left = Q1-1.5(IQR) mean = 100
right = Q3+1.5(IQR)
Ch3 Homework
need to compute:
min usual value = mean - 2(sd) = 100-2(20)=60
max usual value = mean + 2(sd) = 100+2(20)=140
1. Consider a data set with mean = 100 and s = 20. Is 150 an unusual value? Explain.
150 is not b/w the min usual value and max usual value.
2. Consider a data set with Q1 = 15 and Q3 = 20. Is 40 an outlier? Explain.
IQR = Q3-Q1 = 20-15=5
40 is not between the left fence and right fence, thus it is an outlier.
3. How does standard deviation (sd) affect the shape of the normal distribution? Sketch 2
normal distributions, one with a small sd and one with a big sd.
normal small big
4. Twenty hikers report the time in hours it took each one to complete Half-dome hike:
8,9,9,10,10,10,10,10,11,11,11,11,11,12,12,12,13,14,14,20
a) Find the mean and the standard deviation of the data.
b) Find the minimum usual value, the maximum usual value, and all unusual values.
c) How many percent of the data is usual?
5. Consider the boxplot below
a) Identify Q1, Q2, Q3, and min/max data values that are not outliers, and all outliers.
b) Is the mean more than the median, less than the median, or equal to the median? Explain.
6. Consider the boxplot of data sets (a), (b), (c), and (d) below. (4pts each)
dots are outliers and outliers skew the mean towards their direction.
outlier on the right side skew to the right biggest mean
outliers on left side to the left smallest mean
Which data set has the smallest mean and which has highest mean? Explain.
b a
7. The age of 30 employees in a small Bay Area company are listed below
19,33,45,56,73,39,44,55,62,39,45,33,45,40,30,35,45,55,51,42,44,56,60,66,67,58,44,45,70,60
a) Find the IQR, left fence, right fence, and all outliers.
b) Sketch a boxplot.
c) Find the minimum usual value, the maximum usual value, and all unusual values.
d) Construct a frequency table begins with a minimum class limit of 10, a class width of 10.
Draw a corresponding histogram and describe the shape of distribution.
