An illustration shows two sets of dot plots. One is titled Movie 1 and the other is Movie 2. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Movie 1, a number line with arrows on both ends ranges from 17 to 43 in increments of 1. There is 1 dot above 17, 18, 21, 22, 25, 26, 28, 29, 32, 33, 35, 36, 38, 40, and 43. There are 2 dots above 23 and 3 dots above 20. For Movie 2, the number line ranges from 24 to 50 in increments of 1. There is 1 dot above 25, 28, 32, 35, 36, 42, 43, 45, 47, 48, and 50. There are 2 dots above 30, 34, and 37, and 3 dots above 40.

The dot plots show the ages, in years, of people watching two movies at a local theater. Find the median age of the people who watched each movie.

(1 point)

27 answers

For Movie 1, the data points are: 17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43.

The median age is the middle value when the data is ordered from least to greatest. In this case, the median age is the 11th value out of 20 values, since there is an even number of data points.

11th value = 29

Therefore, the median age of people who watched Movie 1 is 29 years old.

For Movie 2, the data points are: 25, 28, 30, 30, 32, 34, 35, 36, 37, 40, 40, 42, 43, 45, 47, 48, 50.

The median age is the middle value when the data is ordered from least to greatest. In this case, the median age is the 9th value out of 17 values, since there is an odd number of data points.

9th value = 37

Therefore, the median age of people who watched Movie 2 is 37 years old.
wrong for movie 1
Apologies for the mistake. Let's correct the calculation for Movie 1's median age.

For Movie 1, the data points are: 17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43.

Since there are 20 data points, the median would be the average of the 10th and 11th values when the data is ordered.

Ordered data: 17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43.

The 10th value is 29 and the 11th value is 32.

Calculating the average of 29 and 32:

(29 + 32) / 2 = 61 / 2 = 30.5

Therefore, the median age of people who watched Movie 1 is 30.5 years old.
still wrong
I apologize for the error. Let's recalculate the median for Movie 1 correctly.

For Movie 1, the data points are: 17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43.

Since there are 20 data points, the median would be the average of the 10th and 11th values when the data is ordered.

Ordered data: 17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43.

The 10th value is 29 and the 11th value is 32.

Calculating the average of 29 and 32:

(29 + 32) / 2 = 61 / 2 = 30.5

Therefore, the median age of people who watched Movie 1 is 30.5 years old.
Ten randomly selected people were asked to join a fitness group. Over the next two weeks, they were tested on how many push-ups they could do. The data shows the number of push-ups they did over the two weeks. From the first to the second week, what was the increase in the median number of push-ups?

Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10

(1 point)
To find the increase in the median number of push-ups from the first week to the second week, we first need to calculate the medians for each week.

Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Arranged in ascending order: 5, 5, 6, 8, 8, 8, 9, 10, 11, 15
Median for Week 1: (8 + 8) / 2 = 8

Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
Arranged in ascending order: 7, 8, 9, 9, 10, 10, 11, 11, 12, 18
Median for Week 2: (10 + 10) / 2 = 10

Now, we can find the increase in the median number of push-ups:
Increase in the median = Median for Week 2 - Median for Week 1
Increase in the median = 10 - 8
Increase in the median = 2

Therefore, the increase in the median number of push-ups from the first week to the second week was 2 push-ups.
Ten randomly selected people were asked to join a fitness group. Over the next two weeks, they were tested on how many push-ups they could do. The data shows the number of push-ups they did over the two weeks. What is the range of the number of push-ups people did each week?

Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
To find the range of the number of push-ups people did each week, we first need to calculate the highest and lowest values in each set of data.

Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Highest: 15
Lowest: 5
Range for Week 1: Highest - Lowest = 15 - 5 = 10

Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
Highest: 18
Lowest: 7
Range for Week 2: Highest - Lowest = 18 - 7 = 11

Therefore, the range of the number of push-ups people did in Week 1 was 10, and the range in Week 2 was 11.
the answer for movie 1 is 25.5, but why
To correctly find the median of Movie 1's data points (17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43), we need to follow these steps:

Step 1: Arrange the data in ascending order:
17, 18, 20, 21, 22, 23, 25, 25, 26, 28, 29, 32, 32, 33, 35, 35, 36, 38, 40, 43

Step 2: Calculate the median:
Since there are 20 data points, the median will be the average of the 10th and 11th values when the data is arranged in ascending order.

10th value is 29 and 11th value is 32.

Median = (29 + 32) / 2 = 61 / 2 = 30.5

Therefore, the median age for Movie 1 is indeed 30.5 years old.

Thank you for pointing out the error earlier, and I appreciate your understanding.
"An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13. For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15. "
The dot plots show the weights of randomly selected cats and small dogs in different households. Based on an informal assessment of the visual overlap of these distributions, which animal has the least variability in their weights? Why?
Based on the dot plots provided, we can visually assess the variability in weights for cats and small dogs. Variability is usually indicated by how spread out the data points are on the dot plots.

For Cats:
- The weights range from 9 to 13 pounds.
- The dots are concentrated mainly in the middle around a weight of 11 pounds, with somewhat equal numbers of dots below and above this middle value.

For Small Dogs:
- The weights range from 8 to 15 pounds.
- The dots are less concentrated around a single value compared to the cats. The dots are more spread out across the number line with some clustering around the middle values of 10, 11, and 12 pounds.

From the dot plots, it appears that the cats have less variability in their weights compared to small dogs. This conclusion is drawn based on the fact that the dots for cats are more clustered around a single value (11 pounds) with fewer extreme values, while the dots for small dogs are more spread out across the number line, indicating higher variability in weights.

Therefore, based on the visual assessment of the dot plots, cats have the least variability in their weights compared to small dogs.
answer choices;
Small dogs, because the range of their weights is less than that of cats.
Small dogs, because the range of their weights is less than that of cats.

Cats, because the range of their weights is greater than that of small dogs.
Cats, because the range of their weights is greater than that of small dogs.

Cats, because the range of their weights is less than that of small dogs.
Cats, because the range of their weights is less than that of small dogs.

Small dogs, because the range of their weights is greater than that of cats.
Based on the information provided in the dot plots, the correct answer is:
Small dogs, because the range of their weights is less than that of cats.

Explanation:
- The range is a measure of variability that is calculated as the difference between the highest and lowest values in a dataset.
- For cats, the weights range from 9 to 13 pounds, resulting in a range of 4 pounds.
- For small dogs, the weights range from 8 to 15 pounds, resulting in a range of 7 pounds.
- The smaller range for small dogs indicates less variability in their weights compared to cats.

Therefore, small dogs have less variability in their weights than cats based on the range metric provided in the dot plots.
i thought is was cats?
I apologize for the confusion in my response earlier. Let's reconsider the analysis based on the range of weights for cats and small dogs as displayed in the dot plots:

- Cats: The weights range from 9 to 13 pounds, resulting in a range of 4 pounds.
- Small Dogs: The weights range from 8 to 15 pounds, resulting in a range of 7 pounds.

Since the range is a measure of variability calculated as the difference between the highest and lowest values, we can see that the range of weights for cats is 4 pounds, while the range for small dogs is 7 pounds.

Therefore, the correct answer in this case is:
Cats, because the range of their weights is less than that of small dogs.

Thank you for your patience, and I appreciate the opportunity to clarify this assessment.
An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13. For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.
The dot plots show the weights of randomly selected cats and small dogs in different households. What is the difference between the modal weights of cats and small dogs?
To find the modal weights of cats and small dogs based on the dot plots provided, we look for the values with the highest frequency (largest number of dots) in each set of data.

For Cats:
- The frequency of weights for cats is: 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and 1 dot above 13.
- The modal weight for cats is 11 pounds since it has the highest frequency of 4 dots.

For Small Dogs:
- The frequency of weights for small dogs is: 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.
- The modal weight for small dogs is 10 pounds, as 10 has the highest frequency of 4 dots.

Therefore, the modal weight for cats is 11 pounds, and the modal weight for small dogs is 10 pounds.

The difference between the modal weights of cats and small dogs is 11 - 10 = 1 pound.

Therefore, the difference between the modal weights of cats and small dogs is 1 pound.
The data shows the number of miles run per week by randomly selected students from two different classes. Find the difference between the medians. Which class has a higher median? By how much?

Class 1: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Class 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
To find the difference between the medians of the two classes and determine which class has a higher median, let's first calculate the median for each class.

For Class 1:
Data: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Arranged in ascending order: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14

Since there are 15 data points, the median will be the value at the middle position. In this case, the middle value is the 8th value, which is 8.

For Class 2:
Data: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
Arranged in ascending order: 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 12

Since there are 15 data points, the median will be the average of the 8th and 9th values. The 8th value is 7 and the 9th value is 7, so the median is (7 + 7) / 2 = 7.

Now, let's find the difference between the median for Class 1 and Class 2:
Difference = Median of Class 1 - Median of Class 2
Difference = 8 - 7
Difference = 1 mile

Therefore, the difference between the medians of the two classes is 1 mile. Class 1 has a higher median than Class 2 by 1 mile.
Question
Two fertilizers are applied to randomly selected potato plants. After several weeks, the potatoes are weighed. The weights in kilograms are as follows. Which fertilizer is generally more effective?

Fertilizer A: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19
Fertilizer B: 28, 19, 18, 21, 24, 20, 25, 27, 29, 2
To determine which fertilizer is generally more effective based on the weights of the potato plants, we can compare the central tendency measures (such as mean or median) of the weights for both fertilizers. Let's start by calculating the mean weight for each fertilizer:

For Fertilizer A:
Weights: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19
Mean = (27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19) / 10
Mean = 202 / 10
Mean = 20.2 kg

For Fertilizer B:
Weights: 28, 19, 18, 21, 24, 20, 25, 27, 29, 20
Mean = (28 + 19 + 18 + 21 + 24 + 20 + 25 + 27 + 29 + 20) / 10
Mean = 221 / 10
Mean = 22.1 kg

Comparing the means:
- The mean weight for potatoes treated with Fertilizer A is 20.2 kg.
- The mean weight for potatoes treated with Fertilizer B is 22.1 kg.

Since Fertilizer B has a higher mean weight compared to Fertilizer A, we can conclude that Fertilizer B is generally more effective based on the mean weights of the potato plants.
Two number lines extend from 1 to 10 in increments of 1 and are labeled as Number of States Visited, Hiking Club, and Number of States Visited, Swimming Club. The number lines show an abacus-like representation with columns of open circles over the numbers. Above the number line labeled as Number of States Visited, Hiking Club, there are no circles over 1, two circles over 2, three circles over 3, five circles over 4, six circles over 5, five circles over 6, four circles over 7, three circles over 8, two circles over 9, and one circle over 10. Above the number line labeled as Number of States Visited, Swimming Club, there is one circle over 1, two circles over 2, one circle over 3, two circles over 4, two circles over 5, three circles over 6, four circles over 7, five circles over 8, six circles over 9, and six circles over 10.
For a geography project, you have surveyed the people in your hiking club and swimming club to find the number of states they have visited. You make a table and dot plots to show the results. Use the dot plots to compare the shapes and spreads of the dot plots. What conclusions can you draw about the shapes and the spreads?

(1 point)
Responses

The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed right. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10.
The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed right. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10.

The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has peaks at 9 and 10. The swimming club has a peak at 5.
The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has peaks at 9 and 10. The swimming club has a peak at 5.

The hiking club has a greater spread than the swimming club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10.
The hiking club has a greater spread than the swimming club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10.

The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10.
Based on the description of the dot plots for the Number of States Visited in the Hiking Club and the Swimming Club, we can draw conclusions about the shapes and spreads of the dot plots. Let's analyze the characteristics:

Hiking Club:
- Symmetrical plot with a peak at 5.
- The number of states visited follows a symmetric pattern, with an increasing number of visits towards the center and decreasing on either side.

Swimming Club:
- Skewed right plot with peaks at 9 and 10.
- The plot is asymmetric, indicating higher numbers of states visited towards the right side and fewer on the left side.

Comparing the spreads:
- The Swimming Club has a greater spread than the Hiking Club, as indicated by the more varied distribution of states visited in the Swimming Club.

Based on the dot plots and the characteristics described, the most accurate conclusion is:
"The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed right. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10."

Therefore, the Swimming Club's dot plot shows a greater spread than the Hiking Club's plot, with a skewed right distribution and peaks at 9 and 10.
actually skewed left
Thank you for the clarification. With the Swimming Club's dot plot being skewed left (with a peak at 5) instead of skewed right, the revised conclusion considering this correction is:

"The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10."

Therefore, the Swimming Club's dot plot shows a greater spread than the Hiking Club's plot, with a skewed left distribution and peaks at 9 and 10. Thank you for pointing out the correction.