Zscore Calculator
A Zscore calculator tool is a software application or online tool that helps in calculating the Zscore of a given value in a dataset. The Zscore, also known as the standard score, is a statistical measure that indicates how many standard deviations a data point is away from the mean of the dataset.
What is zscore?
The zscore, also referred to as standard score, zvalue, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive zscores, while values below the mean have negative zscores.
The zscore can be calculated by subtracting the population mean from the raw score, or data point in question (a test score, height, age, etc.), then dividing the difference by the population standard deviation:
z = 

where x is the raw score, μ is the population mean, and σ is the population standard deviation.
The zscore has numerous applications and can be used to perform a ztest, calculate prediction intervals, process control applications, comparison of scores on different scales, and more.
Ztable
A ztable, also known as a standard normal table or unit normal table, is a table that consists of standardized values that are used to determine the probability that a given statistic is below, above, or between the standard normal distribution.
The table below is a righttail ztable. Although there are a number of types of ztables, the righttail ztable is commonly what is meant when a ztable is referenced. It is used to find the area between z = 0 and any positive value, and reference the area to the righthand side of the standard deviation curve.
z  0  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09 
0  0  0.00399  0.00798  0.01197  0.01595  0.01994  0.02392  0.0279  0.03188  0.03586 
0.1  0.03983  0.0438  0.04776  0.05172  0.05567  0.05962  0.06356  0.06749  0.07142  0.07535 
0.2  0.07926  0.08317  0.08706  0.09095  0.09483  0.09871  0.10257  0.10642  0.11026  0.11409 
0.3  0.11791  0.12172  0.12552  0.1293  0.13307  0.13683  0.14058  0.14431  0.14803  0.15173 
0.4  0.15542  0.1591  0.16276  0.1664  0.17003  0.17364  0.17724  0.18082  0.18439  0.18793 
0.5  0.19146  0.19497  0.19847  0.20194  0.2054  0.20884  0.21226  0.21566  0.21904  0.2224 
0.6  0.22575  0.22907  0.23237  0.23565  0.23891  0.24215  0.24537  0.24857  0.25175  0.2549 
0.7  0.25804  0.26115  0.26424  0.2673  0.27035  0.27337  0.27637  0.27935  0.2823  0.28524 
0.8  0.28814  0.29103  0.29389  0.29673  0.29955  0.30234  0.30511  0.30785  0.31057  0.31327 
0.9  0.31594  0.31859  0.32121  0.32381  0.32639  0.32894  0.33147  0.33398  0.33646  0.33891 
1  0.34134  0.34375  0.34614  0.34849  0.35083  0.35314  0.35543  0.35769  0.35993  0.36214 
1.1  0.36433  0.3665  0.36864  0.37076  0.37286  0.37493  0.37698  0.379  0.381  0.38298 
1.2  0.38493  0.38686  0.38877  0.39065  0.39251  0.39435  0.39617  0.39796  0.39973  0.40147 
1.3  0.4032  0.4049  0.40658  0.40824  0.40988  0.41149  0.41308  0.41466  0.41621  0.41774 
1.4  0.41924  0.42073  0.4222  0.42364  0.42507  0.42647  0.42785  0.42922  0.43056  0.43189 
1.5  0.43319  0.43448  0.43574  0.43699  0.43822  0.43943  0.44062  0.44179  0.44295  0.44408 
1.6  0.4452  0.4463  0.44738  0.44845  0.4495  0.45053  0.45154  0.45254  0.45352  0.45449 
1.7  0.45543  0.45637  0.45728  0.45818  0.45907  0.45994  0.4608  0.46164  0.46246  0.46327 
1.8  0.46407  0.46485  0.46562  0.46638  0.46712  0.46784  0.46856  0.46926  0.46995  0.47062 
1.9  0.47128  0.47193  0.47257  0.4732  0.47381  0.47441  0.475  0.47558  0.47615  0.4767 
2  0.47725  0.47778  0.47831  0.47882  0.47932  0.47982  0.4803  0.48077  0.48124  0.48169 
2.1  0.48214  0.48257  0.483  0.48341  0.48382  0.48422  0.48461  0.485  0.48537  0.48574 
2.2  0.4861  0.48645  0.48679  0.48713  0.48745  0.48778  0.48809  0.4884  0.4887  0.48899 
2.3  0.48928  0.48956  0.48983  0.4901  0.49036  0.49061  0.49086  0.49111  0.49134  0.49158 
2.4  0.4918  0.49202  0.49224  0.49245  0.49266  0.49286  0.49305  0.49324  0.49343  0.49361 
2.5  0.49379  0.49396  0.49413  0.4943  0.49446  0.49461  0.49477  0.49492  0.49506  0.4952 
2.6  0.49534  0.49547  0.4956  0.49573  0.49585  0.49598  0.49609  0.49621  0.49632  0.49643 
2.7  0.49653  0.49664  0.49674  0.49683  0.49693  0.49702  0.49711  0.4972  0.49728  0.49736 
2.8  0.49744  0.49752  0.4976  0.49767  0.49774  0.49781  0.49788  0.49795  0.49801  0.49807 
2.9  0.49813  0.49819  0.49825  0.49831  0.49836  0.49841  0.49846  0.49851  0.49856  0.49861 
3  0.49865  0.49869  0.49874  0.49878  0.49882  0.49886  0.49889  0.49893  0.49896  0.499 
3.1  0.49903  0.49906  0.4991  0.49913  0.49916  0.49918  0.49921  0.49924  0.49926  0.49929 
3.2  0.49931  0.49934  0.49936  0.49938  0.4994  0.49942  0.49944  0.49946  0.49948  0.4995 
3.3  0.49952  0.49953  0.49955  0.49957  0.49958  0.4996  0.49961  0.49962  0.49964  0.49965 
3.4  0.49966  0.49968  0.49969  0.4997  0.49971  0.49972  0.49973  0.49974  0.49975  0.49976 
3.5  0.49977  0.49978  0.49978  0.49979  0.4998  0.49981  0.49981  0.49982  0.49983  0.49983 
3.6  0.49984  0.49985  0.49985  0.49986  0.49986  0.49987  0.49987  0.49988  0.49988  0.49989 
3.7  0.49989  0.4999  0.4999  0.4999  0.49991  0.49991  0.49992  0.49992  0.49992  0.49992 
3.8  0.49993  0.49993  0.49993  0.49994  0.49994  0.49994  0.49994  0.49995  0.49995  0.49995 
3.9  0.49995  0.49995  0.49996  0.49996  0.49996  0.49996  0.49996  0.49996  0.49997  0.49997 
4  0.49997  0.49997  0.49997  0.49997  0.49997  0.49997  0.49998  0.49998  0.49998  0.49998 
Zscore Example
Student  Exam Score 

A  85 
B  92 
C  78 
D  88 
E  95 
To calculate the Zscore for each student's exam score, we need to find the mean and standard deviation of the dataset.

Calculate the Mean: The mean (μ) is the average of all the scores. Mean (μ) = (85 + 92 + 78 + 88 + 95) / 5 = 87.6

Calculate the Standard Deviation: The standard deviation (σ) measures the spread or dispersion of the scores around the mean. We use the formula: σ = √[Σ(x  μ)² / N]
where: x = individual score μ = mean N = number of scores
Let's calculate step by step:

Subtract each score from the mean: (85  87.6) = 2.6 (92  87.6) ≈ 4.4 (78  87.6) ≈ 9.6 (88  87.6) = 0.4 (95  87.6) ≈ 7.4

Square each difference: (2.6)² ≈ 6.76 (4.4)² ≈ 19.36 (9.6)² ≈ 92.16 (0.4)² = 0.16 (7.4)² ≈ 54.76

Sum up the squared differences: 6.76 + 19.36 + 92.16 + 0.16 + 54.76 = 173.2

Divide by the number of scores and take the square root: σ = √(173.2 / 5) ≈ √34.64 ≈ 5.88


Calculate the Zscore for each student: The formula to calculate the Zscore is: Z = (x  μ) / σ
Using the mean (μ = 87.6) and standard deviation (σ ≈ 5.88), we can calculate the Zscores:
Z(A) = (85  87.6) / 5.88 ≈ 0.44 Z(B) = (92  87.6) / 5.88 ≈ 0.75 Z(C) = (78  87.6) / 5.88 ≈ 1.63 Z(D) = (88  87.6) / 5.88 ≈ 0.07 Z(E) = (95  87.6) / 5.88 ≈ 1.26
These are the Zscores for each student's exam score. The Zscore indicates the number of standard deviations a particular score is from the mean. A positive Zscore indicates a score above the mean, while a negative Zscore indicates a score below the mean.