![Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Concept explainers
To calculate mean, median, mode, range and standard deviation after adding the given constant.
![Check Mark](/static/check-mark.png)
Answer to Problem 1CYU
Mean is 3.5, Median is 3.5, Mode is 1, Standard deviation is 2.43 and Range is 8
Explanation of Solution
Given information:
Frequency: 10,13,9,8,15,8,13,12,7,8,11,12
Constant to be added: -7
Formula used: Mean formula is,
ˉX=∑fXN
Where, f is frequency
N is total number of items
X is item.
Median formula is,
median=(n2)thterm+(n2+1)thterm2
Where, N cumulative frequency
Mode is the item with the maximum frequency.
Standard deviation is,
SD=√∑(x−ˉx)2n
Where, SD= standard deviation,
x= value
Range is,
range=max−min
Calculation:
According to question,
Add +8 to all the frequency values,
New frequency:
3,6,2,1,8,1,6,5,0,1,4,5
For Mean substituting the values in mean formula,
=3+6+2+1+8+1+6+5+0+1+4+512
So,
=4212
On solving,
=3.5
Hence, Mean is 3.5
For median sorting the frequency
0,1,1,1,2,3,4,5,5,6,6,8
Substituting values in the median formula,
=(122)thterm+(122+1)thterm2
On solving,
=(6)thterm+(7)thterm2
Substituting the values,
=3+42
On solving,
=3.5
Hence, Median is 3.5.
For mode,
Mode is the item with the maximum frequency which is 1.
For standard deviation substituting the values in standard deviation formula,
SD=√(3−3.5)2+(6−3.5)2+(2−3.5)2+(1−3.5)2+(8−3.5)2+(1−3.5)2+(6−3.5)2+(5−3.5)2+(0−3.5)2+(1−3.5)2+(4−3.5)2+(5−3.5)212
So,
SD=√(−0.5)2+(2.5)2+(−1.5)2+(−2.5)2+(4.5)2+(−2.5)2+(2.5)2+(1.5)2+(−3.5)2+(−2.5)2+(0.5)2+(1.5)212
On solving,
SD=√5.91
On solving,
SD=2.43
Hence, Standard deviation is 2.43
For Range substituting the values,
range=8−0
Solving,
range=8
Hence, range is 8
Chapter 10 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Additional Math Textbook Solutions
Introductory Statistics
Elementary Statistics: Picturing the World (7th Edition)
A First Course in Probability (10th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus: Early Transcendentals (2nd Edition)
Pre-Algebra Student Edition
- Determine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forwardThe 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enterarrow_forwardYou are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forward
- Plane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forwardshow that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45arrow_forwardChapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045. 2) Find Θ given sec Θ = 4.213. 3) Find Θ given cot Θ = 0.579. Solve the following three right triangles. B 21.0 34.6° ca 52.5 4)c 26° 5) A b 6) B 84.0 a 42° barrow_forward
- Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.arrow_forward• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0arrow_forwardThree streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less than half of the difference between the rates of Stream A and Stream C. Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x. Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination matrix E such that U = E A, provide also the components of E.arrow_forward
- dent Application X GA spinner is divided into five cox | + 9/26583471/4081d162951bfdf39e254aa2151384b7 A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below: Spinner Results Color Frequency Red 5 Blue 11 Green 18 Yellow 5 Purple 7 Based on these results, express the probability that the next spin will land on purple as a fraction in simplest form. Answer Attempt 1 out of 2 Submit Answer 0 Feb 12 10:11 Oarrow_forward2 5x + 2–49 2 x+10x+21arrow_forward5x 2x+y+ 3x + 3y 4 6arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)