The histogram available below shows the average annual combined premium (in doll
ID: 3042240 • 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 egions, the interval from $500 to $600 or the interval from $600 to $700?
The interval from ($500 to $600/$600 to $700) holds more regions because the bar over this interval is (shorter/taller.)
(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/$650/$850/$750) and the median is approximately ($650/$950/$850/$750).
(c) Which do you think is larger, the mean or median? Why?
The (mean/median) is larger because the distribution is (uniform/right skewed/left skewed/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?
(da) Which explanation below is plausible?
A. Urban regions have higher premiums than rural regions.
B. Coastal regions have higher premiums than desert regions.
C. Wealthy regions have higher premiums than poorer regions.
D. Cooler regions have higher premiums than warmer regions.
(db) If the interval were wider, would there still be two modes?
A. Yes, there will be two modes no matter the interval width.
B. No, the mode for the lower premiums would be obscured.
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. The highest rate is only slightly larger because the interquartile range (IQR) is about 50, so the highest rate is within 1.5times×IQR of the median.
B. Since the interquartile range (IQR) is about 50, the highest rate is not within 1.5times×IQR of the median, so it is an outlier.
C. Since the interquartile range (IQR) is about 300, the highest rate is not within 1.5times×IQR of the 75th percentile, so it is an outlier.
D. The highest rate is only slightly larger because the interquartile range (IQR) is about 300, so the highest rate is within 1.5times×IQR of the 75th percentile.
(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 ($200/$600) because of the data values are less than this value from the mean.
Histogram of Insurance 15- 10 500 600 700 800 900 1,000 1,100 1,200 1,300 Average Premium (S)Explanation / Answer
a)The interval from ($600 to $700) holds more regions because the bar over this interval is (taller.)
b)The mean is approximately ($950 and the median is approximately ($850).
c) Right skewed because mean is greater than median
The (mean/) is larger because the distribution is (right skewed)
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