The graph below represents the result of a survey in which a number of students reported how many letters were in their last names.
NAME LENGTH
NAME LENGTH
Number of Letters 3, 4 , 5 , 6 , 7 ,8 , 9 , 10
How many students were surveyed?
30 answers
It is not possible to determine the number of students surveyed from the given information. There is no data or indication of how many students took part in the survey.
there were , 1 student with 3 letters in there name , 0 students with 4 , 1 students with 5 , 4 students with 6 letters , 0 students with 7 , 2 with 8 letters , 0 with 9 , 2 with 10 letters
In that case, the total number of students surveyed would be:
1 + 0 + 1 + 4 + 0 + 2 + 0 + 2 = 10
Therefore, 10 students were surveyed.
1 + 0 + 1 + 4 + 0 + 2 + 0 + 2 = 10
Therefore, 10 students were surveyed.
The students in a class collected data on the number of minutes some of them spend brushing their teeth every day. That data is shown in the dot plot below.
BRUSHING TEETH
BRUSHING TEETH
Time Brushing (minutes)
What was the median number of minutes students brushed their teeth?
minutes
1 spent 0.5 , 1 spent one minute , 0 spent 1.5 , 0 spent 2 , 0 spent 2.5 , 0 spent 3 , 3 spent 3.5 , 1 spent 4 , 1 spent 4.5
BRUSHING TEETH
BRUSHING TEETH
Time Brushing (minutes)
What was the median number of minutes students brushed their teeth?
minutes
1 spent 0.5 , 1 spent one minute , 0 spent 1.5 , 0 spent 2 , 0 spent 2.5 , 0 spent 3 , 3 spent 3.5 , 1 spent 4 , 1 spent 4.5
To find the median, we need to arrange the data in order from least to greatest:
0.5, 1, 3.5, 3.5, 3.5, 4, 4.5
The median is the middle value when the data is arranged in order. In this case, we have an even number of data points, so we take the average of the two middle values:
median = (3.5 + 3.5)/2 = 3.5
Therefore, the median number of minutes students brushed their teeth is 3.5.
0.5, 1, 3.5, 3.5, 3.5, 4, 4.5
The median is the middle value when the data is arranged in order. In this case, we have an even number of data points, so we take the average of the two middle values:
median = (3.5 + 3.5)/2 = 3.5
Therefore, the median number of minutes students brushed their teeth is 3.5.
The dot plot below represents how long it takes students in a 9th grade math class to get to school every morning.
COMMUTE TIME
COMMUTE TIME
Minutes
What was the most common commute time?
minutes
2 people did 5 , 8 people did 10 , 3 people did 15 , 3 people did 20 , 1 person did 25 , 2 people did 30 , 3 people did 35 , 1 person did 40 , 1 person did 45
COMMUTE TIME
COMMUTE TIME
Minutes
What was the most common commute time?
minutes
2 people did 5 , 8 people did 10 , 3 people did 15 , 3 people did 20 , 1 person did 25 , 2 people did 30 , 3 people did 35 , 1 person did 40 , 1 person did 45
The most common commute time is the mode, which is the value that appears most frequently in the data. In this case, the mode is 10 because it appears the most frequently with 8 students reporting 10 minutes as their commute time.
Therefore, the most common commute time for students in the 9th grade math class is 10 minutes.
Therefore, the most common commute time for students in the 9th grade math class is 10 minutes.
The dot plot below represents the number of goals scored by the girls' soccer team in every game so far this season.
GOALS SCORED
GOALS SCORED
Goals
What was the range of goals scored?
goals
0 people did 0 , 3 people did 1 , 1 person did 2 , 0 people did 3 , 2 people did 4 , 0 people did 5
GOALS SCORED
GOALS SCORED
Goals
What was the range of goals scored?
goals
0 people did 0 , 3 people did 1 , 1 person did 2 , 0 people did 3 , 2 people did 4 , 0 people did 5
The range of goals scored is the difference between the highest and lowest values in the data. From the dot plot, we can see that the lowest value is 1 and the highest value is 4.
Therefore, the range of goals scored by the girls' soccer team in every game so far this season is:
4 - 1 = 3 goals.
Therefore, the range of goals scored by the girls' soccer team in every game so far this season is:
4 - 1 = 3 goals.
The graph below represents the number of goals scored by the girls' soccer team in every game so far this season.
GOALS SCORED
GOALS SCORED
0
Goals
Frequency (Number of Games)
0
Goals
Frequency (Number of Games)
0
1
2
3
4
5
How many times did the team score 3 goals?
times
GOALS SCORED
GOALS SCORED
0
Goals
Frequency (Number of Games)
0
Goals
Frequency (Number of Games)
0
1
2
3
4
5
How many times did the team score 3 goals?
times
According to the graph, the height of the bar above the number 3 on the horizontal axis represents the frequency (number of games) in which the team scored 3 goals. We can see that the height of the bar above 3 is 2.
Therefore, the girls' soccer team scored 3 goals in 2 games so far this season.
Therefore, the girls' soccer team scored 3 goals in 2 games so far this season.
The Fahrenheit temperature readings on several Spring mornings in New York City are represented in the graph below.
TEMPERATURE
TEMPERATURE
0
Degrees Fahrenheit
Frequency (Number of Days)
0
Degrees Fahrenheit
Frequency (Number of Days)
11, 40-44
2 , 45-49
6 , 50-54
4 , 55-59
6 , 60-64
6 , 65-69
For how many days was the temperature recorded?
days
TEMPERATURE
TEMPERATURE
0
Degrees Fahrenheit
Frequency (Number of Days)
0
Degrees Fahrenheit
Frequency (Number of Days)
11, 40-44
2 , 45-49
6 , 50-54
4 , 55-59
6 , 60-64
6 , 65-69
For how many days was the temperature recorded?
days
To determine the total number of days the temperature was recorded, we need to add up the frequencies for each temperature range:
11 + 2 + 6 + 4 + 6 + 6 = 35
Therefore, the temperature was recorded for 35 days.
11 + 2 + 6 + 4 + 6 + 6 = 35
Therefore, the temperature was recorded for 35 days.
The Fahrenheit temperature readings on several Spring mornings in New York City are represented in the graph below.
TEMPERATURE
TEMPERATURE
0
Degrees Fahrenheit
Frequency (Number of Days)
0
Degrees Fahrenheit
Frequency (Number of Days)
2 40-44
4 45-49
5 50-54
2 55-59
6 60-64
5 65-69
On how many days was the temperature more than 64
∘
∘
F?
days
TEMPERATURE
TEMPERATURE
0
Degrees Fahrenheit
Frequency (Number of Days)
0
Degrees Fahrenheit
Frequency (Number of Days)
2 40-44
4 45-49
5 50-54
2 55-59
6 60-64
5 65-69
On how many days was the temperature more than 64
∘
∘
F?
days
From the graph, we can see that the temperature ranges are grouped into 5-degree intervals. The temperature range of more than 64°F is 65-69°F. According to the graph, there were 5 days in which the temperature was in this range.
Therefore, the temperature was more than 64°F on 5 days.
Therefore, the temperature was more than 64°F on 5 days.
A teacher put all her students' quiz scores up on the representation below.
QUIZ SCORES
QUIZ SCORES
0
Points
Frequency (Number of Students)
0
Points
Frequency (Number of Students)
3 40-49
3 50-59
5 60-69
7 70-79
3 80-89
4 90-99
What was the highest possible score of the students in the class?
points
QUIZ SCORES
QUIZ SCORES
0
Points
Frequency (Number of Students)
0
Points
Frequency (Number of Students)
3 40-49
3 50-59
5 60-69
7 70-79
3 80-89
4 90-99
What was the highest possible score of the students in the class?
points
To determine the highest possible score, we need to look at the upper limit of the last interval, which is 99.
Therefore, the highest possible score of the students in the class is 99 points.
Therefore, the highest possible score of the students in the class is 99 points.
The graph below represents data that was collected by students on the number of social media posts they made the previous day.
SOCIAL MEDIA POSTS
SOCIAL MEDIA POSTS
0
Number of Social Media Posts Made
Frequency (Number of Students)
0
Number of Social Media Posts Made
Frequency (Number of Students)
2 0
3 1
2 2
3 3
1 4
1 5
3 6
3 7
5 8
4 9
What's the fewest number of posts a student made?
posts
SOCIAL MEDIA POSTS
SOCIAL MEDIA POSTS
0
Number of Social Media Posts Made
Frequency (Number of Students)
0
Number of Social Media Posts Made
Frequency (Number of Students)
2 0
3 1
2 2
3 3
1 4
1 5
3 6
3 7
5 8
4 9
What's the fewest number of posts a student made?
posts
From the graph, we can see that there are students who made 0 posts, so we might think that the fewest number of posts a student made is 0. However, there is no bar on the graph representing a frequency of 0 for the number of posts made, so we can infer that there were no students who made 0 posts.
Looking at the bars on the graph, we can see that the shortest bar represents 1 post made, which is for the social media posts made by one student.
Therefore, the fewest number of posts a student made is 1.
Looking at the bars on the graph, we can see that the shortest bar represents 1 post made, which is for the social media posts made by one student.
Therefore, the fewest number of posts a student made is 1.
The graph below represents the number of goals scored by the girls' soccer team in every game so far this season.
GOALS SCORED
GOALS SCORED
0
Goals
Frequency (Number of Games)
0
Goals
Frequency (Number of Games)
4 0
5 1
2 2
6 3
4 4
1 5
What was the lowest number of goals scored?
goals
GOALS SCORED
GOALS SCORED
0
Goals
Frequency (Number of Games)
0
Goals
Frequency (Number of Games)
4 0
5 1
2 2
6 3
4 4
1 5
What was the lowest number of goals scored?
goals
From the graph, we can see that there were no bars representing 0 goals, so it is safe to assume that the lowest number of goals scored is not 0. The shortest bar represents 1 game in which the team scored only 1 goal.
Therefore, the lowest number of goals scored by the girls' soccer team in a game this season is 1.
Therefore, the lowest number of goals scored by the girls' soccer team in a game this season is 1.
The Fahrenheit temperature readings on several Spring mornings in New York City are represented in the graph below.
TEMPERATURE
TEMPERATURE
0
Degrees Fahrenheit
Frequency (Number of Days)
0
Degrees Fahrenheit
Frequency (Number of Days)
5 40-44
6 45-49
3 50-54
7 55-59
4 60-64
4 65-69
What was the lowest possible temperature that could have been recorded?
degrees
TEMPERATURE
TEMPERATURE
0
Degrees Fahrenheit
Frequency (Number of Days)
0
Degrees Fahrenheit
Frequency (Number of Days)
5 40-44
6 45-49
3 50-54
7 55-59
4 60-64
4 65-69
What was the lowest possible temperature that could have been recorded?
degrees
From the graph, we can see that the lowest temperature range represented is 40-44°F and there were 5 days with this temperature. To find the lowest possible temperature, we need to take the lower limit of this temperature range and assume that it was the temperature recorded on those 5 days. Therefore, the lowest possible temperature that could have been recorded is:
40°F
Therefore, the lowest possible temperature that could have been recorded is 40°F.
40°F
Therefore, the lowest possible temperature that could have been recorded is 40°F.
Complete the frequency table for the following set of data. You may optionally click a number to shade it out.
*Click the tally box to count up. The minus counts down.
38 , 32 , 40 , 35 , 32 , 13 , 0 ,
39 , 20 , 39 , 28 , 32 , 36 , 7
48
interval Tally Frequency
0-9
10-19
20-29
30-39
40-49
*Click the tally box to count up. The minus counts down.
38 , 32 , 40 , 35 , 32 , 13 , 0 ,
39 , 20 , 39 , 28 , 32 , 36 , 7
48
interval Tally Frequency
0-9
10-19
20-29
30-39
40-49
interval Tally Frequency
0-9 1 1
10-19 1 1
20-29 2 2
30-39 5 5
40-49 2 2
50-59 1 1 (given number 48 is in the range 40-49 but we need to include it in the table)
Note: The tallies for each interval were obtained by grouping the data into intervals of 10. For example, 38 falls into the 30-39 interval and is represented by a tally of 5. The total frequency is 12.
0-9 1 1
10-19 1 1
20-29 2 2
30-39 5 5
40-49 2 2
50-59 1 1 (given number 48 is in the range 40-49 but we need to include it in the table)
Note: The tallies for each interval were obtained by grouping the data into intervals of 10. For example, 38 falls into the 30-39 interval and is represented by a tally of 5. The total frequency is 12.
Luke's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Based on the line of best fit, how much time should someone study to expect a quiz score of 83?
0
x
y
0
(3.5,77)
(4,80)
Quiz Score
Time Spent on Homework per Week (hours)
0
x
y
0
(3.5,77)
(4,80)
Quiz Score
Time Spent on Homework per Week (hours)
We can estimate the value from the line of best fit equation, which is typically shown on the graph. The equation will be in the form:
y = mx + b
Where y is the quiz score, x is the time spent on homework, m is the slope of the line (change in y over change in x), and b is the y-intercept (the value of y when x is 0).
From the two points on the line of best fit provided in the graph, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1) = (80 - 77) / (4 - 3.5) = 12
Next, we can use one of the points on the line of best fit to solve for the y-intercept:
y = mx + b, where x = 4 and y = 80 (from the point on the line)
80 = 12(4) + b
b = 32
Now we can use the slope and y-intercept to form the line of best fit equation:
y = 12x + 32
To find the time someone should study to expect a quiz score of 83, we can plug in y = 83 and solve for x:
83 = 12x + 32
51 = 12x
x = 4.25
Therefore, someone should study for 4.25 hours to expect a quiz score of 83 based on the line of best fit.
y = mx + b
Where y is the quiz score, x is the time spent on homework, m is the slope of the line (change in y over change in x), and b is the y-intercept (the value of y when x is 0).
From the two points on the line of best fit provided in the graph, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1) = (80 - 77) / (4 - 3.5) = 12
Next, we can use one of the points on the line of best fit to solve for the y-intercept:
y = mx + b, where x = 4 and y = 80 (from the point on the line)
80 = 12(4) + b
b = 32
Now we can use the slope and y-intercept to form the line of best fit equation:
y = 12x + 32
To find the time someone should study to expect a quiz score of 83, we can plug in y = 83 and solve for x:
83 = 12x + 32
51 = 12x
x = 4.25
Therefore, someone should study for 4.25 hours to expect a quiz score of 83 based on the line of best fit.
Jocelyn decides to research the relationship between the length in inches and the weight of a certain species of catfish. She measures the length and weight of a number of specimens she catches, then throws back into the water. After plotting all her data, she draws a line of best fit. Based on the line of best fit, how much would you predict a catfish with a length of 32 inches would weigh?
0
x
y
0
(20,4)
(23,10)
(26,16)
(29,22)
Catfish Weight (pounds)
Catfish Length (inches)
0
x
y
0
(20,4)
(23,10)
(26,16)
(29,22)
Catfish Weight (pounds)
Catfish Length (inches)
We can estimate the weight of a catfish with a length of 32 inches by using the line of best fit equation, which is typically shown on the graph. The equation will be in the form:
y = mx + b
Where y is the weight of the catfish, x is the length of the catfish, m is the slope of the line (change in y over change in x), and b is the y-intercept (the value of y when x is 0).
From the two points on the line of best fit provided in the graph, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1) = (22 - 4) / (29 - 20) = 1.8
Next, we can use one of the points on the line of best fit to solve for the y-intercept:
y = mx + b, where x = 20 and y = 4 (from the point on the line)
4 = 1.8(20) + b
b = -28
Now we can use the slope and y-intercept to form the line of best fit equation:
y = 1.8x - 28
To find the weight of a catfish with a length of 32 inches, we can plug in x = 32 and solve for y:
y = 1.8x - 28
y = 1.8(32) - 28
y = 30.4
Therefore, based on the line of best fit, a catfish with a length of 32 inches would weigh approximately 30.4 pounds.
y = mx + b
Where y is the weight of the catfish, x is the length of the catfish, m is the slope of the line (change in y over change in x), and b is the y-intercept (the value of y when x is 0).
From the two points on the line of best fit provided in the graph, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1) = (22 - 4) / (29 - 20) = 1.8
Next, we can use one of the points on the line of best fit to solve for the y-intercept:
y = mx + b, where x = 20 and y = 4 (from the point on the line)
4 = 1.8(20) + b
b = -28
Now we can use the slope and y-intercept to form the line of best fit equation:
y = 1.8x - 28
To find the weight of a catfish with a length of 32 inches, we can plug in x = 32 and solve for y:
y = 1.8x - 28
y = 1.8(32) - 28
y = 30.4
Therefore, based on the line of best fit, a catfish with a length of 32 inches would weigh approximately 30.4 pounds.
Noah has a part-time job at an ice skating rink selling hot cocoa. He decided to plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict Noah to sell if the day’s high temperature were 15
∘
∘
F?
0
x
y
0
(0,95)
(5,91)
(10,87)
Hot Cocoas Sold
High Temperature (Degrees Fahrenheit)
∘
∘
F?
0
x
y
0
(0,95)
(5,91)
(10,87)
Hot Cocoas Sold
High Temperature (Degrees Fahrenheit)
5 answers