The histogram available below shows the average annual combined premium (in doll
ID: 3040849 • Letter: T
Question
The histogram available below shows the average annual combined premium (in dollars) for auto insurance paid in 50 regions. Complete parts (a) through (f) below.
(a) Which holds more regions, the interval from $700 to $800 or the interval from $800 to $900?
The interval from _____ (700 to 800, 800 to 900) hold more regions because the bar over this interval is _____ (taller, shorter).
(b) Estimate the mean and median of the premiums from the histogram. Be sure to attach the appropriate units to your estimates.
The mean is approximately _____(950, 1050, 1150, 1250) and the median is approximately ______ (850, 950, 1050, 1150).
(c) Which do you think is larger, the mean or median? Why?
The ____ (mean, median) is larger because the distribution is ______ (right skewed, left skewed, uniform, symmetric).
(d) Suggest an explanation for the multiple modes that are evident in the histogram. If the intervals in the histogram were wider, do you think there would still be two modes?
Which explanation below is plausible?
A. Cooler regions have higher premiums than warmer regions.
B. Wealthy regions have higher premiums than poorer regions.
C. Coastal regions have higher premiums than desert regions.
D. Urban regions have higher premiums than rural regions.
If the interval were wider, would there still be two modes?
A. No, the mode for the lower premiums would be obscured.
B. Yes, there will be two modes no matter the interval width.
C. Yes, until the interval becomes so wide, it contains all the data values.
D. No, the mode for the higher premiums would be obscured.
(e) Is the region with the highest rate slightly larger than the others or an outlier?
A. Since the interquartile range (IQR) is about 300, the highest rate is not within 1.5×IQR of the 75th percentile, so it is an outlier.
B. The highest rate is only slightly larger because the interquartile range (IQR) is about 300, so the highest rate is within 1.5×IQR of the 75th percentile.
C. The highest rate is only slightly larger because the interquartile range (IQR) is about 50, so the highest rate is within 1.5×IQR of the median.
D.Since the interquartile range (IQR) is about 50, the highest rate is not within 1.5×IQR of the median, so it is an outlier.
(f) Is the SD of these data closer to $200 or $600? (Use what you know about the relationship between the SD and the concentration of the data around the mean rather than trying to calculate the SD from the counts.)
The SD is closer to _____ (600, 200) because _________ (almost all, more than half) of the data values are less than this value from the mean.
15- 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500Explanation / Answer
(a) 800-900 and taller
(b) mean=1050, median=1050
(c) mean, right-skewed
(d)
(e)B. The highest rate is only slightly larger because the interquartile range (IQR) is about 300, so the highest rate is within 1.5×IQR of the 75th percentile.
(f) SD is closer to 200 because more than half
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