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Introduction to Statistical Thinking

Benjamin Yakir

Section 3.5 Exercises

Checkpoint 3.5.1.

Three sequences of data were saved in 3 R objects named “x1”, “x2” and “x3”, respectively. The application of the function “summary” to each of these objects is presented below:
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> summary(x1)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.000   2.498   3.218   3.081   3.840   4.871
> summary(x2)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
0.0001083 0.5772000 1.5070000 1.8420000 2.9050000 4.9880000
> summary(x3)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  2.200   3.391   4.020   4.077   4.690   6.414
In Figure 3.5.2 one may find the histograms of these three data sequences, given in a random order. In Figure 3.5.3 one may find the box plots of the same data, given in yet a different order.
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Three histograms labeled Histogram 1, Histogram 2, and Histogram 3
Figure 3.5.2. Three Histograms
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Three box plots labeled Boxplot 1, Boxplot 2, and Boxplot 3
Figure 3.5.3. Three Box Plots
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  1. Match the summary result with the appropriate histogram and the appropriate box plot.
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  2. Is the value 0.000 in the sequence “x1” an outlier?
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  3. Is the value 6.414 in the sequence “x3” an outlier?
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Checkpoint 3.5.4.

The number of toilet facilities in 30 buildings were counted. The results are recorded in an R object by the name “x”. The frequency table of the data “x” is:
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> table(x)
x
 2  4  6  8 10
10  6 10  2  2
  1. What is the mean (\(\bar x\)) of the data?
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  2. What is the sample standard deviation of the data?
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  3. What is the median of the data?
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  4. What is the inter-quartile range (IQR) of the data?
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  5. How many standard deviations away from the mean is the value 10?
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