atlanta-86
chicago-80
duluth-62
fargo-66
miamai-86
omaha-71
san diego-75
san fransisco-68
which best describes the data?
a-the temperatures vary by 23degrees
b-the interquartile range is 15degrees
i got b but my teacher said it was wrong can you pleaser explain?
To determine which best describes the data, let's first understand what the two options mean:
a) "The temperatures vary by 23 degrees": This statement suggests that there is a large difference between the minimum and maximum temperatures in the data set.
b) "The interquartile range is 15 degrees": The interquartile range (IQR) is a measure of the dispersion or variability in a data set. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). In this case, an IQR of 15 degrees would mean that there is a significant difference between the data points within the middle 50% range.
Now, let's analyze the given data to come to a conclusion:
The given temperatures are as follows:
Atlanta: 86
Chicago: 80
Duluth: 62
Fargo: 66
Miami: 86
Omaha: 71
San Diego: 75
San Francisco: 68
To find the answer, we need to calculate the range and the interquartile range.
1. Range: The range is the difference between the highest and lowest values in the data set. In this case, Atlanta has the highest temperature of 86 degrees, and Duluth has the lowest temperature of 62 degrees. Therefore, the range is 86 - 62 = 24 degrees.
2. Interquartile Range (IQR): To calculate the IQR, we first need to find Q1 and Q3. Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
Arranging the data in ascending order:
62, 66, 68, 71, 75, 80, 86, 86
Q1: The lower half of the data consists of 62, 66, 68. As there are three values, the median of this half is 66.
Q3: The upper half of the data consists of 71, 75, 80, 86, 86. As there are five values, the median of this half is 80.
Now, the IQR is calculated as Q3 - Q1 = 80 - 66 = 14 degrees, not 15 degrees.
So, the correct answer is not b) "The interquartile range is 15 degrees." The correct answer would be a) "The temperatures vary by 23 degrees" since the range of the data set is 24 degrees.
It's possible that your teacher made a mistake, or there may be a misunderstanding. It's worth clarifying with your teacher to ensure accurate grading and understanding of the concepts.