Standard Score Calculator
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About this app
[PLEASE READ FIRST]
This app does not judge anyone's chances at any school, and it holds no list of
school or university scores. It works out a T-score from the numbers you type.
The "top X%" figure is a guide that assumes the marks follow a normal
distribution.
──────────
🔢 Standard Score Calculator — a T-score is not the height of a mark
Eighty marks. On its own that settles nothing.
Mean 60, standard deviation 15 → T-score 63.3
Mean 70, standard deviation 5 → T-score 70
The same 80, two different answers. A T-score reads where a mark sits inside
its group, not how high it is. That is why this app asks for three numbers.
■ A test taken by two people always gives 60 and 40
As long as the standard deviation is the population one — half the gap (÷ n).
A hundred and a zero, fifty-one and fifty: the same answer. The mean sits
halfway between the marks, so the higher is one deviation above and the lower
one below. With the sample deviation (n−1, Excel's STDEV) the same two come out
at 57.1 and 42.9.
Nothing shows more quickly that a T-score reads position and nothing else.
■ One Japanese word, two numbers
z-score (mark − mean) ÷ SD 0 at the mean, 1 one deviation above
T-score 50 + 10 × z 50 at the mean, 60 one deviation above
T-score (50 + 10z) is used in Japan for exam scores, and in psychological
testing elsewhere. The Japanese word for "standard score" covers both numbers,
while in English it normally means the z-score — easy to mix up: one deviation
above the mean is "1" on one scale, "60" on the other.
This app never asks you to pick one. It shows both at once.
■ Three topics
▪ Find the T-score … mark, mean and SD give the T-score and the z-score
▪ Mark needed … target T-score, mean and SD give the mark and the gap
▪ Top % … a T-score gives the top per cent and the rank out of 100
■ No ceiling and no floor
A T-score can go above 100 and below 0. If one person in a group of n stands
right out on their own, and the deviation is the population one (dividing by n),
the highest they can reach is 50 + 10√(n−1).
2 people 60
10 people 80
100 people 149.5
1000 people 366.1
With the sample deviation (n−1) the highest out of a hundred is 149.0 instead.
If one person out of a hundred gets full marks and the other ninety-nine score
the same, that person is at 149.5 and the rest at 49.
That is why the mark for a target T-score can come out above full marks; this
app does not know what they are.
■ Top per cent
T-score 30 97.72%
T-score 40 84.13%
T-score 50 50%
T-score 60 15.87%
T-score 70 2.28%
T-score 80 0.13%
An eleven-row chart in steps of five sits on the same screen, with the rank out
of a hundred beside it. These figures assume a normal distribution, which real
marks never quite follow, so treat them as a rough guide — furthest off when
the group is small.
■ When the standard deviation is zero
If everyone scored the same there is no T-score: you would be dividing by zero.
Type a zero and the app stops and says why.
The other way round: the smaller the deviation, the further one mark moves it.
With a mean of 60 and a deviation of 2, 62 is already a T-score of 60.
■ What this app does not do
▪ It does not estimate anyone's chances at a school
▪ It holds no list of school or university scores
▪ It keeps no record of results over time
▪ It does not work out a mean and SD from a list of marks
▪ It does not distinguish sample and population deviation; it uses what you type
▪ It draws no bell curve. Numbers only
No account is needed.
The calculation happens on your device, and nothing you type is sent out.
■ What the screen holds
▪ One to three input fields. No settings screen
▪ Common values are one tap away
▪ The last five entries stay in the history; results copy out in one tap
▪ A quick chart on the top-per-cent topic, and six short notes
▪ Japanese and English, chosen by your device language
──────────
For when a result lands and you want to know where the number came from.
NISAKE GAME
This app does not judge anyone's chances at any school, and it holds no list of
school or university scores. It works out a T-score from the numbers you type.
The "top X%" figure is a guide that assumes the marks follow a normal
distribution.
──────────
🔢 Standard Score Calculator — a T-score is not the height of a mark
Eighty marks. On its own that settles nothing.
Mean 60, standard deviation 15 → T-score 63.3
Mean 70, standard deviation 5 → T-score 70
The same 80, two different answers. A T-score reads where a mark sits inside
its group, not how high it is. That is why this app asks for three numbers.
■ A test taken by two people always gives 60 and 40
As long as the standard deviation is the population one — half the gap (÷ n).
A hundred and a zero, fifty-one and fifty: the same answer. The mean sits
halfway between the marks, so the higher is one deviation above and the lower
one below. With the sample deviation (n−1, Excel's STDEV) the same two come out
at 57.1 and 42.9.
Nothing shows more quickly that a T-score reads position and nothing else.
■ One Japanese word, two numbers
z-score (mark − mean) ÷ SD 0 at the mean, 1 one deviation above
T-score 50 + 10 × z 50 at the mean, 60 one deviation above
T-score (50 + 10z) is used in Japan for exam scores, and in psychological
testing elsewhere. The Japanese word for "standard score" covers both numbers,
while in English it normally means the z-score — easy to mix up: one deviation
above the mean is "1" on one scale, "60" on the other.
This app never asks you to pick one. It shows both at once.
■ Three topics
▪ Find the T-score … mark, mean and SD give the T-score and the z-score
▪ Mark needed … target T-score, mean and SD give the mark and the gap
▪ Top % … a T-score gives the top per cent and the rank out of 100
■ No ceiling and no floor
A T-score can go above 100 and below 0. If one person in a group of n stands
right out on their own, and the deviation is the population one (dividing by n),
the highest they can reach is 50 + 10√(n−1).
2 people 60
10 people 80
100 people 149.5
1000 people 366.1
With the sample deviation (n−1) the highest out of a hundred is 149.0 instead.
If one person out of a hundred gets full marks and the other ninety-nine score
the same, that person is at 149.5 and the rest at 49.
That is why the mark for a target T-score can come out above full marks; this
app does not know what they are.
■ Top per cent
T-score 30 97.72%
T-score 40 84.13%
T-score 50 50%
T-score 60 15.87%
T-score 70 2.28%
T-score 80 0.13%
An eleven-row chart in steps of five sits on the same screen, with the rank out
of a hundred beside it. These figures assume a normal distribution, which real
marks never quite follow, so treat them as a rough guide — furthest off when
the group is small.
■ When the standard deviation is zero
If everyone scored the same there is no T-score: you would be dividing by zero.
Type a zero and the app stops and says why.
The other way round: the smaller the deviation, the further one mark moves it.
With a mean of 60 and a deviation of 2, 62 is already a T-score of 60.
■ What this app does not do
▪ It does not estimate anyone's chances at a school
▪ It holds no list of school or university scores
▪ It keeps no record of results over time
▪ It does not work out a mean and SD from a list of marks
▪ It does not distinguish sample and population deviation; it uses what you type
▪ It draws no bell curve. Numbers only
No account is needed.
The calculation happens on your device, and nothing you type is sent out.
■ What the screen holds
▪ One to three input fields. No settings screen
▪ Common values are one tap away
▪ The last five entries stay in the history; results copy out in one tap
▪ A quick chart on the top-per-cent topic, and six short notes
▪ Japanese and English, chosen by your device language
──────────
For when a result lands and you want to know where the number came from.
NISAKE GAME
Mark, mean and SD in: T-score and z-score out. A T-score of 60 is top 15.87%
Updated on
Safety starts with understanding how developers collect and share your data. Data privacy and security practices may vary based on your use, region, and age. The developer provided this information and may update it over time.
What’s new
• An ad now appears when the app starts
• The top percentage now always shows two decimals, so the table lines up and a T-score of 50 reads as exactly 50.00%
• History rows now separate the figures with commas instead of "×", since a mark, a mean and a standard deviation are not multiplied together
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About the developer
NISAKE GAME
nisakegame@gmail.com
5-3, MARUYAMACHO
MIEUX SHIBUYA BLDG. 8F.
SHIBUYA-KU, 東京都 150-0044
Japan
+81 80-5429-5695
