Here are the high temperatures (in Fahrenheit) for a 10-day period in Salinas, California, in December:
58, 59, 61, 62, 62, 62, 63, 64, 66, 67
Find the range and explain what the value means for this dataset.
(2 points)
The range is
degrees Fahrenheit; this is the difference in degrees Fahrenheit between
degrees, the minimum temperature, and
degrees, the maximum
temperature. The range for this dataset is 9 degrees Fahrenheit; this means that the highest temperature during this period was 67 degrees Fahrenheit and the lowest temperature was 58 degrees Fahrenheit.
Here are the science test scores from Ms. O’Donnell’s class:
55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100
Find the MAD.
(1 point)
The MAD is
.
To find the Mean Absolute Deviation (MAD), we need to first find the mean of the data set.
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100)/ 17
Mean = 1355/17
Mean ≈ 79.71
Next, we find the absolute deviation for each score by subtracting the mean from each score and taking the absolute value:
|55 - 79.71| = 24.71
|60 - 79.71| = 19.71
|70 - 79.71| = 9.71
|70 - 79.71| = 9.71
|75 - 79.71| = 4.71
|75 - 79.71| = 4.71
|75 - 79.71| = 4.71
|80 - 79.71| = 0.29
|80 - 79.71| = 0.29
|85 - 79.71| = 5.29
|85 - 79.71| = 5.29
|85 - 79.71| = 5.29
|85 - 79.71| = 5.29
|90 - 79.71| = 10.29
|90 - 79.71| = 10.29
|95 - 79.71| = 15.29
|100 - 79.71| = 20.29
Next, we find the mean of the absolute deviations:
MAD = (24.71 + 19.71 + 9.71 + 9.71 + 4.71 + 4.71 + 4.71 + 0.29 + 0.29 + 5.29 + 5.29 + 5.29 + 5.29 + 10.29 + 10.29 + 15.29 + 20.29)/ 17
MAD = 144.71/17
MAD ≈ 8.51
Therefore, the Mean Absolute Deviation (MAD) is approximately 8.51.
Its wrong
Apologies for the error. Let's calculate the Mean Absolute Deviation (MAD) correctly.
To calculate the MAD, we need to find the deviation of each score from the mean, take the absolute value of each deviation, and then find the mean of those absolute deviations.
First, let's find the mean of the data set:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1410 / 17
Mean ≈ 82.94
Next, calculate the deviation for each score by subtracting the mean from each score:
|55 - 82.94| = 27.94
|60 - 82.94| = 22.94
|70 - 82.94| = 12.94
|70 - 82.94| = 12.94
|75 - 82.94| = 7.94
|75 - 82.94| = 7.94
|75 - 82.94| = 7.94
|80 - 82.94| = 2.94
|80 - 82.94| = 2.94
|85 - 82.94| = 2.06
|85 - 82.94| = 2.06
|85 - 82.94| = 2.06
|85 - 82.94| = 2.06
|90 - 82.94| = 7.06
|90 - 82.94| = 7.06
|95 - 82.94| = 12.06
|100 - 82.94| = 17.06
Now, find the mean of the absolute deviations:
MAD = (27.94 + 22.94 + 12.94 + 12.94 + 7.94 + 7.94 + 7.94 + 2.94 + 2.94 + 2.06 + 2.06 + 2.06 + 2.06 + 7.06 + 7.06 + 12.06 + 17.06) / 17
MAD = 187.68 / 17
MAD ≈ 11.04
Therefore, the Mean Absolute Deviation (MAD) is approximately 11.04.
temperature.
To find the range, we subtract the minimum temperature from the maximum temperature:
Max temperature: 67°F
Min temperature: 58°F
Range = Max temperature - Min temperature
Range = 67°F - 58°F
Range = 9°F
So, the range of temperatures for this dataset is 9 degrees Fahrenheit. This means that the highest temperature recorded during this 10-day period was 9 degrees Fahrenheit warmer than the lowest temperature recorded.
temperature.
To find the range in this dataset, you need to subtract the minimum temperature from the maximum temperature. In this case, the minimum temperature is 58 degrees Fahrenheit, and the maximum temperature is 67 degrees Fahrenheit.
So, the range = maximum temperature - minimum temperature.
Range = 67°F - 58°F
Range = 9°F
Therefore, the range for this dataset is 9 degrees Fahrenheit. The range represents the difference between the highest and lowest values in the dataset. In this case, it means that the temperature varied by 9 degrees Fahrenheit over the 10-day period in Salinas, California in December.