- A gym records the number of minutes 48 members spend on a treadmill during one visit, measured by the machine's timer and rounded to the nearest minute. The dotplot below shows the distribution of times (minutes).
Dotplot (each dot = 1 member)
10 | ••
15 | •••
20 | •••••
25 | ••••••••
30 | ••••••••••
35 | ••••••••
40 | •••••
45 | •••
50 | ••
Which feature of the distribution is most evident?
Answer: A roughly symmetric, unimodal shape centered near 30 minutes
This question tests the skill of representing and describing a quantitative variable using graphs, specifically identifying the shape of a distribution from a dotplot in AP Statistics. The dotplot of treadmill times shows the densest clustering at 30 minutes with 10 dots, symmetrically decreasing to both lower and higher values, such as 8 dots at 25 and 35, and 5 at 20 and 40, indicating a roughly symmetric, unimodal shape. A distractor like option D (strong right skew) might appeal if one miscounts the dots and sees the tail to 50 as longer, but the left tail to 10 mirrors it in spread and density. When describing distributions, focus on shape (here, symmetric and unimodal), center (near 30 minutes), spread (from 10 to 50), and any outliers or gaps, none of which are prominent here. This symmetric shape suggests that members' treadmill times are consistently around 30 minutes without strong pulls to extremes.
- A cross-country team recorded the time (in minutes) it took each of 30 runners at the school to complete a 1-mile trial on the same flat course, timing each runner with a stopwatch. The dotplot below shows the distribution of mile times. Which feature of the distribution is most evident?
Answer: A clear right-skew with a possible high outlier near 12 minutes
This question tests your ability to identify the shape of a distribution from a dotplot. Looking at the dotplot of mile times, we can see that most runners completed the mile between 6-8 minutes, with the data clustering on the left side. However, there are a few runners who took much longer, with times extending out to around 12 minutes, creating a long tail to the right. This pattern where most data values are concentrated on the left with a tail extending to the right is called right-skew. The value near 12 minutes appears separated from the main cluster, making it a possible high outlier. When describing distributions, always look for the overall shape (symmetric, skewed, uniform), the presence of outliers, and any unusual features like gaps or multiple peaks.
- A school nurse recorded the number of minutes 60 students spent on a treadmill during a fitness screening, rounding to the nearest minute. The dotplot below shows the distribution of treadmill times (minutes) for these students. Which feature of the distribution is most evident?
Answer: Skewed right (longer tail toward larger times)
This question tests your ability to identify the shape of a distribution from a dotplot. Looking at the dotplot of treadmill times, we can see that most students have times clustered on the left side (shorter times), with the frequency gradually decreasing as we move toward longer times on the right. The distribution has a long tail extending toward the higher values (longer treadmill times), which is the defining characteristic of a right-skewed distribution. Choice A (symmetric) is incorrect because the data clearly has more values on one side than the other. When describing distributions, remember that skewness is named for the direction of the tail: right-skewed means the tail points right toward larger values, while left-skewed means the tail points left toward smaller values.
- A librarian recorded the number of books checked out by each of 45 patrons during a particular week, using the library's checkout database. The dotplot shows the distribution of books checked out. Which feature of the distribution is most evident?
Answer: The distribution is right-skewed with most patrons checking out few books and a tail toward larger counts.
This question tests your ability to describe the shape of a distribution from a dotplot of count data. The dotplot shows that most library patrons checked out between 0-4 books, with the frequency decreasing as the number of books increases. There's a long tail extending toward higher values (up to 12 books), with just a few patrons checking out many books. This creates a right-skewed distribution, which is typical for count data where most observations are small values but a few are much larger. Option A incorrectly describes this as left-skewed with most patrons checking out many books, which is the opposite of what the dotplot shows. Count data often exhibits right-skew because there's a natural lower bound (0) but no strict upper limit.
- A meteorologist recorded daily rainfall amounts (in inches) for 45 days in a spring season at one weather station using a standard rain gauge. The dotplot below shows the distribution.
Dotplot (rainfall in inches):
0.0 | •••••••••••••••••••
0.1 | •••••••••
0.2 | •••••
0.3 | •••
0.4 | ••
0.5 | •
0.6 | •
0.7 |
0.8 |
0.9 |
1.0 | •
Which feature of the distribution is most evident?
Answer: A strong right skew, with many low-rainfall days and a tail toward higher amounts
This question involves identifying features in dotplots of quantitative data like rainfall amounts. The dotplot shows a high stack at 0.0 inches (19 days), decreasing frequencies toward higher amounts, with a tail extending to 1.0 inches, indicating strong right skew. Most days have little to no rain, with infrequent higher rainfall days. Choice B distracts by suggesting left skew, but the long tail is to the right, toward higher values. Key lesson: right-skewed distributions often occur with non-negative variables like rainfall; describe shape, center (low due to skew), spread, and peaks to highlight common versus rare events.
- A teacher records scores (out of 10) on a short quiz for 50 students, graded consistently using an answer key. The dotplot shows the distribution.
Dotplot of quiz score
2 | •
3 | ••
4 | •••
5 | ••••
6 | •••••
7 | •••••••
8 | ••••••••••
9 | ••••••••••••
10| •••••••
Which feature is most evident?
Answer: Strong left skew with a long tail toward lower scores
This AP Statistics question involves analyzing a dotplot to describe the distribution of quiz scores as a quantitative variable. The dotplot has denser dots at higher scores like 9 with 12 and 8 with 10, tapering to a long tail at lower scores down to 2 with 1, demonstrating a strong left skew. A distractor such as option A (strong right skew) might arise from confusing tail direction, but left skew features the tail toward lower values as seen here. When describing distributions, evaluate shape (left-skewed), center (high, near 8–9), spread (2 to 10), and outliers, with the skew most prominent due to many high performers and few low ones. This left skew suggests overall strong quiz performance with a pull from some lower scores.
- A shipping clerk recorded the weights (in pounds) of 55 packages sent from a small business in one week using the same digital scale. The dotplot shows the distribution of package weights. Which feature of the distribution is most evident?
Answer: The distribution is right-skewed, and there is a possible high outlier near 22 pounds.
This question tests your ability to identify skewness and outliers in a dotplot. The package weight distribution shows most packages clustered between 2-10 pounds, with the frequency decreasing as weight increases. There's a clear gap in the data, and then we see one or two packages around 22 pounds, which are separated from the main body of data. This creates a right-skewed distribution (tail extending toward higher values) with a possible high outlier at 22 pounds. Option C incorrectly identifies this as left-skewed with a low outlier - remember that outliers are extreme values separated from the main data, and the direction of skew follows the tail. When analyzing distributions, look for gaps that might indicate outliers, as these can significantly affect measures of center and spread.
- A bookstore tracked the number of books purchased per transaction for 52 customers on a Saturday, counting the total items on each receipt. The dotplot shows the distribution.
Which feature of the distribution is most evident?
Answer: The distribution is skewed right, with a tail toward larger numbers of books
This question tests your understanding of skewness in count data. Looking at the dotplot showing books purchased per transaction, you can observe that most customers bought a small number of books (many dots at 1, 2, or 3 books), with progressively fewer customers buying larger numbers of books extending toward the right. This creates a distribution with a long tail toward the larger values, which defines a right-skewed distribution. Choice B correctly identifies this pattern - the distribution is skewed right with a tail toward larger numbers of books. This shape is typical for purchase data because while most customers buy just a few items, occasional customers make large purchases. Count data often exhibits right skewness because there's a natural lower bound (0 or 1) but no strict upper limit for enthusiastic customers.
- A city planner measured commute times (in minutes) for 55 workers who drive to downtown, using self-reported times from a survey completed the same week. The dotplot below shows the distribution of commute times. Which feature of the distribution is most evident?
Answer: Bimodal with two clusters (short and long commutes)
This question asks you to identify the shape of a distribution from a dotplot of commute times. Looking at the dotplot, we can clearly see two distinct clusters of data points - one group with shorter commute times (around 10-20 minutes) and another group with longer commute times (around 40-50 minutes), with relatively few values in between. This pattern creates a bimodal distribution with two separate peaks. Choice D (skewed right) is incorrect because while there may be some values extending to the right, the defining feature is the two distinct modes. Bimodal distributions in commute data often reflect different groups of workers - perhaps those who live nearby versus those who commute from suburbs. When analyzing dotplots, look for clustering patterns that might indicate multiple modes rather than focusing only on the overall spread.
- A delivery company recorded the number of packages delivered per route for 52 routes on a particular day, using the company's route logs. The dotplot below summarizes the distribution.
Dotplot (packages per route):
60 | •
65 | ••
70 | •••
75 | ••••
80 | •••••
85 | ••••••
90 | •••••••
95 | ••••••
100| •••••
105| ••••
110| •••
115| ••
120| •
Which feature of the distribution is most evident?
Answer: A roughly symmetric distribution with a single peak around 90 packages
This question assesses interpreting dotplots for quantitative data like packages per route. The dotplot builds to a peak at 90 packages (7 routes), with symmetric decreases to both lower and higher values, showing a roughly symmetric, unimodal distribution centered around 90. The shape is bell-like without skew or gaps. Choice D could distract by suggesting bimodality, but there's only one peak, not two distinct ones. A mini-lesson: symmetric distributions often have mean ≈ median; always describe shape, center, spread (e.g., from 60 to 120), and any unusual features to understand the data's central tendency and variability.
- A librarian recorded the number of pages in each of 36 books returned on a particular day, using the page count printed in each book. The dotplot below shows the distribution of page counts. Which feature of the distribution is most evident?
Answer: A bimodal distribution with clusters around about 150 pages and 350 pages
This question tests your ability to identify a bimodal distribution from a dotplot. Looking at the distribution of page counts, we can clearly see two distinct clusters of dots: one group centered around 150 pages and another group centered around 350 pages, with a noticeable gap between them. This pattern with two separate peaks is called bimodal, suggesting the library received two different types of books - perhaps shorter novels/non-fiction and longer novels. The distribution is not unimodal (which would have one peak), uniform (which would have dots evenly spread), or skewed in either direction. When examining dotplots, look for clustering patterns and gaps that might indicate multiple groups within your data. Bimodal distributions often suggest that the data comes from two different populations or categories.
- A meteorology club recorded the daily rainfall (in inches) for 50 days in spring at a local weather station, using the station's rain gauge reading each day. The dotplot summarizes the rainfall amounts.
Which feature of the distribution is most evident?
Answer: The distribution is skewed right, with many small amounts and a few large amounts
This question tests your ability to recognize skewness in rainfall data. Looking at the dotplot, you can see that most days had small amounts of rainfall (many dots clustered near 0), with progressively fewer days having larger amounts of rain extending toward the right. This creates a distribution with a long tail toward the larger rainfall amounts, which is characteristic of a right-skewed distribution. Choice B correctly identifies this pattern - the distribution is skewed right with many small amounts and a few large amounts. This shape is typical for rainfall data because most days have little or no rain, while occasional storms can produce much larger amounts. In environmental data like rainfall, right skewness is common because there's a natural lower bound (0 inches) but no strict upper limit for extreme events.
- A librarian recorded the number of books checked out by each of 55 patrons on a Saturday, using the library's checkout system. The dotplot below shows the distribution.
Dotplot (books checked out):
0 | ••••••••••••••••
1 | •••••••••••
2 | •••••••
3 | ••••
4 | •••
5 | ••
6 | •
7 | •
8 |
9 |
10| •
Which feature of the distribution is most evident?
Answer: A strong right skew with a long tail toward larger numbers of books
This question tests describing distributions from dotplots for quantitative data like books checked out. The dotplot reveals a high frequency at 0 books (16 patrons), with frequencies decreasing as the number increases, but a long tail extending to 10 books, creating a strong right skew. Most data points are clustered at lower values, with fewer high values stretching the tail. Choice B could mislead by suggesting left skew, but the tail is toward higher numbers, not lower. When analyzing distributions, note the shape (e.g., right-skewed means tail to the right), center (pulled toward the tail in skewed data), spread, and any peaks or gaps to understand the variable's behavior.
- A city planner recorded the ages (in years) of 52 people who attended a public meeting, based on self-reported age on a sign-in sheet. The dotplot shows the distribution of ages. Which feature of the distribution is most evident?
Answer: The distribution is bimodal, with clusters among young adults and older adults.
This question tests your ability to recognize a bimodal distribution in a dotplot of ages. The dotplot clearly shows two distinct clusters: one group of younger adults (roughly 20-35 years) and another group of older adults (roughly 55-70 years), with very few people in the middle age ranges. This creates two separate peaks or modes, making the distribution bimodal. This pattern is common in community meetings where both younger and older residents attend, but middle-aged residents may be less represented. Option A incorrectly describes this as unimodal and symmetric, missing the clear separation between the two age groups. Bimodal distributions often indicate that the data comes from two distinct populations or groups with different characteristics.
- A real estate analyst records the sale prices (in thousands of dollars) for 45 recently sold homes in one neighborhood, taken from public records and rounded to the nearest $1,000. The dotplot shows the distribution.
Dotplot of sale price ($1000s)
180 | •
200 | ••
220 | ••••
240 | ••••••
260 | •••••••
280 | ••••••
300 | ••••
320 | ••
340 | •
500 | •
Which feature is most evident?
Answer: A clear high outlier around $500,000 relative to the main cluster
This AP Statistics question examines using a dotplot to identify features in the distribution of home sale prices as a quantitative variable. The dotplot clusters symmetrically around 260–280 with peaks like 7 at 260 and 6 at 280, but includes an isolated dot at 500, highlighting a clear high outlier. Option D (strong right skew with no outliers) might appeal if the outlier is viewed as part of a tail, but the large gap from 340 to 500 marks it as separate. Core to describing distributions is identifying shape (roughly symmetric main cluster), center (around 260), spread (180 to 500), and unusual features like this outlier. The outlier is most evident, suggesting one exceptionally high-priced home amid typical values.
- A teacher recorded the number of minutes 35 students spent studying for a quiz the night before, based on a self-reported survey completed the next day. The dotplot below shows the distribution of study times. Which feature of the distribution is most evident?
Answer: A clear right-skew with a long tail toward larger study times
This question tests your ability to recognize skewness in a dotplot. Looking at the distribution of study times, we can see that most students studied for relatively short periods (clustering around 0-60 minutes), but there are several students who studied for much longer times, with dots extending out to 180 minutes. This creates a long tail stretching to the right, which is the defining characteristic of a right-skewed distribution. The incorrect choice of left-skew would mean most students studied for long times with a few studying very little, which is opposite to what we observe. When identifying skewness, remember that the direction of the skew is named for where the tail points: right-skew has a tail pointing right (toward larger values), while left-skew has a tail pointing left (toward smaller values).
- A wildlife biologist measured the lengths (in centimeters) of 60 fish captured from a lake using the same measuring board, then released them. The dotplot shows the distribution of fish lengths. Which feature of the distribution is most evident?
Answer: The distribution is bimodal, suggesting two common length groups.
This question tests your ability to recognize a bimodal distribution in a dotplot. Looking at the fish length data, we can see two distinct clusters of dots: one group centered around 15-20 cm and another group centered around 35-40 cm, with relatively few fish in between. This creates two clear peaks or modes in the distribution, making it bimodal. This pattern often suggests two different populations or groups within the data - perhaps two different species of fish or fish at different life stages. Option C incorrectly identifies this as right-skewed with an outlier, but the second cluster is too substantial to be considered outliers. When examining distributions, bimodal patterns indicate that the data may come from two distinct groups that should potentially be analyzed separately.
- A delivery company recorded the distance (in miles) of each of 30 delivery routes completed in one day, using GPS totals for each route. The dotplot below shows the distribution of route distances. Which feature of the distribution is most evident?
Answer: A clear right-skew with a long tail toward larger distances
This question tests your ability to recognize skewness in a dotplot of delivery distances. Looking at the distribution, we can see that most delivery routes are relatively short (clustering around 5-15 miles), but there are several routes that extend out to much longer distances, with dots spreading out toward 30-35 miles. This creates a long tail extending to the right, which is the defining characteristic of a right-skewed distribution. The pattern makes practical sense for delivery routes, where most are kept short for efficiency, but some longer routes are necessary to reach distant customers. The distribution is clearly not left-skewed, symmetric, uniform, or bimodal. When analyzing business operations data, right-skew often appears when most cases are routine but some require extra resources or distance.
- In a study of 50 randomly selected customers at a coffee shop, a manager recorded the number of minutes each customer waited from ordering to receiving a drink during the morning rush. The dotplot shows the distribution of wait times (in minutes). Which feature of the distribution is most evident?
Answer: The distribution is right-skewed with a possible high outlier around 12 minutes.
This question tests your ability to describe the shape of a distribution from a dotplot. Looking at the dotplot of wait times, we can see that most customers waited between 2-6 minutes, with the frequency decreasing as wait times increase. There appears to be one or two customers who waited around 12 minutes, which stands out from the main cluster. This creates a distribution that has a longer tail extending to the right (toward higher values), which is the definition of right-skewed. The value around 12 minutes could be considered a high outlier since it's separated from the main body of data. When describing distributions, always look for the overall shape (symmetric, skewed, uniform), the number of peaks (unimodal, bimodal), and any unusual observations (outliers).
- A city planner recorded the ages (in years) of 70 people attending a community meeting by asking each attendee to self-report their age. The dotplot below summarizes the ages.
Dotplot (age in years):
18 | ••••••••
19 | •••••
20 | ••••
21 | •••
22 | ••
23 | ••
24 | •
25 | •
26 | •
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 | •
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
50 | •
51 |
52 |
53 |
54 |
55 |
56 |
57 |
58 |
59 |
60 | •
Which feature of the distribution is most evident?
Answer: A clear gap between the early 20s and the older ages, suggesting possible outliers at 40, 50, and 60
This question assesses recognizing unusual features in dotplots of quantitative variables like ages. The dotplot clusters most dots from 18 to 26 years, with a large gap from 27 to 39, followed by isolated dots at 40, 50, and 60, highlighting a clear gap and potential outliers in older ages. The main body is skewed right within the young group, but the gap is the most striking feature. Choice E distracts by suggesting bimodality with equal peaks at 18 and 60, but the 'peak' at 60 is just one dot, not comparable. In distribution descriptions, always scan for gaps or outliers, as they can indicate data collection issues or distinct subpopulations, alongside shape, center, and spread.
