http://www.ck12.org Chapter 2. Visualizations of Data
3.
If we disregard the three outliers, the distribution of water capacities in Utah is higher than that of Idaho
at every point in the five number summary. From this we might conclude it is centered higher and that
the reservoir system is overall at safer levels in Utah, than in Idaho. Again eliminating the outliers, both
distributions are roughly symmetric and their spreads are also fairly similar. The middle 50% of the data for
Utah is just slightly more closely grouped.- (e) If the mean is greater than the median, then it has been pulled to the right either by an outlier, or by a
skewed right shape. The median will not be affected by either of those things. - (a) 3. 12 , 3. 22 , 3. 282 , 3. 393 , 3 .528 (b)
IQR=. 173
1. 5 ∗IQR=. 2595Upper bound for outliers>. 2595 + 3. 393 = 3 .6525. There is no data above 3.528 Lower bound for outliers
< 3. 22 −. 2595 = 2 .9605. There is no data below 3.12, so there are no outliers. (c)(d) By dividing the data by 3.7854, we will obtain the average cost per liter. The mean, median will be
decreased, being divided by 3.7854. The same is true for the measures of spread (range, IQR, and standard
deviation), which will result in the data being compressed into a smaller area if we were to graph both
distributions on the same scale. The shape of the distributions will remain the same. (e)TABLE2.31:
State Average Price of a Gallon of
Gasoline(US$)Average Price of a Liter of Gaso-
line
Alaska 3. 458 0. 914
Washington 3. 528 0. 932
Idaho 3. 26 0. 861
Montana 3. 22 0. 851