Analyze Data Shape and Context Quick Check
1 of 51 of 5 Items
Question
Summarize the dataset by finding its measures of center—mean, median, and mode.
20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32
(1 point)
Responses
mean: 22.5; median: 21; mode: 20
mean: 22.5; median: 21; mode: 20
mean: 24; median: 21; mode: 32
mean: 24; median: 21; mode: 32
mean: 21; median: 24; mode: 32
mean: 21; median: 24; mode: 32
mean: 24; median: 24.5; mode: 20
I apologize for the incorrect response. Let's analyze the dataset again:
20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32
The correct measures of center are:
- Mean: the sum of all the values divided by the total number of values. Here, the mean is (20+30+32+16+31+32+13+20+28+32+15+18+20+21+32) / 15 = 24.
- Median: the middle value when the data is arranged in ascending order. Here, when the data is sorted in ascending order, the values are 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32. Since there are 15 values, the middle value is the 8th value, which is 21.
- Mode: the most common value(s) in the dataset. Here, the mode is 32, as it appears the most times in the dataset.
Therefore, the correct answer is:
mean: 24; median: 21; mode: 32
Analyze Data Shape and Context Quick Check
1 of 51 of 5 Items
Question
Summarize the dataset by finding its measures of center—mean, median, and mode.
20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32
(1 point)
Responses
mean: 22.5; median: 21; mode: 20
mean: 22.5; median: 21; mode: 20
mean: 24; median: 21; mode: 32
mean: 24; median: 21; mode: 32
mean: 21; median: 24; mode: 32
mean: 21; median: 24; mode: 32
mean: 24; median: 24.5; mode: 20
its wrong
Analyze Data Shape and Context Quick Check
2 of 52 of 5 Items
Question
Here are the prices for biweekly lawn mowing services for 13 local companies:
15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
Which measure of center—mean or median—best represents the shape of the distribution?
(1 point)
Responses
Median; the shape of the distribution is skewed to the right.
Median; the shape of the distribution is skewed to the right.
Mean; the shape of the distribution is close to symmetrical.
Mean; the shape of the distribution is close to symmetrical.
Median; the shape of the distribution is skewed to the left.
Median; the shape of the distribution is skewed to the left.
Mean; the shape of the distribution is skewed to the left.
Mean; the shape of the distribution is skewed to the left.
To determine which measure of center best represents the shape of the distribution, we can look at the data:
15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
The data appears to have a few values that are lower (15, 20) and a few values that are higher (50), with the majority of values centered around 40. This suggests that the distribution is skewed to the right.
In this case, the median is a better measure of center because it is less affected by extreme values. The median divides the data into two halves, with 50% of the values below it and 50% of the values above it. This measure is not influenced by the extreme values of 15 and 50, giving a better representation of the central tendency of the data.
Therefore, the correct answer is:
Median; the shape of the distribution is skewed to the right.
Analyze Data Shape and Context Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A number line ranges from 2 to 9.5 in increments of 0.5. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 4 to 5.5. The second box extends from 5.5 to 7. A line extends from each end of the box, terminating at 2 on the left and terminating at 9.5 on the right.
For the given box plot, which measure of variability—range or IQR—best represents the shape of the distribution?
(1 point)
Responses
Range; the shape of the distribution is symmetrical, or close to it.
Range; the shape of the distribution is symmetrical, or close to it.
IQR, the shape of the distribution is skewed to the right.
IQR, the shape of the distribution is skewed to the right.
IQR, the shape of the distribution is symmetrical, or close to it.
IQR, the shape of the distribution is symmetrical, or close to it.
Range, the shape of the distribution is skewed to the right.
Range, the shape of the distribution is skewed to the right.
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To determine which measure of variability best represents the shape of the distribution, we need to analyze the box plot provided.
A box plot represents the five-number summary of the dataset, which includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box in the plot represents the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The line extending from each end of the box indicates the range, which is the distance between the minimum and maximum values.
In this case, the box plot shows the box extending from 4 to 7, indicating that the majority of the data is clustered within this range. The range, which is the distance between the minimum and maximum values on the number line, is not as representative of the shape of the distribution, as it considers all the data points.
Therefore, the IQR, which shows the range between the first quartile (Q1) and third quartile (Q3) and represents the middle 50% of the data, is a better measure of variability for this distribution.
Thus, the correct answer is:
IQR; the shape of the distribution is symmetrical, or close to it.
Analyze Data Shape and Context Quick Check
4 of 54 of 5 Items
Question
The ages (in years) of 10 randomly selected individuals are 24, 15, 18, 30, 32, 40, 22, 27, 33, and 35. Form a new dataset by replacing the maximum age with 50. Which statement best compares the two datasets?(1 point)
Responses
The mean of the new dataset is higher than the mean of the original dataset.
The mean of the new dataset is higher than the mean of the original dataset.
The mean of the new dataset is lower than the mean of the original dataset.
The mean of the new dataset is lower than the mean of the original dataset.
The original dataset is more dispersed than the new dataset.
The original dataset is more dispersed than the new dataset.
The range of the original dataset is higher than the range of the new dataset.
To compare the two datasets, let's first analyze the original dataset and the new dataset after replacing the maximum age:
Original dataset: 24, 15, 18, 30, 32, 40, 22, 27, 33, 35
New dataset: 24, 15, 18, 30, 32, 40, 22, 27, 33, 50
To compare the means of the two datasets, we calculate the average of the values:
Mean of the original dataset = (24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 35) / 10 = 26.6
Mean of the new dataset = (24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 50) / 10 = 28.1
Therefore, the mean of the new dataset (28.1) is indeed higher than the mean of the original dataset (26.6).
Now, let's analyze the range of the two datasets:
Range of the original dataset = Maximum value - Minimum value = 40 - 15 = 25
Range of the new dataset = Maximum value - Minimum value = 50 - 15 = 35
Therefore, the range of the new dataset (35) is higher than the range of the original dataset (25).
To summarize:
- The mean of the new dataset is higher than the mean of the original dataset.
- The range of the new dataset is higher than the range of the original dataset.
Thus, the correct answer is:
The mean of the new dataset is higher than the mean of the original dataset.
The range of the original dataset is higher than the range of the new dataset.