Deviation Score Table Calculator

Enter Calculation

Score table (rows = people, columns = subjects) 80, 60, 90 50, 70, 40 70, 90, 60 90, 50, 80 60, 80, 70 Enter a numeric grid. One row per line; separate values with commas or spaces. Example: 80,60,90

Results

Deviation Score (first cell)

57.07

T-score (mean = 50, scale = 10)

Row	Col 1	Col 2	Col 3	Col 4	Total
0	57.07	42.93	62.79	58.86	58.86
1	35.86	50	33.73	30.66	30.66
2	50	64.14	45.35	54.83	54.83
3	64.14	35.86	56.97	54.83	54.83
4	42.93	57.07	51.16	50.81	50.81

Statistic	Col 1	Col 2	Col 3	Col 4	Total
Mean	70	70	68	208
Std Dev (pop.)	14.14	14.14	17.2	24.82

What is a deviation score?

A deviation score, known in Japan as hensachi, is a T-score: a way of expressing how far a single value sits from the average of its group, measured in standard-deviation units and rescaled so the mean is exactly 50. Add 10 points for every standard deviation above the mean, subtract 10 for every standard deviation below. It is a pure statistical transform, so it works for any list of numbers, but it is most famous in the Japanese school and exam system for comparing performance across different tests.

A deviation score of 50 sits at the mean, with each 10 points equal to one standard deviation.

How to use this calculator

Enter your raw scores as a grid: one row per line (each row is a person or item), with values separated by commas or spaces (each column is a subject or test). The calculator standardizes each column independently and returns a deviation score for every cell. It also adds a Total column: it sums each row, then standardizes those row totals against one another. A column mean and population standard deviation are shown for reference.

The formula

For one column of values \(x_1 .. x_m\): first the mean \(\mu = \frac{1}{m}\cdot\sum x_i\), then the population standard deviation \(\sigma = \sqrt{\frac{1}{m}\cdot\sum (x_i-\mu)^2}\). The deviation score of a value is $$T = 50 + 10\cdot\frac{x-\mu}{\sigma}$$ If a column is perfectly flat (\(\sigma = 0\)) every cell scores exactly 50 to avoid dividing by zero.

Each raw score is rescaled relative to the column mean and standard deviation.

Worked example

Take column 1 of the default data: 80, 50, 70, 90, 60. The mean is \(350/5 = 70\). The squared deviations sum to 1000, so the variance is 200 and \(\sigma \approx 14.1421\). The first cell, 80, scores $$50 + 10\cdot\frac{10}{14.1421} \approx 57.07$$ The row totals are 230, 160, 220, 220, 210; their mean is 208 and \(\sigma \approx 24.8193\), giving the appended Total column.

FAQ

Why population, not sample, standard deviation? Hensachi convention divides by \(m\), not \(m-1\), so this tool uses the population formula.

What if all scores in a column are equal? The standard deviation is zero, so every cell is assigned a deviation score of 50.

Can columns have different lengths? Each row is padded to the widest row with zeros; for clean results enter a complete rectangular grid.