Home / Digital SAT Math: One-variable data: distributions and measures of centre and spread-Practice Questions

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

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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  Easy

Which of the following dot plots, each with 9 data values, represents a data set with a median value that is less than 70 ?

▶️Answer/Explanation

Ans:C

To determine which dot plot represents a data set with a median value less than 70, we need to understand the concept of the median and analyze each dot plot. The median is the middle value when the data values are arranged in ascending order.

Given that each dot plot has 9 data values, the median will be the 5th value when the values are arranged in order.

Let’s analyze each dot plot:

Dot Plot A:

Data values: 55, 55, 55, 65, 70, 75, 75, 75, 80

  • Median (5th value): 70

Dot Plot B:

Data values: 55, 60, 65, 70, 75, 80, 80, 85, 85

  • Median (5th value): 75

Dot Plot C:

Data values: 60, 60, 60, 65, 65, 70, 80, 80, 80

  • Median (5th value):65

Dot Plot D:

Data values: 65, 65, 65, 70, 70, 75, 80, 85, 85

  • Median (5th value): 70

▶️Formula Booklet

[Calc]  Question  Easy

Data set \(A: 2,4,6,6,8,12\)
Data set B: \(2,4,6,6,8,12,26\)
Two data sets are shown. Which statement best compares the medians of the data sets?
A. The median of data set \(A\) is greater than the median of data set \(B\).
B. The median of data set \(A\) is less than the median of data set B.
C. The medians of data sets \(A\) and \(B\) are equal.
D. There is not enough information to compare the medians.

▶️Answer/Explanation

Ans:C

 To compare the medians of the two data sets, let’s first find the medians.

For Data Set A: \(2, 4, 6, 6, 8, 12\), the median is the middle value when the data is arranged in ascending order. Since there are \(6\) values, the median is the average of the third and fourth values, which are both \(6\). So, the median of Data Set A is \(6\).

For Data Set B: \(2, 4, 6, 6, 8, 12, 26\), again, the median is the middle value. With \(7\) values, the median is the fourth value, which is \(6\).

So, the medians of both data sets are equal.

Therefore, the correct answer is option C: The medians of data sets \(A\) and \(B\) are equal.

▶️Formula Booklet

[Calc]  Question Easy

Line \(l\) has a slope of -3 and an \(x\)-intercept of \(\left(\frac{9}{2}, 0\right)\). What is the \(y\)-intercept of line \(l\) ?
A) \(\left(\frac{9}{2}, 0\right)\)
B) \(\left(0, \frac{9}{2}\right)\)
C) \(\left(\frac{27}{2}, 0\right)\)
D) \(\left(0, \frac{27}{2}\right)\)

▶️Answer/Explanation

D

To find the \(y\)-intercept of line \(l\), we can use the point-slope form of a linear equation:

\[ y – y_1 = m(x – x_1) \]

Where:
\(m\) is the slope of the line.
\((x_1, y_1)\) is a point on the line.

Using the given \(x\)-intercept \(\left(\frac{9}{2}, 0\right)\) and the slope \(m = -3\), we have:

\[ y – 0 = -3(x – \frac{9}{2}) \]
\[ y = -3x + \frac{27}{2} \]

Now, we need to find the \(y\)-intercept, which occurs when \(x = 0\):
\[ y = -3(0) + \frac{27}{2} \]
\[ y = \frac{27}{2} \]

So the \(y\)-intercept of line \(l\) is \(\left(0, \frac{27}{2}\right)\).

Therefore, the answer is:
\[ \boxed{D) \, \left(0, \frac{27}{2}\right)} \]

[Calc]  Question  Easy

Questions 8 and 9 refer to the following information.
The table shows the approximate land areas, in thousands of acres, of four national parks in West Virginia.

What is the range of the land areas, in thousands of acres, of the four parks in the table?
A) 91.8
B) 72.2
C) 68.5
D) 36.1

▶️Answer/Explanation

C

The range of a data set is the difference between the largest and smallest values in the set.

From the table, the largest area is 72.2 and the smallest area is 3.7.

Therefore, the range is:
\[ \text{Range} = 72.2 – 3.7 = 68.5 \]

So the answer is:
\[ \boxed{C) \, 68.5} \]

[Calc]  Question  Easy

The list shown gives the heights, in inches, for the 6 ten-year-old children in a group.

52, 53, 54, 54, 55, 56

A seventh child with a height of 60 inches will be added to the group. Which of the following correctly describes how the mean and the median of the group will change when the seventh child is added?

A)The mean and the median will increase.

B)The mean and the median will decrease.

C)The mean will increase, and the median will remain the same.

D)The mean will decrease, and the median will remain the same.

▶️Answer/Explanation

C)The mean will increase, and the median will remain the same.

Given the heights of the 6 ten-year-old children in a group:
\[ 52, 53, 54, 54, 55, 56 \]

First, let’s find the mean and median of the initial group:

Mean:
\[ \text{Mean} = \frac{52 + 53 + 54 + 54 + 55 + 56}{6} = \frac{324}{6} = 54 \]

Median:
Since the number of data points (6) is even, the median is the average of the 3rd and 4th numbers when the data is ordered:
\[ \text{Median} = \frac{54 + 54}{2} = 54 \]

Now, a seventh child with a height of 60 inches is added. The new group of heights becomes:
\[ 52, 53, 54, 54, 55, 56, 60 \]

New Mean:
\[ \text{New Mean} = \frac{52 + 53 + 54 + 54 + 55 + 56 + 60}{7} = \frac{384}{7} \approx 54.86 \]

New Median:
Since the number of data points (7) is odd, the median is the middle value:
\[ \text{New Median} = 54 \]

Therefore, the mean will increase, and the median will remain the same.

The correct answer is: C) The mean will increase, and the median will remain the same.

[Calc]  Questions  Easy

A sample of water was taken from each of ten different locations in a pond. The pH of each sample was measured. The measurements are summarized in the frequency table shown.

How many samples have a pH of 7.4 or greater?
A) 3
B) 4
C) 6
D) 7

▶️Answer/Explanation

Ans: D

To find how many samples have a \(\mathrm{pH}\) of 7.4 or greater, we look at the frequencies for the \(\mathrm{pH}\) ranges 7.4 to 7.6 and 7.7 to 7.9.

The frequency for 7.4 to 7.6 is 4.
The frequency for 7.7 to 7.9 is 3.

Adding these frequencies together:
\[ 4 + 3 = 7 \]

Therefore, the number of samples with a \(\mathrm{pH}\) of 7.4 or greater is: \[ \boxed{7} \]

[Calc]  Question Easy

Each of the 25 data values in a data set is a different integer between 1 and 50 , inclusive. The table gives the frequency of the data for five intervals. Which of the following intervals contains exactly $\frac{2}{5}$ of the values in the data set?
A) 1 to 20
B) 11 to 30
C) 21 to 40
D) 31 to 50

▶️Answer/Explanation

D

[Calc]  Question Easy

The box plot summarizes the data for the annual cost of automobile insurance for automobile owners in a certain US city. Which of the following could be the median annual cost of automobile insurance for automobile owners in this city?
A) $\$ 1,625$
B) $\$ 2,000$
C) $\$ 2,100$
D) $\$ 2,750$

▶️Answer/Explanation

A

[Calc]  Question Easy

$$
4,13,5,8, R, 5,11
$$

In the data set shown, $R$ is an integer. If the median of the data set is 8 and $R<11$, what is a possible value of $R$ ?

▶️Answer/Explanation

8,9,10

Question

Data sets A and B are summarized in the graphs above. Each data set consists of 12 whole numbers. Which of the following statements must be true?

  1. Data sets A and B have the same mean, but the standard deviation of data set A is greater than the standard deviation of data set B.
  2. Data sets A and B have the same mean, but the standard deviation of data set B is greater than the standard deviation of data set A.
  3. Data sets A and B have the same standard deviation, but the mean of data set A is greater than the mean of data set B.
  4. Data sets A and B have the same standard deviation, but the mean of data set B is greater than the mean of data set A.
Answer/Explanation

Ans: B

Question

The box plot summarizes the number of seats in the US House of Representatives currently allocated to each of the 50 states. What is the median number of allocated seats in the US House of Representatives?

  1. 2
  2. 5
  3. 10
  4. 53
Answer/Explanatio

Ans: B

Question

Data set X: 5.50, 5.50, 5.60, 5.65, 5.66
Data set Y: 4.00, 5.50, 5.50, 5.60, 5.65, 5.66

Data sets X and Y show the acidity, or pH, of rainwater samples from two different locations. Which statement about the mean pH of data set X and data set Y is true?

  1. The mean pH of data set X is greater than the mean pH of data set Y.
  2. The mean pH of data set X is less than the mean pH of data set Y.
  3. The mean pH of data set X is equal to the mean pH of data set Y.
  4. There is not enough information to compare the mean pH of the two data sets.
Answer/Explanation

Ans: A

Question

Data set X and data set Y are displayed by the two dot plots shown. Which of the following is(are) the same for both data sets?
1. The mean
2. The median

  1. I only
  2. II only
  3. I and II
  4. Neither I nor II
Answer/Explanation

Ans: B

Question

The Metropolitan Museum of Art has plates on display from the Roman Empire and ancient Greece. The box plots shown summarize the distributions of the diameters, in centimeters, of all the museum’s plates from each region. How does the median diameter of the plates from the Roman Empire, \(r\), compare to the median diameter of the plates from ancient Greece, \(g\) ? 

  1. \(r\)<\(g\)
  2. \(r\)>\(g\)
  3. \(r\)=\(g\)
  4. There is not enough information to compare the medians.
Answer/Explanation

Ans: A

Question

The scatterplot shows the average price per square foot of a house in the United States each year for several years. A line of best fit for the data is also shown.

The line of best fit predicted that the average price per square foot in 2001 would be \($\)76. What is the difference between the predicted value and the actual average price per square foot in 2001? 

  1. \($\)0
  2. \($\)2
  3. \($\)4
  4. \($\)6
▶️Answer/Explanation

C

Questions 

The scatterplot above represents the head lengths, in centimeters (cm), and body lengths, in cm, of 14 adult crocodiles. The line of best fit for the data is also shown. The box plot above summarizes the body lengths of the 14 crocodiles.

For an adult crocodile with a head length of 30 cm, which of the following is closest to the body length, in cm, predicted by the line of best fit?

  1. 180
  2. 215
  3. 250
  4. 275
    ▶️Answer/Explanation

    Ans: B

Questions 

The scatterplot above represents the head lengths, in centimeters (cm), and body lengths, in cm, of 14 adult crocodiles. The line of best fit for the data is also shown. The box plot above summarizes the body lengths of the 14 crocodiles.

Based on the line of best fit, of the following, which is the best estimate of the increase in predicted body length, in cm, for every 10 cm increase in head length?

  1. 25
  2. 75
  3. 125
  4. 150
    ▶️Answer/Explanation

    Ans: B

Questions 

The scatterplot above represents the head lengths, in centimeters (cm), and body lengths, in cm, of 14 adult crocodiles. The line of best fit for the data is also shown. The box plot above summarizes the body lengths of the 14 crocodiles.

Based on the box plot, of the following, which is the best estimate of the median body length, in cm, of the 14 adult crocodiles?

  1. 260
  2. 300
  3. 320
  4. 370
    ▶️Answer/Explanation

    Ans: C

Question

The box plot summarizes the number of seats in the US House of Representatives currently allocated to each of the 50 states. What is the median number of allocated seats in the US House of Representatives?

  1. 2
  2. 5
  3. 10
  4. 53
▶️Answer/Explanation

B

Questions 

The number of people who rode a certain bus each day of a week is shown in the table below.

Which of the following is true based on these data?

  1. The bus had the most riders on Tuesday.
  2. Each day from Tuesday through Sunday, the number of riders on the bus was greater than the previous day.
  3. Each day from Tuesday through Sunday, the number of riders on the bus was less than the previous day.
  4. The two days with the fewest number of riders were Saturday and Sunday.
    ▶️Answer/Explanation

    Ans: D

Questions 

The line graph above shows the average price of one metric ton of oranges, in dollars, for each of seven months in 2014.

Which of the following is closest to the median price, in dollars, of the seven recorded prices of one metric ton of oranges?

  1. 834
  2. 808
  3. 783
  4. 768
    ▶️Answer/Explanation

    Ans: B

Questions 

The line graph above shows the average price of one metric ton of oranges, in dollars, for each of seven months in 2014.

In 2014, the average price of one metric ton of oranges decreased by 2.36% from January (not shown) to February. Which of the following is closest to the price of one metric ton of oranges in January 2014?

  1. 700
  2. 770
  3. 790
  4. 830
    ▶️Answer/Explanation

    Ans: C

Question

To determine whether residents of a community would vote in favor of a ballot proposal to use $\$ 100,000$ of local taxes for additional playground equipment at a community park, Jennifer surveyed 60 adults visiting the park with their children during one week in June. She found that 45 of those surveyed reported that they would vote in favor of the proposal. Which of the following statements must be true? 

A. When the actual vote is taken, 75 percent of the votes will be in favor of the proposal.
B. No prediction should be made about the vote on the proposal because the sample size is too small.
C. The sampling method is flawed and may produce biased results.
D. The sampling method is not flawed and is likely to produce unbiased results

▶️Answer/Explanation

. Ans: C

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