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
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.
▶️Answer/Explanation
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:
\[ \boxed{\text{B) The median of data set 1 is greater than the median of data set 2.}} \]
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
▶️Answer/Explanation
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
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.
▶️Answer/Explanation
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:
\[ \boxed{\text{B) The median is 3.5 greater than the mean.}} \]
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?
▶️Answer/Explanation
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:
\[
\text { Median }=5,000
\]
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.
▶️Answer/Explanation
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.