Center measurements about the mean

Transform numeric columns separately to prepare measurements for a subsequent analysis.

Guides · Worksheets and data tools · 4 min read

Example: drying batches

A drying study records wet batch mass, inlet temperature, drying time and electricity use for 48 batches. Transform each measurement using this sample’s values.

Download the drying-batch measurements (CSV)

This is the same example used in Help. The CSV contains the measurements to import. The four numeric columns use kg, °C, minutes and kWh; batch_id keeps track of the batch.

1. Create the analysis

In the sidebar, open Data utilities, choose Standardize & Normalize, and name the analysis. Select New blank worksheet and Create analysis.

2. Import the data

On Worksheet, choose Import. Select the downloaded file or paste its contents. Set the delimiter to Comma, use Decimal dot, and check First row contains column names. Preview the import, then choose Import into worksheet.

3. Select the input columns

On Inputs, open the column picker for Variables to transform. Select wet_batch_mass_kg, inlet_temperature_c, drying_time_min and electricity_kwh, in that order. Use the up and down arrows to correct their order if needed.

Leave batch_id unselected; it identifies a batch, rather than a measurement.

4. Set the method and output names

In Method, choose Center about the mean. Under Output names, enter the matching name for each source column.

Source columnOutput name
wet_batch_mass_kgwet_batch_mass_kg_center
inlet_temperature_cinlet_temperature_c_center
drying_time_mindrying_time_min_center
electricity_kwhelectricity_kwh_center

Check the destination worksheet and the note showing 4 new columns. The original columns are retained.

Standardize & Normalize: Inputs with the example’s assignments and settings
The four selected source columns, Center about the mean method and four output names on Inputs. View full-size image (opens in a new tab)

5. Transform

Choose Transform, then open Results. Open Worksheet to see the four new columns beside the originals. Each successful transform appends new columns; repeating it does not replace the earlier output.

6. Interpret results

  1. Read the source summary

    The summary describes the four original columns, each with 48 values and no missing readings. For mass, the average is 45.4906 kg, sample standard deviation is 7.00915 kg, and observed range is 32.57–66.24 kg.

  2. Understand the transformation

    Subtract each column’s own mean. Zero means the source average; positive values are above it. Centering preserves the original units and spread.

  3. Read the first transformed batch

    For the first batch, mass is 50 kg. Subtract the source average of 45.4906 kg to get about +4.5094 kg. This batch is that much heavier than the average batch. Each other column subtracts its own mean.

  4. Choose the next analysis

    Centered values show differences from each source average. The values remain in kg, °C, minutes and kWh, so their numerical sizes still use different units. Select the new columns explicitly for your next analysis. Scaling does not make the data normally distributed, remove dependence or establish acceptable process performance.

  5. Keep the saved operation in context

    All 48 rows remain in batch order and the originals are preserved. Results records the transformation as it ran. Later worksheet edits or Undo can change the worksheet without changing that saved result.

More details: read each result section

Complete result tables use six significant digits, as in Help.

Transformation summary

Source and Output column identify each original and new column. Valid values counts usable source readings; Missing counts missing readings. Source mean, Source SD, Source minimum and Source maximum describe the original column in its measurement unit. Subtract each column’s own mean. Zero means the source average; positive values are above it. Centering preserves the original units and spread.

Calculated example output. Running a practice copy writes new columns to its independent worksheet.

Transformation summary · 4 rows
SourceOutput columnMethodValid valuesMissingSource meanSource SDSource minimumSource maximum
wet_batch_mass_kgwet_batch_mass_kg_centerCenter about the mean48045.49067.0091532.5766.24
inlet_temperature_cinlet_temperature_c_centerCenter about the mean48064.50833.2456757.170.4
drying_time_mindrying_time_min_centerCenter about the mean48030.5944.5197823.0241.72
electricity_kwhelectricity_kwh_centerCenter about the mean48017.12391.7496114.26522.814

Transformed values

Row 1 is the first imported batch. Each column contains its transformed measurements, with all 48 rows kept in collection order. For the first batch, mass is 50 kg. Subtract the source average of 45.4906 kg to get about +4.5094 kg. This batch is that much heavier than the average batch.

Captured values in original row order. Exports retain full precision.

Transformed values · 48 rows
Rowwet_batch_mass_kg_centerinlet_temperature_c_centerdrying_time_min_centerelectricity_kwh_center
14.509371.291673.046040.571104
2-10.5506-4.30833-4.84396-1.8959
34.849380.3916677.216040.727104
44.49938-6.108330.3760421.1571
5-3.360623.191673.26604-1.0139
615.71941.2916711.1264.4491
7-3.05063-0.508333-1.79396-1.4349
8-7.42063-7.40833-6.24396-2.8589
920.74942.791679.896045.6901
10-3.66063-3.408331.46604-1.2159
11-9.28063-1.60833-1.71396-2.4779
12-0.580625-2.00833-1.68396-0.449896
130.179375-5.40833-6.52396-1.7569
14-0.910625-0.908333-4.46396-0.511896
15-3.580633.09167-2.063960.0431042
162.65937-1.70833-0.9239581.2841
17-2.99063-1.108330.126042-0.672896
181.169375.491673.166040.864104
19-4.620632.691670.156042-0.875896
2014.46941.891675.466042.7611
21-0.7206254.09167-5.06396-0.468896
22-11.4006-2.60833-7.57396-2.5549
230.2393752.191674.666040.0481042
24-6.770633.79167-5.91396-0.811896
25-5.920634.79167-0.823958-1.0799
26-5.49063-1.008330.276042-1.5109
27-7.84063-1.00833-1.94396-1.4059
284.999383.191672.436041.3841
29-3.63063-2.70833-5.97396-1.7599
30-0.730625-5.10833-2.92396-0.138896
313.179381.09167-1.553960.377104
32-4.09063-3.20833-2.72396-0.458896
33-2.90062-1.60833-2.633960.211104
34-3.360622.69167-3.18396-0.151896
350.189375-3.508333.136040.303104
36-3.98063-3.10833-6.52396-1.1619
372.69937-1.408333.146040.344104
381.959385.491670.5060420.589104
393.739372.79167-1.663960.214104
405.76937-0.6083335.116040.300104
41-0.940625-1.208330.376042-0.466896
4210.97940.7916671.756042.1591
4312.34945.891673.676043.3281
44-12.9206-2.90833-4.60396-2.4879
45-2.690631.091672.32604-0.160896
46-4.650623.99167-3.74396-1.1279
476.52938-0.8083334.796041.9231
486.609381.291679.586042.1841

7. Create a report

Keep Transformation summary and all rows of Transformed values. Record the selected method, source columns and output names. The summary describes the original measurements; the values table contains the transformed output.

Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.

Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.

Complete native output for this Help example, including applicable tables, charts and run notes. Report numbers use the app’s displayed precision. Exported charts are static. On narrow screens, scroll wide charts and tables sideways.
View example report: Mean centering for drying batches

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