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 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
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.
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:
\[ \boxed{D) \, \left(0, \frac{27}{2}\right)} \]
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:
\[ \boxed{C) \, 68.5} \]
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.