The area of Ohio is 44,826 square miles, the area of Kentucky is 40,408 square miles, and the area of Indiana is 37,420 square miles. Round to the nearest hundred to estimate the area of all 3 states.
Rounded to the nearest hundred, the estimated area of all three states is 44,800 + 40,400 + 37,400 = 122,600 square miles.
Use the image to answer the question.
A number line ranges from 60 to 100 in increments of 5. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 65 to 70. The second box extends from 70 to 80. A line extends from each end of the box, terminating at 60 on the left and terminating at 100 on the right.
For the given box plot, which measure of center—mean or median—best represents the shape of the distribution? Enter 1 for median or 2 for mean.
(1 point)
1
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. In years, how much higher is the mean of the new dataset than the mean of the original dataset?(1 point)
year(s)
To find the mean of the original dataset, we sum up all the ages and divide by the number of individuals:
Original mean = (24 + 15 + 18 + 30 + 32 + 40 + 22 + 27 + 33 + 35) / 10 = 276 / 10 = 27.6.
Now, to form the new dataset, we replace the maximum age (40) with 50. The new dataset is: 24, 15, 18, 30, 32, 50, 22, 27, 33, 35.
New mean = (24 + 15 + 18 + 30 + 32 + 50 + 22 + 27 + 33 + 35) / 10 = 306 / 10 = 30.6.
To find the difference in means, we subtract the original mean from the new mean: 30.6 - 27.6 = 3.
Therefore, the mean of the new dataset is 3 years higher than the mean of the original dataset.
Use the table to answer the question.
Group 1 20 22 14 25 18 33 28 35 43 18
Group 2 16 24 30 26 28 32 34 23 25 33
The math scores of the two groups of students are summarized in the table.
Which group of scores is more dispersed than the other?
(1 point)
Group
To determine which group of scores is more dispersed, we can compare the measures of spread, such as the range or the interquartile range.
For Group 1:
Range = maximum score - minimum score = 43 - 14 = 29
For Group 2:
Range = maximum score - minimum score = 34 - 16 = 18
Since the range of Group 1 (29) is larger than the range of Group 2 (18), we can conclude that Group 1 has more dispersion or is more spread out compared to Group 2.
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: 21; median: 24; mode: 32
mean: 21; median: 24; mode: 32
mean: 24; median: 24.5; mode: 20
mean: 24; median: 24.5; mode: 20
mean: 24; median: 21; mode: 32
mean: 24; median: 21; mode: 32
The correct answer is:
mean: 22.5; median: 21; mode: 32
To estimate the combined area of Ohio, Kentucky, and Indiana, we need to add up the individual areas of each state and round to the nearest hundred.
The area of Ohio is 44,826 square miles.
The area of Kentucky is 40,408 square miles.
The area of Indiana is 37,420 square miles.
To estimate the combined area, we add up these values: 44,826 + 40,408 + 37,420 = 122,654
Rounding 122,654 to the nearest hundred, we find that the estimated combined area of Ohio, Kentucky, and Indiana is 122,700 square miles.