# Digital SAT Math Practice Questions – Advanced : One-variable data: distributions and measures of centre and spread

## SAT MAth Practice questions – all topics

• Problem-solving and Data Analysis Weightage: 15%  Questions: 5-7
• Ratios, rates, proportional relationships, and units
• Percentages
• One-variable data: distributions and measures of centre and spread
• Two-variable data: models and scatterplots
• Probability and conditional probability
• Inference from sample statistics and margin of error
• Evaluating statistical claims: observational studies and Experiments

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question  Hard

Each of the frequency tables represents a data set.

Which statement best compares the medians of the two data sets?

A. The median of data set 2 is greater than the median of data set 1.
B. The median of data set 1 is greater than the median of data set 2.
C. The medians are the same.
D. There is not enough information to compare the medians.

Ans: B

To compare the medians of the two data sets, we first need to find the median of each data set.

Data Set 1

Values and frequencies:

• 3 (1 time)
• 4 (0 times)
• 5 (2 times)
• 6 (4 times)
• 7 (2 times)

First, we list all the values in order:
$3, 5, 5, 6, 6, 6, 6, 7, 7$

There are 9 values in total. The median is the middle value, which is the 5th value in this ordered list:
$\text{Median of Data Set 1} = 6$

Data Set 2

Values and frequencies:

• 3 (2 times)
• 4 (3 times)
• 5 (2 times)
• 6 (1 time)
• 7 (1 time)

First, we list all the values in order:

$3, 3, 4, 4, 4, 5, 5, 6, 7$

There are 9 values in total. The median is the middle value, which is the 5th value in this ordered list:
$\text{Median of Data Set 2} = 4$

Comparison

The median of Data Set 1 is 6, and the median of Data Set 2 is 4.

Therefore, the statement that best compares the medians of the two data sets is:

$\boxed{\text{B) The median of data set 1 is greater than the median of data set 2.}}$

[Calc]  Question  Hard

The histograms shown summarize two data sets, P and Q. Which of the following statements best compares the ranges and standard deviations of the two data sets?

A) Data set P has a greater range and a greater standard deviation than data set Q

B) Data set Q has a greater range and a greater standard deviation than data set P

C) Data set P has a greater range but a smaller standard deviation than data set Q

D) Data set Q has a greater range but a smaller standard deviation than data set P

A) Data set P has a greater range and a greater standard deviation than data set Q

To compare the ranges and standard deviations of the two data sets P and Q based on the given histograms, I will make the following observations:

Range: The range of a data set is the difference between the maximum and minimum values. For data set P, the values range from around 0 to a little over 30. For data set Q, the values range from around 5 to around 30. Therefore, data set P has a greater range than data set Q.

Standard deviation: The standard deviation measures the spread or dispersion of the data values around the mean. A higher standard deviation indicates the values are more spread out from the mean. In the histograms, a higher and wider distribution suggests a greater standard deviation. The histogram for data set P has a wider spread compared to data set Q. Therefore, data set P likely has a greater standard deviation than data set Q.

Based on these observations, the statement that best compares the ranges and standard deviations is:A

[Calc]  Question  Hard

Which of the following statements best compares the mean and the median of the data shown in the frequency table ?
A) The median is 5 greater than the mean.
B) The median is 3.5 greater than the mean.
C) The median is equal to the mean.
D) The median is LS less than the mean.

B) The median is 3.5 greater than the mean.

To find the mean and median of the data:

$\text{Mean} = \frac{\text{Sum of all values} \times \text{Frequency}}{\text{Total frequency}}$
$\text{Mean} = \frac{(10 \times 4) + (15 \times 3) + (20 \times 2) + (25 \times 5) + (30 \times 6)}{4 + 3 + 2 + 5 + 6}$
$\text{Mean} = \frac{40 + 45 + 40 + 125 + 180}{20}$
$\text{Mean} = \frac{430}{20}$
$\text{Mean} = 21.5$

Since the total frequency is 20 (4 + 3 + 2 + 5 + 6 = 20), the median will be the 10th value when the data is arranged in ascending order. Since there are 20 values in total, the 10th and 11th values will be the middle two values, and the median will be their average.

Arrange the data:
$10, 10, 10, 10, 15, 15, 15, 20, 20, 25, 25, 25, 25, 25, 30, 30, 30, 30, 30, 30$
The 10th and 11th values are both 25, so the median is $$(25 + 25) / 2 = 25$$.

Comparing the mean and median:
$\text{Mean} = 21.5$
$\text{Median} = 25$

The median is $$25 – 21.5 = 3.5$$ greater than the mean.

So, the best statement that compares the mean and the median is:
$\boxed{\text{B) The median is 3.5 greater than the mean.}}$

[Calc]  Question Hard

The bar graph above shows the total number of scheduled flights and the number of delayed flights for five airlines in a one-month period. Values have been rounded to the nearest 1000 flights.

According to the graph, what is the median number of delayed flights for the airlines shown?

Ans:5000

From the graph, the approximate number of delayed flights for each airline is:

• Airline A: 6,000
• Airline B: 15,000
• Airline C: 1,000
• Airline D: 5,000
• Airline E: 900

Listing these in ascending order:
$900,1,000,5,000,6,000,15,000$

The median is the middle value:
$\text { Median }=5,000$

[Calc]  Questions Hard

The two histograms show the distribution of data set A and data set B, respectively. Data set B is the result of removing the outlier from data set A. Which of the following statements about the means of data set A and data set B is true?

A) The means of data set A and B are the same.
B) The mean of data set A is greater than the mean of data set B.
C) The mean of data set A is less than the mean of data set B.
D) No comparison about the means of the data sets can be made.

Ans: B

To determine the correct statement about the means of the two data sets, I’ll analyze the visual information provided in the histograms.

Data set A has a single bar extending far to the right, indicating the presence of an outlier or extreme value that is much larger than the rest of the data points.

Data set B appears to have the same general distribution as Data set A, but without that outlier bar on the far right.

The presence of an outlier that is significantly larger than the other values will pull the mean up towards that extreme value.

Therefore, with the outlier removed in Data set B, its mean should be lower than the mean of Data set A which includes that outlier.

So the correct statement is: B) The mean of data set A is greater than the mean of data set B.

[Calc]  Question  Hard

During a car trip, a passenger recorded the car’s instantaneous fuel economy, in miles per
gallon (mpg), 20 different times. The histogram summarizes the distribution of these data. The first bar represents an instantaneous fuel economy of at least 32 mpg but less than 33 mpg. The second bar represents an instantaneous fuel economy of at least 33 mpg but less than 34 mpg, and so on.

During the trip, how many times did the passenger record an instantaneous fuel economy of at least 34 mpg but less than 36 mpg ?

10

To determine the number of times the passenger recorded an instantaneous fuel economy of at least 34 mpg but less than 36 mpg, we need to analyze the histogram and sum the frequencies of the relevant bars.

From the histogram:

• The bar representing fuel economy from 34 mpg to less than 35 mpg has a frequency of 6.
• The bar representing fuel economy from 35 mpg to less than 36 mpg has a frequency of 4.

Therefore, the total number of times the passenger recorded an instantaneous fuel economy in the range of 34 mpg to less than 36 mpg is: $6+4\Rightarrow 10$

[Calc]  Question  Hard

The dot plots shown each represent a data set. Which of the following statements best compares the means and the standard deviations of the two data sets?
A) The means are equal; the standard deviation of data set A is less than the standard deviation of data set B.
B) The means are equal; the standard deviation of data set A is greater than the standard deviation of data set B.
C) The standard deviations are equal; the mean of data set $\mathrm{A}$ is less than the mean of data set B.
D) The standard deviations are equal; the mean of data set A is greater than the mean of data set B.

A

[Calc]  Question Hard

The table shows the distribution of class sizes for the 109 classes of a high school. What is the median class size at the high school?

24

Question

.

The bar graph shows the frequency of each data value in a certain data set. What is the minimum data value in the data set? 3.6

1. 10
2. 11
3. 12
4. 13

A

Question

The histogram shows the distribution of book prices, in dollars, for the 27 books for sale at a store.

The first bar represents books with prices of less than 5. The second bar represents books with prices of at least 5 but less than 10, and so on. In which interval will the median price of books for sale be included when the book that costs at least 35 but less than 40 is sold? 3.6

1. At least 0 but less than 5
2. At least 5 but less than 10
3. At least 10 but less than 15
4. At least 35 but less than 40

B

Question

For a certain computer game, individuals receive an integer score that ranges from 2 through 10. The table below shows the frequency distribution of the scores of the 9 players in group A and the 11 players in group B.

The median of the scores for group B is how much greater than the median of the scores of group A?

Ans: 1

Question

For a certain computer game, individuals receive an integer score that ranges from 2 through 10. The table below shows the frequency distribution of the scores of the 9 players in group A and the 11 players in group B.

The mean of the scores for group A is 5, and the mean of the scores for group B is 7. What is the mean of the scores for the 20 players in groups A and B combined?

Ans: 6.1, 61/10

Questions

The box plots above summarize the distribution of the number of fish caught each day on two commercial fishing boats for a season. By how many fish does the median number of fish caught each day on Boat B exceed the median number on Boat A?

Ans: 5

Questions

The table above shows monthly enrollments in art classes at two community centers for 7 consecutive months. Based on the table, by how much does the median monthly enrollment in community center B exceed the median monthly enrollment in community center A for the 7 months?

Ans: 296

Questions

2, 10, 3, 7, 6

The mean of the list of numbers above is what fraction of the sum of the five numbers?

Ans: $1 / 5, .2$

Questions

A baker is gathering the ingredients required to make 15 batches of oatmeal cookies and 1 cake. The cake will require one-quarter bag of flour. The baker needs a total of more than 3 but less than 4 bags of flour. What is one possible value for the fraction of one bag of flour required for each batch of cookies?

Ans: $11 / 60<\mathrm{x}<1 / 4, .183<\mathrm{X}<.25$

Questions

The histogram summarizes the distribution of a data set composed of 50 integers. The first bar represents the number of integers that are at least 0 but less than 5. The second bar represents the number of integers that are at least 5 but less than 10, and so on. What is a possible value of the median of the data set?

Ans: 10,11,12,13,14

Question

The boiling point of water at sea level is 212 degrees Fahrenheit $\left({ }^{\circ} \mathrm{F}\right)$. For every increase of 1,000 feet above sea level, the boiling point of water drops approximately $1.84^{\circ} \mathrm{F}$. Which of the following equations gives the approximate boiling point $B$, in ${ }^{\circ} \mathrm{F}$, at $h$ feet above sea level?
A. $B=212-1.84 h$
B. $B=212-(0.00184) h$
C. $B=212 h$
D. $B=1.84(212)-1,000 h$

Ans: B

Question

The numbers of people, in millions, who visited Amusement Park A and Amusement Park B in 2009 through 2013 are listed in the table below. What is the positive difference between the mean number of people, in millions, who visited Amusement Park B  and the mean number of people, in millions, who visited Amusement Park A during those years? (Round your answer to the nearest tenth.)

Ans: 1.7, 17/10

Question

The price of a ticket to a play is based on the row the seat is in, as shown in the table above. A group wants to purchase 10 tickets for the play.
They will purchase 3 tickets for seats in row 1.
They will purchase 2 tickets for seats in row 3.
They will purchase 2 tickets for seats in row 4.
They will purchase 3 tickets for seats in row 12.
What is the average (arithmetic mean) ticket price, in dollars, for the 10 tickets? (Disregard the  sign when gridding your answer.)