Maths-
General
Easy
Question
Paulina has 28 books in her collection. The frequency table summarizes the number of pages in each book. If she buys a new book that has 62 pages, how will this impact the mean and median numbers of pages of the books in her collection?
- The mean and median will both increase.
- The mean and median will both decrease.
- The mean will increase, and the median will remain the same.
- The mean will decrease, and the median will remain the same.
The correct answer is: The mean will increase, and the median will remain the same.
We calculate the mean and the median for the data. We use cumulative frequency to calculate the median.
Explanations:
Step 1 of 3:
Consider the following table—
Step 2 of 3:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The mean number of pages was— 
After buying a book of 62 pages, the mean becomes— 
So, the mean increases.
Step 3 of 3:
The median is the middle value when a data set is ordered from least to greatest.
Before buying there were 28 books. So, after rearranging the books by number of pages in an ascending order, the mean number of pages of 
and 
book would be the median. From the cumulative frequency column, observe that the number of pages in 14th and 15th books were 50 and 50, respectively.
Hence, the median number of pages was— 
After buying the 29th book of 62 pages, the median number of pages would be the page number of 
book. So, the median number of pages is— 50. Therefore, the median remains the same.
Final Answer:
The right choice is— The mean will increase, and the median will remain the same.
Related Questions to study
Maths-
The solution to which system of inequalities is represented by the shaded region of the graph?
The solution to which system of inequalities is represented by the shaded region of the graph?
Maths-General
Maths-
Which of the following additional measurements to the triangle provides enough information to determine the length of 
?
I. The length of 
II. The measure of 
Which of the following additional measurements to the triangle provides enough information to determine the length of ?
I. The length of
II. The measure of
Maths-General
Maths-
Line 
is defined by 
. Line 
is parallel to line m in the xy - plane and passes through the point (4, - 3). Which equation defines line p ?
Line is defined by . Line is parallel to line m in the xy - plane and passes through the point (4, - 3). Which equation defines line p ?
Maths-General
Maths-
An analyst estimates that the cost of each of the paperback books will increase $0.50 each year after 2016. Which of the following models the cost 
, in dollars, of each of the paperback books t years after 2016 ?
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
An analyst estimates that the cost of each of the paperback books will increase $0.50 each year after 2016. Which of the following models the cost , in dollars, of each of the paperback books t years after 2016 ?
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
Maths-General
Maths-
In 2016 the total cost for 200 of the books that were sold was between $2,200 and $2,400. Which of the following could be the number of hardcover books that were sold?
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
In 2016 the total cost for 200 of the books that were sold was between $2,200 and $2,400. Which of the following could be the number of hardcover books that were sold?
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
Maths-General
Maths-
The table gives some values of possible lengths x, in miles, of a monorail system, and their corresponding costs to build f(x), in millions of dollars. Which of the following equations models this relationship?
The table gives some values of possible lengths x, in miles, of a monorail system, and their corresponding costs to build f(x), in millions of dollars. Which of the following equations models this relationship?
Maths-General
Maths-
In the given equation, is a constant. If the equation has exactly one solution, what is the value of c ?
In the given equation, is a constant. If the equation has exactly one solution, what is the value of c ?
Maths-General
Maths-
The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans. Let d represent the number of Democrats who vote yes for a bill, and let r represent the number of Republicans who vote yes for a bill. For a bill to pass, more than half of the 30 senators must vote yes. Which of the following inequalities represents all possible values of d and r for a bill to pass?
The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans. Let d represent the number of Democrats who vote yes for a bill, and let r represent the number of Republicans who vote yes for a bill. For a bill to pass, more than half of the 30 senators must vote yes. Which of the following inequalities represents all possible values of d and r for a bill to pass?
Maths-General
Maths-
For the linear function f, the graph of y = f(x) in the xy -plane passes through the points (0, 2) and (2, 6). Which equation defines f ?
For the linear function f, the graph of y = f(x) in the xy -plane passes through the points (0, 2) and (2, 6). Which equation defines f ?
Maths-General
Maths-
In triangle ABC, the measure of angle C is 
. If 
, what is 
?
In triangle ABC, the measure of angle C is . If , what is ?
Maths-General
Maths-
2a + b = 17
a + 2b = 19
The solution to the given system of equations is (a, b). What is the value of 3a + 3b ?
2a + b = 17
a + 2b = 19
The solution to the given system of equations is (a, b). What is the value of 3a + 3b ?
Maths-General
Maths-
The daily high temperatures, in degrees Fahrenheit, for a city in the month of February in 2017 are summarized in the box plot shown. Which of the following is closest to the median of the high temperatures, in degrees Fahrenheit, of the city in February 2017?
The daily high temperatures, in degrees Fahrenheit, for a city in the month of February in 2017 are summarized in the box plot shown. Which of the following is closest to the median of the high temperatures, in degrees Fahrenheit, of the city in February 2017?
Maths-General
Maths-
After a new car is purchased, the value of the car is modeled by a function that decreases exponentially over time. Which of the following could describe how the value of the car changes each year?
After a new car is purchased, the value of the car is modeled by a function that decreases exponentially over time. Which of the following could describe how the value of the car changes each year?
Maths-General
Maths-
The relative yield of corn, expressed as a percent, and soil pH were recorded for 5 samples. For the 5 samples, the relative yield of corn reached a maximum when the soil had a 
of 
, and then decreased as the soil pH increased. Which scatterplot could represent these data?
The relative yield of corn, expressed as a percent, and soil pH were recorded for 5 samples. For the 5 samples, the relative yield of corn reached a maximum when the soil had a of , and then decreased as the soil pH increased. Which scatterplot could represent these data?
Maths-General
Maths-
The table shows the maximum depth, in meters, of the 5 deepest oceanic trenches.
What is the range, in meters, of these 5 trench depths?
The table shows the maximum depth, in meters, of the 5 deepest oceanic trenches.
What is the range, in meters, of these 5 trench depths?
Maths-General
