the time between 2034 and 2014 is 2034-2014= 20
100(1.02)²⁰=148.5947396
which we can round to 148.59
148.5 is the cost in 2034 of an item that costs $100 in 2014
What is Simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan
[tex]A=P(1+r)^{t}[/tex]
where A is the Actual amount
P is Initial amount
t is time period
r is rate of interest
Given,
The rate of inflation measures the percentage increase in the price of consumer goods
The rate of inflation in the year 2014 was 2% per year.
2% is converted to decimal by dividing with 100
2/100=0.02
The time gap between 2014 and 2034 is
2034-2014=20 years
The initial amount is 100
A=100(1+0.02)²⁰
A=100(1.02)²⁰
A=100×1.485
A=148.5
Hence 148.5 is the cost in 2034 of an item that costs $100 in 2014.
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Which choice describes symmetry?
A. When something is exactly the same on one side as it is on the
other side.
B. When something looks completely different on one side than
the other side.
C. When something has a spherical shape.
Answers
Answer: A. When something is exactly the same on one side as it is on the
other side
Step-by-step explanation: symmetry mean symmetrical: aka they look the same :) hope this helped!
John made this model to show 4/7 * 13/9
Using John's model, what is 4/7 * 13/9? (has to be in fractions)
Answers
Answer:
52/63
Step-by-step explanation:
Given the expression
4/7 * 13/9
Taking the product
= (4*13)/(7*9)
= 52/63
Hence the product of both fractions is 52/63
Which polygon has
an interior angle sum of
1080°?
Answers
Answer:
OctagonStep-by-step explanation:
An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees.
Because the octagon is regular, all of its sides and angles are congruent
Answer:
It's an octagon. So should be the first one with 8 points.
Step-by-step explanation:
 Marsha has a bag that contains 4 green marbles, 8 yellow marbles , and 20 red marbles . If she chooses one marble from the bag, what is the probability that the marble is not red?
PLEASE HELP IF YOURE GOOD AT GEOMETRY!!
Answers
Answer:
C. 3/8
HOPE THIS HELPS :)
Answer:
c. 3/8
Step-by-step explanation:
first you need the denomerator by adding all marbles together which equals 32. now for the munerator you need the sum of the green and yellow marbles. this equals 12. so your fraction is 12/32. next we simplify. we can divide both numbers by 4. getting us a fraction of 3/8.
find the value of x. if necessary, round to the nearest tenth
a. 13.7 in
b. 11.7 in
c. 6.9 in
d. 9.7 in
Answers
I need help with this math problem
Answers
Answer: A) (x + 12) and (x + 9)
Step-by-step explanation:
You need to get x^2 + 21x + 108.
A) (x + 12) (x + 9) = x^2 + 12x + 9x + 108 = x^2 + 21x + 108
B) (x - 12) (x - 9) = x^2 - 9x - 12x + 108 = x^2 -21x + 108
C) (x - 27) (x - 4) = x^2 - 4x - 27x + 108 = x^2 - 31x + 108
D) (x + 27) (x + 4) = x^2 + 27x + 4x + 31 = x^2 + 31x + 31
So, the answer is A).
If this the graph of f(x), then which of the following could be the graph of f-1(x)
Answers
The graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a graph of f(x) is shown in the picture.
As we know, if f(x) has ordered double (x, y)
Then inverse of function g(x) must have ordered double (y, x)
From the given options graph (C) satisfy the condition.
Thus, the graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.
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Answer:
the answer would be option C
There are currently 441 dairy cows at Dancing Dairy Farm. Due to some considerations, the number of dairy cows is decreasing at the rate of 13 cows per year. Currently, each cow produces an average of 1157 gallons of milk per year, and production of milk is increasing at the rate of 39 gallons per cow per year. Use the product rule to determine the rate at which milk production at Dancing Dairy Farm is currently changing.
Answers
Answer:
the production of milk at the Dancing Dairy Farm is increasing by 2158 gallons/year
Step-by-step explanation:
Given the data in the question;
Let us represent the number of cows at the farm with x and
each cow produces y gallons of milk
Total mil production will be T.
so
T = x × y
now, differentiating with respect to t
dT/dt = d( xy )/dt
dT/dt = xdy/dt + ydx/dt
given that;
x = 441
y = 1157
dx/dt = -13
dy/dt = 39
so we substitute
dT/dt = ( 441 )( 39 ) + ( 1157 )( -13 )
dT/dt = 17199 - 15041
dt/dT = 2158
Therefore, the production of milk at the Dancing Dairy Farm is increasing by 2158 gallons/year
Which pairs in the form x,y are solutions to the equation 7x-5y=28?
Answers
Answer:
x=4 y=0
Step-by-step explanation:
7(4)-5(0)=28
28-0=28
28=28
The sum of and is -15/32 and 7/32 is
Answers
Answer:
-8/32 or -1/4(if simplified)
Step-by-step explanation:
-15+7 = -8
-8/32 or -1/4
what is the midpoint with the line segments with end points (-4, 6) (2,-1)
Answers
Answer:
(-1, 5/2)
Step-by-step explanation:
Midpoint = (-4 + 2)/ 2 , (6 - 1)/2
= (-2/2), (5/2)
= (-1, 5/2)
Answer:
Step-by-step explanation:
The midpoints of two coordinate is = [tex]\frac{x2 + x1}{2}[/tex] , [tex]\frac{y2 +y1}{2}[/tex].
Let x2 = 2
x1 = -4
y2 = -1
y1 = 6
Solution:
[tex]\frac{2+-4}{2} , \frac{-1+6}{2} \\\\\\= (-1,\frac{5}{2})[/tex]
A market has two check out lines. Let X be the number of customers at the express checkout line at a particular time of day. Let Y denote the number of customers in the super-express line at the same time. The joint probability mass function of (X, Y) is given below. What is the probability of having only one customer at the express checkout line when there are more than two customers in the super-express line at the same time
Answers
What is the missing number in the table?
Answers
Answer:
1296
Step-by-step explanation:
the y is multiplying by six each time 6*6 = 36
36*6 = 216
216*6 = 1296
2196 = 7776
The resale value V, in thousands of dollars, of a boat is a function of the number of years t since the start of 2011, and the formula is
V = 12.5 − 1.3t.
(a) Calculate V(3).
(b) In what year will the resale value be 7.3 thousand dollars?
(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.
(d) In what year will the resale value be 3.4 thousand dollars?
Answers
Answer:
a) V(3) = 8.6.
b) The resale value will be 7.3 thousand dollars at the start of 2015.
c) [tex]t(V) = \frac{12.5 - V}{1.3}[/tex]
d) 2017
Step-by-step explanation:
We are given the following function:
[tex]V(t) = 12.5 - 1.3t[/tex]
(a) Calculate V(3).
This is V when t = 3. So
[tex]V(3) = 12.5 - 1.3(3) = 8.6[/tex]
So
V(3) = 8.6.
(b) In what year will the resale value be 7.3 thousand dollars?
t years after the start of 2011, and t is found when [tex]V(t) = 7.3[/tex]. So
[tex]V(t) = 12.5 - 1.3t[/tex]
[tex]7.3 = 12.5 - 1.3t[/tex]
[tex]1.3t = 5.2[/tex]
[tex]t = \frac{5.2}{1.3}[/tex]
[tex]t = 4[/tex]
2011 + 4 = 2015
The resale value will be 7.3 thousand dollars at the start of 2015.
(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.
[tex]V(t) = 12.5 - 1.3t[/tex]
[tex]1.3t(V) = 12.5 - V[/tex]
[tex]t(V) = \frac{12.5 - V}{1.3}[/tex]
(d) In what year will the resale value be 3.4 thousand dollars?
t years after 2011, and t is found t when [tex]V = 3.4[/tex]. So
[tex]V(t) = 12.5 - 1.3t[/tex]
[tex]3.9 = 12.5 - 1.3t[/tex]
[tex]1.3t = 8.6[/tex]
[tex]t = \frac{8.6}{1.3}[/tex]
[tex]t = 6.62[/tex]
2011 + 6.62 = 2017
So the year is 2017.
Jed bought a generator that will run for 2 hours on a liter of gas. The gas tank on the generator is a rectangular prism with dimensions 20 cm by 15 cm by 10 cm, as shown. If Jed fills the tank with gas, how long will the generator run? Show how you arrived at your answer. [1000 cm 3= 1 liter] Explain your answer.
Answers
Answer:
The generator will run for 6 hours.
Step-by-step explanation:
First, find the volume of the gas tank that is on the generator. I am told that the gas tank is a rectangular prism that has the dimensions of 20 cm, 15 cm, and 10cm.
Area of any prism = height * width * length
Area of prism = 20 cm * 15 cm * 10 cm = 3,000 cm cubed
I am told the important info that 1,000 cm cubed = 1 liter
Therefore, 3,000 cm cubed = 3 liters
I am also told that the generator will run for 2 hours on 1 liter of gas
Lets make a ratio table:
Hours the generator will run for : liters of gas
2 : 1
6 : 3
the generator will run for 6 hours.
You have savings of 30,000. You invest in a bond mutual fund that pays 3% simple interest. What are your total savings after 20 years?
Answers
Answer:
54,183.34
Step-by-step explanation:
a = 30,000(1.03)²⁰
a = 54,183.34
HELP ME PLEASEEEEEEEEEEEEEE
Answers
Answer:
a
Step-by-step explanation: