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Summary Statistics and Basic Plots in R

The original guide’s Module 5 loaded ten years of AAPL closing prices and used R to derive the summary statistics and rudimentary plots that Excel and StatTools users already know: histogram, range, quartiles, mean/median, box plot, variance/standard deviation, Z score, range normalisation, skewness/kurtosis, normal probabilities and the log transform.

The original training bundle’s AAPL.csv (Bundle\Data\Equity\Equity\AAPL.csv) is not present in this validation environment, so every snippet below runs against a synthetic ten-year daily series (Interim_Buffer_Date, Interim_Close, 2,518 rows, generated with set.seed(42) from a drifting, noisy random walk rescaled to the same 50.67-to-702.10 range the original guide describes) rather than the real historical prices. The series keeps the same character the guide discusses — a positive skew, a mean above the median — but the individual statistic values differ from the original text and should be read as illustrative, not as the historical AAPL numbers. readr::read_csv() was also swapped for base R’s read.csv(), which is already present in the container and returns an equivalent data frame; readr itself failed to build in the shared validation container. The moments package (needed for skewness()/kurtosis(), Procedure 10) was installed cleanly into the shared library.

Procedure 1: Create a Histogram of Time Series Data in R

A data frame is loaded from the CSV and its Interim_Close column — the column of interest throughout this module — is histogrammed with the base hist() function:

AAPL <- read.csv("AAPL.csv")

head(AAPL)

hist(AAPL$Interim_Close)

Console output:

  Interim_Buffer_Date Interim_Close
1          2005-01-03         63.44
2          2005-01-04         62.80
3          2005-01-05         63.30
4          2005-01-06         64.16
5          2005-01-07         64.73
6          2005-01-08         64.65

hist() draws to the graphics device rather than the console, so the snippet’s only console effect is the head() call above it; the chart itself shows a strong positive skew, the bulk of the mass at low prices and a thinning tail towards the historical maximum.

Tool equivalent: Jube.Charting.Chart.Histogram() — Chart.Histogram().Values("Interim Close", values).Render() bins the same array with Freedman-Diaconis nice bins (or precomputed bins/an overlay of several series) and renders it as a dependency-free SVG string. This, not hist() or ggplot2, is what the product draws.

Procedure 2: Establish Range in R

min() and max() give the extremes; range() returns both in one call, and diff(range(x)) collapses that to a single spread value:

AAPL <- read.csv("AAPL.csv")

min(AAPL$Interim_Close)
max(AAPL$Interim_Close)
range(AAPL$Interim_Close)
diff(range(AAPL$Interim_Close))

Console output:

[1] 50.67
[1] 702.1
[1]  50.67 702.10
[1] 651.43

Tool equivalent: Jube.Service.Agent.AdvancedAnalyticsTools.DescriptiveStatistics .CentralTendencyTools / tool "MinimumMaximumRange" — one call returns the minimum, maximum, their difference (the range) and their midpoint (the midrange) together, explicitly flagging that the range is sensitive to outliers and pointing at InterquartileRange for a robust alternative.

Procedure 3: Calculate Quartiles and the Interquartile Range

IQR() gives the spread of the middle half directly; quantile() gives the full five-point breakdown (minimum, three quartiles, maximum) that the IQR is derived from:

AAPL <- read.csv("AAPL.csv")

IQR(AAPL$Interim_Close)
quantile(AAPL$Interim_Close)

Console output:

[1] 173.8625
      0%      25%      50%      75%     100% 
 50.6700  73.8900  98.8100 247.7525 702.1000

Tool equivalent: DescriptiveStatistics.SpreadAndShapeTools / tool "InterquartileRange" for the single IQR value (robust to outliers, the basis of the box-plot fence), and DescriptiveStatistics.QuantileRankAndFrequencyTools / tool "FiveNumberSummary" for the full minimum/Q1/median/Q3/maximum breakdown — it also returns the standard 1.5x and 3x IQR box-plot fences that quantile() alone does not.

Procedure 4: Establish the Mean and Median in R

The mean sums and divides by the count; the median is the middle value once the vector is sorted:

AAPL <- read.csv("AAPL.csv")

mean(AAPL$Interim_Close)
median(AAPL$Interim_Close)

Console output:

[1] 169.0461
[1] 98.81

The mean sitting well above the median is itself a symptom of the positive skew visible in Procedure 1’s histogram.

Tool equivalent: DescriptiveStatistics.CentralTendencyTools / tools "Mean" and "Median" — the same default-versus-robust framing carries over: Mean is the default measure of typical level for roughly symmetric data, and the tool description itself recommends Median once extreme outliers are present.

Procedure 5: Create a Box Plot

boxplot() draws the five-point summary (whiskers at the observed minimum and maximum, box at Q1 and Q3, thick line at the median) in one call:

AAPL <- read.csv("AAPL.csv")

boxplot(AAPL$Interim_Close)

boxplot(), like hist(), only draws to the graphics device — there is no console output to capture. The box is visibly compressed towards the lower end of the range with a long upper whisker, the same skew already read off the histogram and the mean/median gap.

AdvancedAnalytics equivalent: Jube.Charting.Chart.BoxPlot() — Chart.BoxPlot().FromValues("Interim Close", values).Render() computes the Tukey fences and outliers from the raw array (or accepts stated statistics directly) and renders the box plot as SVG. As with the histogram, this is the product’s only charting path — never ggplot2, never a base R graphics device.

Procedure 6: Navigate Plots and Export Visualisations

This procedure is pure RStudio interface touring: paging back and forth between the Plots pane’s history with the back/forward arrows, and using the Export button to copy a plot to the clipboard as a bitmap for pasting into Word, PowerPoint or Excel. It has no statistical content and no Tool equivalent to discuss — a chart built with Jube.Charting is an SVG string returned to the caller (or embedded in a page), not an image copied between desktop applications.

Procedure 7: Create the Variance and Standard Deviation

summary() gives the min/Q1/median/mean/Q3/max in one call but omits variance and standard deviation, which need var() and sd() directly:

AAPL <- read.csv("AAPL.csv")

summary(AAPL$Interim_Close)
var(AAPL$Interim_Close)
sd(AAPL$Interim_Close)
mean(AAPL$Interim_Close) + sd(AAPL$Interim_Close)

Console output:

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  50.67   73.89   98.81  169.05  247.75  702.10 
[1] 19018.95
[1] 137.9092
[1] 306.9553

Adding the standard deviation to the mean gives an upper one-sigma band of 306.96; because the equivalent lower band (mean minus one standard deviation) falls below the series’ own minimum, the “68% within one standard deviation” rule of thumb for a normal distribution does not really hold here, consistent with the skew already seen in Procedures 1 and 5.

Tool equivalent: DescriptiveStatistics.TableAndTransformTools / tool "DescribeColumn" for the summary() step — a single richer profile (count, missing, mean, median, spread, quartiles, skewness, kurtosis, percentiles 1-99, outlier counts by three different rules and a plain-language reading of the shape) rather than six bare numbers. DescriptiveStatistics.SpreadAndShapeTools / tools "Variance" and "StandardDeviation" cover var() and sd() directly.

Procedure 8: Calculate a Z Score

A Z score expresses how many standard deviations a value sits from the mean: (value - mean) / sd. Taking 150 as the test value:

AAPL <- read.csv("AAPL.csv")

(150 - mean(AAPL$Interim_Close)) / sd(AAPL$Interim_Close)

Console output:

[1] -0.1381057

150 sits a little under one-seventh of a standard deviation below the mean — close to average by this measure, though the same reservations about non-normal shape from Procedure 7 apply to how much that should be trusted.

Tool equivalent: DescriptiveStatistics.TableAndTransformTools / tool "ZScores" — standardises every value in a series to (value - mean) / standard deviation in one call and returns the centre and scale it used, rather than requiring the formula to be written out by hand for a single value.

Procedure 9: Create a Range Normalisation for a Value

Range (min-max) normalisation places a value on a 0-to-1 scale between the observed minimum and maximum: (value - min) / (max - min). Taking the same test value of 150:

AAPL <- read.csv("AAPL.csv")

(150 - min(AAPL$Interim_Close)) / (max(AAPL$Interim_Close) - min(AAPL$Interim_Close))

Console output:

[1] 0.1524799

150 sits at about 15% of the way from the observed minimum to the observed maximum.

Tool equivalent: Jube.Service.Agent.AdvancedAnalyticsTools.DataPreparationAndResampling .ScalingTools / tool "FitTableScaler" with TableScalingMethod.MinMax — learns the same (value - minimum) / range rescaling per column from a batch of rows and returns the centres/scales so "ApplyTableScaler" can transform new data identically later; this lives in DataPreparationAndResampling rather than DescriptiveStatistics, since range normalisation is a data-preparation transform rather than a descriptive measurement.

Procedure 10: Create the Skewness and Kurtosis Statistics

Skewness and kurtosis are not in base R; they come from the moments package. Skewness measures the lean towards or away from the y-axis, and kurtosis measures how tall or flat the distribution is relative to normal:

library(moments)

AAPL <- read.csv("AAPL.csv")

skewness(AAPL$Interim_Close)
kurtosis(AAPL$Interim_Close)

Console output:

[1] 1.639552
[1] 5.197058

The positive skewness confirms the right-lean already seen in the histogram; the kurtosis well above 3 means the distribution is more sharply peaked with heavier tails than a normal distribution of the same variance.

Tool equivalent: DescriptiveStatistics.SpreadAndShapeTools / tools "Skewness" and "Kurtosis" — Kurtosis is the Pearson (non-excess) form scoring 3 for a normal distribution, matching what moments::kurtosis() returns (as opposed to the tool "ExcessKurtosis", which is centred on 0). Both tools state their rule-of-thumb thresholds (skewness beyond +/-1 is “strongly skewed”) directly in their descriptions.

Procedure 11: Create Probabilities from a Test Value in a Normal Distribution

dnorm() gives a value’s height on the standard normal density curve; pnorm() gives the cumulative probability of drawing a value at or below it. Both take a Z score directly:

dnorm(1.5)
pnorm(1.5)

Console output:

[1] 0.1295176
[1] 0.9331928

A Z score of 1.5 sits at about 93.3% cumulative probability under a standard normal curve.

Tool equivalent: Jube.Service.Agent.AdvancedAnalyticsTools.DistributionsAndHistograms .UnivariateDistributionTools / tools "DistributionDensity" and "DistributionCumulativeProbability" — both take a DistributionKind (Normal, with parameters = [mean, standardDeviation]) and an array of points, so dnorm(1.5) becomes DistributionDensity(Normal, [0, 1], [1.5]) and pnorm(1.5) becomes DistributionCumulativeProbability(Normal, [0, 1], [1.5]) — evaluated over many points and many distribution families in one call, not just the normal.

Procedure 12: Create a Log Transformation

A natural log transform compresses a right-skewed series like this one towards symmetry, which is why it is a common first step before methods that assume roughly normal input:

AAPL <- read.csv("AAPL.csv")

AAPL$Log_Close <- log(AAPL$Interim_Close)

head(AAPL)

skewness_before <- moments::skewness(AAPL$Interim_Close)
skewness_after <- moments::skewness(AAPL$Log_Close)
skewness_before
skewness_after

Console output:

  Interim_Buffer_Date Interim_Close Log_Close
1          2005-01-03         63.44  4.150095
2          2005-01-04         62.80  4.139955
3          2005-01-05         63.30  4.147885
4          2005-01-06         64.16  4.161380
5          2005-01-07         64.73  4.170225
6          2005-01-08         64.65  4.168988
[1] 1.639552
[1] 0.7134221

The log-transformed column’s skewness (0.71) is markedly lower than the original series’ skewness (1.64): the transform has genuinely pulled the distribution’s shape towards symmetry, not just changed its scale.

Tool equivalent: DataPreparationAndResampling.ScalingTools / tool "ApplyColumnFunction" with ColumnFunction.NaturalLog — applies ln(x + offset) to every cell of a table in one call (offset handles zeros), alongside log10, log2, log1p, signed-log1p and several other fixed functions, and reports how many cells were undefined for the function chosen.

Procedure 13: Reverse a Log Transformation

The natural log is undone with exp(); applying it to the logged column should recover the original values exactly, subject to floating-point rounding:

AAPL <- read.csv("AAPL.csv")

AAPL$Log_Close <- log(AAPL$Interim_Close)

AAPL$Restored_Close <- exp(AAPL$Log_Close)

head(AAPL)

all.equal(AAPL$Interim_Close, AAPL$Restored_Close)

Console output:

  Interim_Buffer_Date Interim_Close Log_Close Restored_Close
1          2005-01-03         63.44  4.150095          63.44
2          2005-01-04         62.80  4.139955          62.80
3          2005-01-05         63.30  4.147885          63.30
4          2005-01-06         64.16  4.161380          64.16
5          2005-01-07         64.73  4.170225          64.73
6          2005-01-08         64.65  4.168988          64.65
[1] TRUE

Tool equivalent: none found — ApplyColumnFunction’s ColumnFunction enum (NaturalLog, Log10, Log2, Log1P, SignedLog1P, Sqrt, SignedSqrt, CubeRoot, Reciprocal, Square, AbsoluteValue) has no exponential entry to reverse a log transform it applied; FitTableScaler / InvertTableScaler (Procedure 9) invert a scaler they fitted, not an arbitrary column function. Reversing ApplyColumnFunction(NaturalLog) today has no dedicated tool and would need to be done by the caller.