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 Medium
The dot plot represents a data set.
What is the median of the 19 values in the data set?
▶️Answer/Explanation
Ans:42
First, let’s count the dots above each value on the x-axis:
- 36: 2 dots
- 38: 3 dots
- 40: 2 dots
- 42: 3 dots
- 44: 4 dots
- 46: 3 dots
- 48: 2 dots
With 19 values, the median will be the 10th value when arranged in order. Counting to the 10th value:
So, the median value is 42.
Question Medium
A list of 10 data values is shown below.
\[
4,6,7,2,8,9,6,3,3,3
\]
What is the mean of the data?
▶️Answer/Explanation
Ans:51/10
To find the mean of the given data, you sum up all the values and then divide by the total number of values.
Given data: \(4, 6, 7, 2, 8, 9, 6, 3, 3, 3\)
Sum of the data: \(4 + 6 + 7 + 2 + 8 + 9 + 6 + 3 + 3 + 3 = 51\)
Number of data values: \(10\)
Mean \( = \frac{\text{Sum of data}}{\text{Number of data values}} = \frac{51}{10} = 5.1\)
So, the mean of the data is \(5.1\).
Question Medium
Data set P: 12, 18, 19, 19, 19, 19, 19, 21, 21, 22, 22
Data set \(P\) contains the lengths, in inches, of 11 objects. The length 12 inches is removed from data set \(\mathrm{P}\) to create data set \(\mathrm{N}\), which contains the lengths, in inches, of 10 objects. Which statement best compares the mean \(q\) and the median \(r\) of data set \(\mathrm{P}\) with the mean \(s\) and the median \(t\) of data set \(\mathrm{N}\) ?
A) \(q<s ; r>t\)
B) \(q=s ; r>t\)
C) \(q<s ; r=t\)
D) \(q=s ; r=t\)
▶️Answer/Explanation
Ans:C
Data set \(P\): 12, 18, 19, 19, 19, 19, 19, 21, 21, 22, 22
When 12 inches is removed, data set \(N\) becomes: 18, 19, 19, 19, 19, 19, 21, 21, 22, 22
Mean Comparison:
Mean of \(P\) (\(q\)):
\[
q = \frac{\sum P}{11} = \frac{12 + 18 + 19 + 19 + 19 + 19 + 19 + 21 + 21 + 22 + 22}{11} = \frac{211}{11} = 19.18
\]
Mean of \(N\) (\(s\)):
\[
s = \frac{\sum N}{10} = \frac{18 + 19 + 19 + 19 + 19 + 19 + 21 + 21 + 22 + 22}{10} = \frac{199}{10} = 19.9
\]
Since the smallest value (12) was removed, the mean increased:
\[
q < s
\]
Median Comparison:
Median of \(P\) (\(r\)):
Middle value of sorted list of 11 items, \(r = 19\)
Median of \(N\) (\(t\)):
Middle value of sorted list of 10 items, average of 5th and 6th values:
\[
t = \frac{19 + 19}{2} = 19
\]
Since the median value (19) was not affected by removing the smallest value:
\[
r = t
\]
So, the correct answer is:
\[
\boxed{q < s; r = t}
\]
Question Medium
$
0,2,3,4,5,5,5,6,6,7
$
The given list shows a baseball team’s score for each of its first 10 games. In the eleventh game, the team had score of 18. Which of the following best describes the mean and the median of the team’s scores for the first 11 games compared to the first 10 games?
A) The mean increased and the median remained unchanged.
B) The median increased and the mean remained unchanged.
C) Both the mean and the median remained unchanged.
D) Both the mean and the median increased.
▶️Answer/Explanation
Ans:A
Initial Scores (10 games):
\[0, 2, 3, 4, 5, 5, 5, 6, 6, 7\]
Mean of the first 10 games:
\[
\text{Mean} = \frac{\sum \text{scores}}{\text{number of games}} = \frac{0 + 2 + 3 + 4 + 5 + 5 + 5 + 6 + 6 + 7}{10} = \frac{43}{10} = 4.3
\]
Median of the first 10 games:
Since there are an even number of games, the median is the average of the 5th and 6th scores:
\[
\text{Median} = \frac{5 + 5}{2} = 5
\]
Scores with the 11th game:
\[0, 2, 3, 4, 5, 5, 5, 6, 6, 7, 18\]
Mean of the first 11 games:
\[
\text{Mean} = \frac{\sum \text{scores}}{\text{number of games}} = \frac{43 + 18}{11} = \frac{61}{11} \approx 5.545
\]
Median of the first 11 games:
Since there are now an odd number of games, the median is the middle score (6th score):
\[
\text{Median} = 5
\]
Comparing the changes:
The mean increased from 4.3 to approximately 5.545.
The median remained unchanged at 5.
Question Medium
The tables show the frequencies of data values for two data sets.
Which statement best compares the mean \(a\) and standard deviation \(b\) of data set \(\mathrm{P}\) with the mean \(c\) and standard deviation \(d\) of data set \(\mathrm{Q}\) ?
A) \(a<c ; b<d\)
B) \(a<c ; b=d\)
C) \(a>c ; b=d\)
D) \(a>c ; b>d\)
▶️Answer/Explanation
B
To compare the mean and standard deviation of data set P with those of data set Q, we need to calculate the mean and standard deviation for both sets.
For data set P:
Mean (\(a\)) can be calculated as the sum of (Value * Frequency) divided by the total frequency.
Standard deviation (\(b\)) can be calculated based on the formula for standard deviation.
For data set Q:
Mean (\(c\)) and standard deviation (\(d\)) can be calculated similarly.
However, without calculating these values, we can infer some information from the given data:
Data set Q has fewer unique values than data set P.
The frequencies of the values in data set Q seem to be similar to those in data set P, but with a shift (e.g., the frequency distribution in Q seems to be a subset of that in P).
From this, we can conclude that:
The mean of data set Q (\(c\)) might be slightly lower than that of data set P (\(a\)) due to the smaller values.
The standard deviation of both data sets (\(b\) and \(d\)) might be similar, considering the similarity in the frequency distributions.
Therefore, the best comparison would be:
\[ \boxed{B) \, a<c ; b=d} \]