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z分数计算器

使用此计算器计算正态分布的z得分。

原始分数, x
人口平均数, & mu
标准偏差, & sigma

z得分和概率转换器

请提供任意一个值以在z得分和概率之间转换。这相当于引用z表。

z值, Z
概率, P(x《Z)
概率, P(x》Z)
概率, P(0至Z或Z至0)
概率, P(-Z《x《Z)
概率, P(x《-Z或x》Z)


两个Z值之间的概率

z分数

使用此计算器计算两个z得分之间的概率(图表中的区域P)。

向左, Z
右边界, Z2

有关系的标准偏差计算器


什么是z-score?

z得分也称为标准得分、z值和正常得分等,是一个无量纲的量,用于指示事件高于所测量平均值的标准偏差的带符号分数。高于平均值的值具有正z得分,而低于平均值的值具有负z得分。

可以通过从原始得分或相关数据点(测试得分、身高、年龄等)中减去总体均值来计算z得分。),然后将差值除以总体标准差:

z =
x-& mu;
& sigma

其中x是原始得分,& mu是总体均值,且& sigma是总体标准差。对于样本,公式类似,只是使用样本均值和总体标准差代替总体均值和总体标准差。

z得分有多种应用,可用于执行z测试、计算预测区间、过程控制应用、比较不同等级的得分等。

z表

z表也称为标准正态表或单位正态表,是由标准化值组成的表,这些值用于确定给定统计数据低于、高于或介于标准正态分布之间的概率。z得分为0表示给定点等于平均值。在标准正态分布图中,z = 0因此是曲线的中心。z值为正值表示该点位于平均值的右侧,z值为负值表示该点位于平均值的左侧。有几种不同类型的z表。

下表中的值表示z = 0和给定z得分之间的区域。

平均值Z表(0到Z)
z00.010.020.030.040.050.060.070.080.09
000.003990.007980.011970.015950.019940.023920.02790.031880.03586
0.10.039830.04380.047760.051720.055670.059620.063560.067490.071420.07535
0.20.079260.083170.087060.090950.094830.098710.102570.106420.110260.11409
0.30.117910.121720.125520.12930.133070.136830.140580.144310.148030.15173
0.40.155420.15910.162760.16640.170030.173640.177240.180820.184390.18793
0.50.191460.194970.198470.201940.20540.208840.212260.215660.219040.2224
0.60.225750.229070.232370.235650.238910.242150.245370.248570.251750.2549
0.70.258040.261150.264240.26730.270350.273370.276370.279350.28230.28524
0.80.288140.291030.293890.296730.299550.302340.305110.307850.310570.31327
0.90.315940.318590.321210.323810.326390.328940.331470.333980.336460.33891
0.341340.343750.346140.348490.350830.353140.355430.357690.359930.36214
1.10.364330.36650.368640.370760.372860.374930.376980.3790.3810.38298
1.20.384930.386860.388770.390650.392510.394350.396170.397960.399730.40147
1.30.40320.40490.406580.408240.409880.411490.413080.414660.416210.41774
1.40.419240.420730.42220.423640.425070.426470.427850.429220.430560.43189
1.50.433190.434480.435740.436990.438220.439430.440620.441790.442950.44408
1.60.44520.44630.447380.448450.44950.450530.451540.452540.453520.45449
1.70.455430.456370.457280.458180.459070.459940.46080.461640.462460.46327
1.80.464070.464850.465620.466380.467120.467840.468560.469260.469950.47062
1.90.471280.471930.472570.47320.473810.474410.4750.475580.476150.4767
20.477250.477780.478310.478820.479320.479820.48030.480770.481240.48169
2.10.482140.482570.4830.483410.483820.484220.484610.4850.485370.48574
2.20.48610.486450.486790.487130.487450.487780.488090.48840.48870.48899
2.30.489280.489560.489830.49010.490360.490610.490860.491110.491340.49158
2.40.49180.492020.492240.492450.492660.492860.493050.493240.493430.49361
2.50.493790.493960.494130.49430.494460.494610.494770.494920.495060.4952
2.60.495340.495470.49560.495730.495850.495980.496090.496210.496320.49643
2.70.496530.496640.496740.496830.496930.497020.497110.49720.497280.49736
2.80.497440.497520.49760.497670.497740.497810.497880.497950.498010.49807
2.90.498130.498190.498250.498310.498360.498410.498460.498510.498560.49861
30.498650.498690.498740.498780.498820.498860.498890.498930.498960.499
3.10.499030.499060.49910.499130.499160.499180.499210.499240.499260.49929
3.20.499310.499340.499360.499380.49940.499420.499440.499460.499480.4995
3.30.499520.499530.499550.499570.499580.49960.499610.499620.499640.49965
3.40.499660.499680.499690.49970.499710.499720.499730.499740.499750.49976
3.50.499770.499780.499780.499790.49980.499810.499810.499820.499830.49983
3.60.499840.499850.499850.499860.499860.499870.499870.499880.499880.49989
3.70.499890.49990.49990.49990.499910.499910.499920.499920.499920.49992
3.80.499930.499930.499930.499940.499940.499940.499940.499950.499950.49995
3.90.499950.499950.499960.499960.499960.499960.499960.499960.499970.49997
0.499970.499970.499970.499970.499970.499970.499980.499980.499980.49998

如何阅读z表

在上表中,

例如,参考上面的右尾z表,z得分为1.12的数据点对应于0.36864的面积(第13行第4列)。这意味着对于正态分布的人群,有36.864%的概率,一个数据点将具有0到1.12之间的z得分。

因为有各种z表,所以关注给定的z表以了解所引用的区域非常重要。

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