Turn logged data into fancy plot

The golden rule of using the Macro Recorder:

The code is more what you'd call "guidelines" than actual rules.

It's there to tell you which objects/properties/methods to look at. Not to write your code for you.

Step 1: Clean up all the implicit references (Selection, Active*), indenting and line continuations

When the Recorder spits out this code:

Thing.Select
Selection.DoThing
Selection.Child.DoThing
Selection.Child.Child.Property =  _
    Value

You re-write it like so:

Thing.DoThing
Thing.Child.DoThing
Thing.Child.Child.Property = Value

And then like so:

With Thing
    .DoThing
    With .Child
        .DoThing
        .Child.Property = Value
    End With
End With

And then you go and put Thing in a proper variable so you can apply it to any generic ThingObject:

Dim targetThing as ThingObject
Set targetThing = Thing

With targetThing 
    .DoThing
    With .Child
        .DoThing
        .Child.Property = Value
    End With
End With

Applying to your code:

Dim targetCol As Range
Set targetCol = Columns("A:A")

With targetCol
    .FormatConditions.AddColorScale ColorScaleType:=3
    .FormatConditions(.FormatConditions.Count).SetFirstPriority
    .FormatConditions(1).ColorScaleCriteria(1).Type = xlConditionValueLowestValue
End With

With targetCol.FormatConditions(1).ColorScaleCriteria(1).FormatColor
    .Color = 7039480
    .TintAndShade = 0
End With

With targetCol.FormatConditions(1).ColorScaleCriteria(2)
    .Type = xlConditionValuePercentile
    .value = 50
    With .FormatColor
        .Color = 8711167
        .TintAndShade = 0
    End With
End With

With targetCol.FormatConditions(1).ColorScaleCriteria(3)
    .Type = xlConditionValueHighestValue
    With .FormatColor
        .Color = 8109667
        .TintAndShade = 0
    End With
End With

Dim targetSheet As Worksheet
Set targetSheet = ActiveSheet

Dim targetChart As Chart
Set targetChart = targetSheet.AddChart2(227, xlLine)

targetChart.SetSourceData source:=Range("Sheet1!$A:$A")
targetChart.FullSeriesCollection(1).Trendlines.Add Type:=xlMovingAvg, Period:=2, Forward:=0, Backward:=0 _
, DisplayEquation:=0, DisplayRSquared:=0, Name:="2 per. Mov. Avg. (Series1)"
targetChart.ClearToMatchStyle
targetChart.ChartStyle = 233

With targetChart.FullSeriesCollection(1).Trendlines(1).Format.Line
    .Visible = msoTrue
    .ForeColor.ObjectThemeColor = msoThemeColorAccent2
    .ForeColor.TintAndShade = 0
    .ForeColor.Brightness = -0.25
    .Transparency = 0
End With

Range("C1").FormulaR1C1 = "Average:"
Range("D1").FormulaR1C1 = "=AVERAGE(C[-3])"
Range("C2").FormulaR1C1 = "Minimum:"
Range("D2").FormulaR1C1 = "=MIN(C[-3])"
Range("C3").FormulaR1C1 = "Maximum:"
Range("D3").FormulaR1C1 = "=MAX(C[-3])"
Range("C4").FormulaR1C1 = "Median:"
Range("D4").FormulaR1C1 = "=MEDIAN(C[-3])"

and already it's much clearer how things are structured and what's going on. It's also clearly separated into 3 distinct operations (Add conditional Formatting, Add Chart, Add Summary Stats) which should be refactored into separate Subs.

Step 2: Initial Refactoring

Moving the 3 stages to separate subs. Tweaked the naming. Made AddLineChart a function which returns the chart object after creation for further manipulation (if desired). Made the summary stat ranges relative to the topLeftCell so you can move the table around by changing just one range declaration:

Option Explicit

Public Sub Stats()

    Dim dataRange As Range
    Set dataRange = Columns("A:A")

    AddConditionalFormatting dataRange


    Dim targetSheet As Worksheet
    Set targetSheet = ActiveSheet

    Dim targetChart As Chart
    Set targetChart = CreateLineChart(dataRange, targetSheet)


    Dim summaryStartCell As Range
    Set summaryStartCell = targetSheet.Range("C1")
    AddSumaryStats summaryStartCell '/ Moved the range declarations to be relative to base cell for portability.

End Sub

Public Sub AddConditionalFormatting(ByRef dataRange As Range)

    With dataRange
        .FormatConditions.AddColorScale ColorScaleType:=3
        .FormatConditions(.FormatConditions.Count).SetFirstPriority
        .FormatConditions(1).ColorScaleCriteria(1).Type = xlConditionValueLowestValue
    End With

    With dataRange.FormatConditions(1).ColorScaleCriteria(1).FormatColor
        .Color = 7039480
        .TintAndShade = 0
    End With

    With dataRange.FormatConditions(1).ColorScaleCriteria(2)
        .Type = xlConditionValuePercentile
        .value = 50
        With .FormatColor
            .Color = 8711167
            .TintAndShade = 0
        End With
    End With

    With dataRange.FormatConditions(1).ColorScaleCriteria(3)
        .Type = xlConditionValueHighestValue
        With .FormatColor
            .Color = 8109667
            .TintAndShade = 0
        End With
    End With

End Sub

Public Function CreateLineChart(ByRef dataRange As Range, ByRef targetSheet As Worksheet) As Chart

    Dim newChart As Chart
    Set newChart = targetSheet.AddChart2(227, xlLine)

    With newChart
        .SetSourceData source:=dataRange

        .FullSeriesCollection(1).Trendlines.Add Type:=xlMovingAvg, Period:=2, Forward:=0, Backward:=0 _
        , DisplayEquation:=0, DisplayRSquared:=0, Name:="2 per. Mov. Avg. (Series1)"

        .ClearToMatchStyle
        .ChartStyle = 233
    End With

    With newChart.FullSeriesCollection(1).Trendlines(1).Format.Line
        .Visible = msoTrue
        With .ForeColor
            .ObjectThemeColor = msoThemeColorAccent2
            .TintAndShade = 0
            .Brightness = -0.25
        End With
        .Transparency = 0
    End With

    Set CreateLineChart = newChart

End Function

Public Sub AddSummaryStats(ByRef baseCell As Range)

    Dim rowOffset As Long

    rowOffset = 0
    baseCell.Offset(rowOffset, 0).FormulaR1C1 = "Average:"
    baseCell.Offset(rowOffset, 1).FormulaR1C1 = "=AVERAGE(C[-3])"

    rowOffset = rowOffset + 1
    baseCell.Offset(rowOffset, 0).FormulaR1C1 = "Minimum:"
    baseCell.Offset(rowOffset, 1).FormulaR1C1 = "=MIN(C[-3])"

    rowOffset = rowOffset + 1
    baseCell.Offset(rowOffset, 0).FormulaR1C1 = "Maximum:"
    baseCell.Offset(rowOffset, 1).FormulaR1C1 = "=MAX(C[-3])"

    rowOffset = rowOffset + 1
    baseCell.Offset(rowOffset, 0).FormulaR1C1 = "Median:"
    baseCell.Offset(rowOffset, 1).FormulaR1C1 = "=MEDIAN(C[-3])"

End Sub

And now we've successfully split our task into 3 small, distinct, operations that can be further analysed/improved/refactored as necessary.