Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 12 Data Analysis and Probability Exercise 12
Algebra 1 Common Core Solutions
Chapter 12 Data Analysis and Probability Exercise 12 1CR
Each numerical item of the data in a matrix is called an element.
Explanation: The above statement can be understood using the definition of Matrix: A set of mn numerical items are arranged in a form of m row and n column, then a rectangular array is formed, which is called matrix, and the numerical items in a matrix is called an element.
Chapter 12 Data Analysis and Probability Exercise 12 1CT
Chapter 12 Data Analysis and Probability Exercise 12 1MC
Chapter 12 Data Analysis and Probability Exercise 12 1PAT
Chapter 12 Data Analysis and Probability Exercise 12 2CR
The number of data values in an interval is the frequency of the interval.
Explanation: The frequency of an interval means that how many numbers are there in that interval that is number of data value in the interval is called frequency of the interval.
Chapter 12 Data Analysis and Probability Exercise 12 2CT
Chapter 12 Data Analysis and Probability Exercise 12 2MC
Chapter 12 Data Analysis and Probability Exercise 12 2PAT
a. Consider a survey question, “Would you rather go on a beach vacation, a city vacation, or stay home” This survey question is bias question. because if a person want to visit a place out beach vacation, a city vacation, or stay home, then their opinion is reflect by the survey question Therefore, by the definition of bias question a question is said to be bias if it contain the assumption which may or may not be true and that reflect the opinion of the answerer The survey question is bias
Chapter 12 Data Analysis and Probability Exercise 12 3CR
An outlier is a data value much greater or less than the other values in a data set.
Explanation: An outlier is also the data value of the same set but it is either much greater or less than the other data value in the set
Chapter 12 Data Analysis and Probability Exercise 12 3CT
From the above histogram we see that it has one peak this is not in the centre. By the definition of skewed histogram, “if the histogram has one peak that is not in center then the histogram is skewed”.
Thus, the above histogram is skewed.
Chapter 12 Data Analysis and Probability Exercise 12 4CR
The median of the lower half of an ordered data set is the first quartile.
Explanation:
First Quartile: If the data set is divided into four equal parts, then the first quartile is the median of the lower half of an ordered data set and it is represented by.Q1
Chapter 12 Data Analysis and Probability Exercise 12 4CT
From the above histogram we see that if we draw vertical line in the middle of the histogram, then the line divide the histogram into two parts that are close to mirror images. Therefore by the definition of symmetric histogram, “if a vertical line can divide the histogram into two parts that are close to mirror images, then the histogram is symmetric”. Thus, the above histogram is symmetric.
Chapter 12 Data Analysis and Probability Exercise 12 4MC
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Chapter 12 Data Analysis and Probability Exercise 12 6CR
Chapter 12 Data Analysis and Probability Exercise 12 6CT
Chapter 12 Data Analysis and Probability Exercise 12 6MC
Consider the statement given in the question:
From the graph given in the question check for the suitable table model which will satisfy the graph properly Clearly, the points (—6,— 1),(—3,O.5),(O,2)and(6,5) satisfy the graph As, for the given graph in the question the left side of the curve satisfies (—6,— 1)and then comes the point (—3,0.5) repeating like this and joining all the points obtained, the graph is obtained as given in the question Hence, the option G is correct
Chapter 12 Data Analysis and Probability Exercise 12 7CR
Chapter 12 Data Analysis and Probability Exercise 12 7CT
Let us consider the weights of 8 scuba divers, without tank are: Weights (kg): 85. 103. 94. 97, 88. 91, 104. 95 …… (1) We have to find the mean. median. mode, and range
Chapter 12 Data Analysis and Probability Exercise 12 7MC
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Chapter 12 Data Analysis and Probability Exercise 12 8MC
Consider the statement given in the question:
For the given graph in the statement, for positive values of x. the x axis values are always increasing and are greater than the values on the y -axis.
In options F. G and I. the statement is not satisfying the given graph in the question Hence, the correct option is H.
Chapter 12 Data Analysis and Probability Exercise 12 9CR
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Chapter 12 Data Analysis and Probability Exercise 12 9MC
Chapter 12 Data Analysis and Probability Exercise 12 10CR
From the above histogram we see that it has one peak this is not in the centre By the definition of skewed histogram. “if the histogram has one peak that is not in center then the histogram is skewed’ Thus, the above histogram is skewed.
Chapter 12 Data Analysis and Probability Exercise 12 10CT
Let us consider, out of 10 dogs. 4 weight no more than 125 kg Let us rind what the percentile rank of weight I 25 kg
Chapter 12 Data Analysis and Probability Exercise 12 10MC
Consider the statement given in the question:
First consider the pair of equations given in the question.
2x+5y = -11
10x+3y =11
Solve the given equations by the substitution method to get the correct ordered pair.
Chapter 12 Data Analysis and Probability Exercise 12 11CR
From the above histogram we see that if we draw vertical line in the middle of the histogram. then the line divide the histogram into two parts that are close to mirror images Therefore by the definition of symmetric histogram. “if a vertical line can divide the histogram into two parts that are close to mirror images. then the histogram is symmetric” Thus, the above histogram is symmetric.
Chapter 12 Data Analysis and Probability Exercise 12 11CT
The teacher randomly selected one student from each table and asked the question The objective is to check whether this survey gives a good sample or not Note that, in the stratified sampling method, the population is separated into smaller groups and surveyed at random within each group The entire population of students is divided into smaller groups of tables and teacher asked one student from each table for his or her opinion of school food So, the sampling is a stratified sampling method to know the opinion of the student. Hence, the survey gives a good sample.
Chapter 12 Data Analysis and Probability Exercise 12 11MC
Chapter 12 Data Analysis and Probability Exercise 12 12CR
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Chapter 12 Data Analysis and Probability Exercise 12 12MC
Consider the statement given in the question:
For the given graph the line is given to be a dotted so, it will not be included as the solution That is only the shaded portion can be included as the solution
Now. putting the different values of x:
First put x=1,
y>2×1 >2
Which is true, similarly for the other values of x. y> 2x. satisfies the equationS
Hence, option H is correct.
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Chapter 12 Data Analysis and Probability Exercise 12 13MC
Chapter 12 Data Analysis and Probability Exercise 12 14CR
Let us consider, the weights of the cats are:
13.4 lb. 131 lb, 10.4 lb, 6.8 lb. 11.4 lb. 10.8 lb. 13.4 lb. 1t3 lb. 9.3 lb …… (1) To find the mean. median. mode, and range. Also which measure of central tendency best describes the data set?
Chapter 12 Data Analysis and Probability Exercise 12 14CT
Chapter 12 Data Analysis and Probability Exercise 12 14MC
Consider the statement given in the question:
The minimum point of the parabola is said to be the point where the curve is at the lowest point
For the given parabola. (—2,2) and (0.2) are not having the least value Clearly, the point (2.—2)is having the least value for the given paraboIa Hence, the correct option is G.
Chapter 12 Data Analysis and Probability Exercise 12 15CR
Let us consider the basketball player scores 22. 19. 25, and 17 points in tour games How many points does basketball player need to score in the fifth game so that the average become 22 points per game The average is 22 the data set and its mean;
Let us find the score of fifth game& So, that the average becomes 22 points per game.
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Chapter 12 Data Analysis and Probability Exercise 12 17MC
First define the Vertex of the parabola: The point of intersection of parabola and its axis is called the vertex of the parabola. The graph of the parabola shows that, it intersects the axis at the point (3, 2). Therefore, the coordinate of the vertex is (3. 2) Thus, the option C is the correct option.
Chapter 12 Data Analysis and Probability Exercise 12 18CR
Chapter 12 Data Analysis and Probability Exercise 12 18CT
Chapter 12 Data Analysis and Probability Exercise 12 18MC
Consider the statement given in the question:
The given coordinate is (—3. —2) and the slope is m = 2
Also, the normal form of equation is:
y = mx + c
Substitute the value of coordinate and the slope in the general form of equation:
—2=2(—3) + c
Further solving:
—2 = – 6 + c
c= -2+6
=4
In the given option only the equation y = 2x + 4 is satisfying the condition Hence, the option I is correct.
Chapter 12 Data Analysis and Probability Exercise 12 19CR
Interquartile range: The interquartile range is defined as the length of the box or difference
between third and first quartiles The graph of the box-and-whisker plot shows that, the length of box in B box-and-whisker plot is more widely than the length of the box of A. Therefore, the interquartile range of the box-and-whisker plot of B is greater than the interquartile range of the box-and-whisker plot of A.
Chapter 12 Data Analysis and Probability Exercise 12 19CT
Chapter 12 Data Analysis and Probability Exercise 12 19MC
Chapter 12 Data Analysis and Probability Exercise 12 20CR
Consider an interviewer ask every third person in line outside a movie theatre whether he or she will see more of fewer movie in the coming year The objective is to determine the sampling method and then write the unbiased survey question Systematic Sampling method: In this method select any number k at random, and then survey every k th person in the sample
Put the value 3 for k, then survey on every third is systematic Thus the sampling method is systematic The word more or fewer influence the result of the survey, so the result of the survey question is biased Also, the survey question contains assumption that is it conducted at every third person of the outside of the movie theater, therefore it gives bias sample The unbiased survey question is, an interviewer ask to randomly select some person outside the theater “whether he or she will watch the movies in coming year”.
This survey question is not bias, the result of this survey question gives an unbiased sample
Chapter 12 Data Analysis and Probability Exercise 12 20CT
Interquartile Range is defined as the length of the box or difference between third and first quartiles of a set of data To calculate the interquartile range. use the following steps:
Calculate First Quartile: If the data set is divided into four equal parts. then the first quartile is the median of the lower half of the data and it is represented by Q1
Calculate Third Quartile: If the data set is divided into four equal parts. then the third quartile is the median of the upper half of the data and it is represented by Q3
Find the difference of third quartile and first quartile. which is the interquartile range
Interquartile range = Q, — Q1
The interquartile range represents the middle of the data set: therefore it is not affected by minimum, maximum, and any outlier in the data set Thus. interquartile range is useful to represent the middle of the data set.
Chapter 12 Data Analysis and Probability Exercise 12 20MC
Clearly, the line symmetry is the imaginary line where you could fold the image and have both halves match exactly
Thus, from the above graph it is clear that the line of symmetry is x = —1
Hence, the correct option is F
Chapter 12 Data Analysis and Probability Exercise 12 21CR
Consider the situation, ten randomly selected students in each class are asked that whom they will support for the student council president The objective is to determine the sampling method and then write the unbiased survey question.
Stratified sampling method: In this method, population is divided into the number of groups. and then random samples are taken from each groups and survey Here the ten students are randomly selected from each class, so by the definition stratified sampling, the sampling method is stratified The result of the stratified sampling method gives the unbiased sample since the sample is randomly chosen The un biased question is. “who do you support for the student council president ?
Chapter 12 Data Analysis and Probability Exercise 12 21CT
The univariate data is defined follows as:
Univariate data set: A set of data that uses only one variable to represent the set of data is called univariate data set.
For example: The weight of students in the class. Here there is only one variable that is student weight. Therefore the data set is defined by the weight of the student in the particular class is univariate.
Bivariate data set: A set of data that uses two variables to represent the set of data is called bivariate data set
For example The length and height of the class rooms in a school. Here there are two variables, first the length of the class rooms and the second is the height of
the class rooms. Therefore the data set is defined by the length and height of the class rooms in a school is bivariate. The univariate data is differ with bivariate. because the univariate data is represented in one dimension, but the bivariate data set is represented into two dimensions. Therefore, univariate and bivariate data are differing in dimension.
Chapter 12 Data Analysis and Probability Exercise 12 21MC
Chapter 12 Data Analysis and Probability Exercise 12 22CR
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Chapter 12 Data Analysis and Probability Exercise 12 25MC
Chapter 12 Data Analysis and Probability Exercise 12 26CR
Chapter 12 Data Analysis and Probability Exercise 12 26MC
Consider the statement given in the question:
Mean is defined as the sum of observations to the number of observations of any given data
Chapter 12 Data Analysis and Probability Exercise 12 27CR
Chapter 12 Data Analysis and Probability Exercise 12 27MC
Chapter 12 Data Analysis and Probability Exercise 12 28CR
Consider the statement given in the question:
The value of the modulus has one positive and one negative value Then solve it for each value to obtain the required result
Chapter 12 Data Analysis and Probability Exercise 12 28MC
Chapter 12 Data Analysis and Probability Exercise 12 29CR
Chapter 12 Data Analysis and Probability Exercise 12 29MC
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Chapter 12 Data Analysis and Probability Exercise 12 32CR
Chapter 12 Data Analysis and Probability Exercise 12 32MC
Consider the statement given in the question:
Reasonable trend line is that line which will accommodate maximum number of points of the given expression
Chapter 12 Data Analysis and Probability Exercise 12 33CR
Chapter 12 Data Analysis and Probability Exercise 12 33MC
Chapter 12 Data Analysis and Probability Exercise 12 34CR
Suppose there are five dishes: Mashed potatoes. Cole slaw, French fries. Applesauce. or Rica Find the number of different combination of dish, if choose any two dishes out of five dished In the given selection, it is mention that can choose any two dishes at a time, so the order of selection does not mailer Therefore, use the definition of combination to find the number of different combination of dishes
Chapter 12 Data Analysis and Probability Exercise 12 34MC
Consider the statement given in the question:
A function is said to be a function if every function in the domain is having only one and unique image in the range
Clearly, in option F. H and I the domain is having unique image in the range Hence, these are not the correct options Thus, the option is G correct.
Chapter 12 Data Analysis and Probability Exercise 12 35CR
Suppose there are 8 groups are participating in a talent show. Let us determine how many different orders they can be groups. so that they can perfume in talent show. Since there are 8 groups in the talent show So. there are 8 choices for the first group to performed on show. 7 choices for the second group to performed on show. 6 choice for the third group to performed on show, 5 choice for the fourth group to performed on show. 4 choice for the fifth group to performed on show, 3 choices for the sixth group to performed on show, 2 choices for the seventh s group to performed on show, and 1 choices for the eighth group to performed on show Use the multiplication principle: Multiply the number of ways to make the total number of different possible orders:
8•76•5•4•32•I = 40,320
Therefore, the total number of different possible orders so that each group is performed on talent show is 40,320
Chapter 12 Data Analysis and Probability Exercise 12 35MC
Chapter 12 Data Analysis and Probability Exercise 12 36CR
Consider 6 shirts. 7 pairs of pants. and 3 pairs of shoes Use the multiplication rule: If m. n and p are three positive integers, and there are m ways to make first selection, n ways to make second selection, and p way to make third selection, then there are m.n.p ways to make the number different selections Therefore, substitute the value 6 for m, 4 for n, and 3 for p. then obtained the total number of outfits you can make from 6 shirt. 7 pairs of pants. and 3 pairs of shoes
6.4.3 = 72
Thus, there are 72 outfit can make with shirt, 7 pairs of pants. and 3 pairs of shoes
Chapter 12 Data Analysis and Probability Exercise 12 36MC
Consider the statement given in the question:
Uniform histogram means the data having the upper and lower class of the other interval equaL Now, symmetric means the cutting the graph into two similar curves And skew symmetric means either having a positive tail or a negative tail
First draw a frequency polygon for the given histogram. Now, it can be noticed that there tail towards the negative side of x-aXiS
Hence, the given histogram is skewed Therefore, the correct option is F.
Chapter 12 Data Analysis and Probability Exercise 12 37CR
Chapter 12 Data Analysis and Probability Exercise 12 37MC
Chapter 12 Data Analysis and Probability Exercise 12 38CR
Chapter 12 Data Analysis and Probability Exercise 12 38MC
Consider the statement given in the question:
First make the like terms together and then solve it for getting the required soIution
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Chapter 12 Data Analysis and Probability Exercise 12 46SR
Consider the survey question: “Do you prefer delicious steak or ordinary meatloaf for dinner’ is biased. The survey question is biased
Explanation:
The survey question contains the word delicious and ordinary, which reflect the answer of the question.
By the definition of bias question. a question is said to be bias if it contain the assumption which may or may not be true and that reflect the opinion of the answerer Therefore, by the definition of the bias questions, the question “Do you prefer delicious steak or ordinary meatloaf for dinner” is biased
Chapter 12 Data Analysis and Probability Exercise 12 47CR
Chapter 12 Data Analysis and Probability Exercise 12 47SR
Chapter 12 Data Analysis and Probability Exercise 12 48CR
Chapter 12 Data Analysis and Probability Exercise 12 48SR
Chapter 12 Data Analysis and Probability Exercise 12 49CR
Consider the following data:
- A spinner contains 5 equal sections.
- A bag contains 2 green marbles and 4 blue marbles.
First event: Spin the spinner with 5 equal sections. Second event: Pick a marble from the bag. Objective is to determine whether the two events are dependent or independent. Dependent events. Two events are said to be dependent if the occurrence of first event affect the probability of second events.
Independent events: if the occurrence of first event does not affect the probability of second events, then both events are independent events. It can be observed that, every time when the spinner is spin which contain five equal sections. the spinner shows only one section at a time. So. the occurrence of first event does not affect the probability of second event. The occurrence of first event does not affect the probability of the second event. Therefore, spin a spinner contain 5 equal section and pick a marble from bag containing 2 green marbles and 4 blue marbles are independent events
Chapter 12 Data Analysis and Probability Exercise 12 49ER
A box-and-whisker plot, represent a set of data graphically It consist two whiskers and one box The box contain 50% of the data and the first whisker represent the 25% of the data from the data set, similarly the second whisker represent the 25% of the data from the data set The box is divide by a line, this line represent the median of the data set
Here, the median tell the Team A obtained 40 points per game, while the Team B obtained 35 points per game.
Chapter 12 Data Analysis and Probability Exercise 12 50ER
Consider Natalia spent $153. of her saving at the mall, and she brought clothes, a few paperback novels, and an $18DVD. Consider she spent 4 times as much on clothes as on the paperbacks:
