数据的分布特征:

  • 分布的集中趋势,反应各数据向其中心值靠拢或聚集的程度(平均数,中位数,四分位数,众数)
  • 分布的离散程度,反应各数据远离其中心值的趋势(极差,四分位差,方差,标准差,离散系数)
  • 分布的形状,反应数据分布的偏斜程度和峰度(偏态系数,峰度系数)

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平均数(均值):一组数据相加后除以数据的个数而得到结果,称为平均数(mean)

中位数:一组数据排序后处于中间位置上的变量值,称为中位数(median)

四分位数:一组数据排序后处于25%(下四分位数)和75%(上四分位数)位置上的值,称为四分位数

  • 先计算位置,然后计算四分位数的值。50%处即为中位数

众数:一组数据中出现频数最多的数值(mode)

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极差(全距):一组数据的最大值与最小值之差,称为极差(range)

四分位差:上四分位数与下四分位数之差,称为四分位差

平均差:各变量值与其平均数离差绝对值的平均数,称为平均差

方差:各变量值与其平均数离差平方的平均数,称为方差(variance)

标准差:方差的平方根称为标准差()

离散系数

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偏态:数据分布的不对称性,称为偏态

峰态:数据分布的平峰或尖峰程度,称为峰态

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描述性统计量:主要包括分布的集中程度,分布的离散程度和分布的偏斜程度。

方法一:summary()函数——最大值,最小值,四分位数(上,下),均值

summary(mtcars) #结果有以下几条

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" alt="" />

 vars<-c('mpg','hp','wt')
head(mtcars[vars])

aaarticlea/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXYAAAC+CAIAAACu8LNfAAAXmUlEQVR4nO2du24bSxKG+QIKHRPCCYQDAc5sLKDAgENuSEAZ4UgBEwdKFBFiIkAZQShyqDfaYIF9j+Nz7HSDGXL6UlV9n55p/sAXSByyu/r2T3dPT9Xi56/fP//5/fPXwF9///r5z++///n985/u719///r919+/uw9xFVdxFVf9ry7+89//AQBAIRaL288Um+37+9uZ3Yb5GsHdTvnh+/7O+4cp3O3kvFbrg2pVWIkq2QxAE9S3AADQMPUtAAA0TH0LAAANU98CAEDD1LegAMuHq5enm+pmXCDLh6vHh4/VzQATIm9yn54WLz8+fBrD9JtvPxZkb14+XL38WHxb167ZTGV8OTMN0fz0pJhktvXH1evihWkXcKHkTa6+xHxZPsZ08Y+r18XL63JZvT18yjgNuLb+9LR4+XG1+lLfQjAJ8iZXW2KilQISEwzf1tOsTFAJ6tOPq9fInl1ZYtYfYpdI0xwVM5WYlIYAzUF+2m1nRCz+T92uX5NTy3J1f8GaTn9ZPiq7D1Yf1fcmrMQ/PVEy8WX5+ONq9aX/7bf1qXSvy+W5pAT64NEMEy7pNvdZq7kYRR4qilpc0BJDbzYZo7qgVUZbk1dvvk1m8whUhr2w/nAeh/7JnfcC+z5t3s20nrd8uNJ78M03JbsuKXPMDL3WHn5Mt/6yfPxx9fh6tfrSTVWuHp9uLMOkWUw3FJW8br6pZjhtHqwycrn5ptXwx9WTYQA3iyFKqg/4olaROYZdBReEdK3viwEdxezN+iCxut3H1St/r9M3bq0ZijX8viwfycm5ok3DTqT5ZV5igvaPjS+bsqirqjtldqFkbamKS6rMVqk28H1j/QGbvmBx697u7dYXvn3F6nbq/Za597ITJXXY2L+1BhW3/lfUZDDPW2KsqZa7uozBzG9J9Gs3fjzzwqELgcvIvFZxba2D7RjQ4frGafvDb13tlhhx18PeGVElxl4WjSAxzgk/b7NzMH+O24uxDCYmgyWt8qsZSAzokK5FLpQCZjEq1i6mOYtxSIy4UCo0ixFt9hnMRlUbXxaXP+eViJVLYau4tmbM8+48oE3YC/HbvZzEyMui7s5p/vY0MMwbtbUFa+Y1kCYx4t1YtjlkMN+SmyDyQ+v+6vLhSre8tFVcWwdcBRcE+WnyQ+vzJ/qwtzYard9qm44vzHbD8uHq5fXDN/Pwjj20hqRcEiO9dkDsYauiydvsGMzrD+yeq1J7wp4IUw+lreLaWkXcyAcXBfVpxqN39DYtc7bFODJjmjG8HfN0QxtJzjj8JGZh7l9og4e/JNrsmi/oyQbtxQzpcz8sZhXX1q6GAJdJfQtyMs1DutHM9HRvY60A0qhvQV7EtdjcmKXEBD7mB61T34LcUDvBM2WGErP+0Erlg0zUt6AArThGmqW/mCZqHuSjvgUAgIapbwEAoGHqWwAAaJj6FgAAGqa+BQCAhqlvAQAlQezwytS3AICSNCoxq/Xh/e3w/bq+JS7qWwBASSAxlalvAQAlgcRUpr4FoA2+fn9+P66/brbv72/v79v7z9fb49v7MAzudt3f/Rfe3t/fdhsrhdOlE9v7VMNOErNaH/o0n7cr7aps1diw2tGZ+q+uVgmmKqP1LQBt8PX78/vx+XBcf+0GyfF5t1nc788ycbfTVeN+r432r9+fh387OTiuv2YwjMz3rFwOq2pwUj3j89X6oMofZjHg0ujmILvNoh+3x/XX/kNVYpRZiTZIzOWMLgQpWPlutoqIyFZV4Xp7PFeFIjea2VOw05f6FoA2MNVkf8d9eEL9pLDEqPlutspqSLaqDvf70wyuW751xkBiwIUTLjHq7ZpaKOUZ56ESo1lVtybv92+H/fbwvr3XanKoIkgMuCDSZjHdtKXE5uX8ZjG3m+1pv/x5u7reHt92m9Nu+vk7kBhwaQRLjLp/aexl5iRQYgpa4s1qfXh/3m7Wh/N+1v7ufk/YCYkBF0SgxAxbwrfE1YwESYxhVS3651y9gpwet+uC0p0JyLJdVZb6FoA28JIYBfMOrJxMyXcoZuElMYJVdejk47y5258wsuZW19oZGZyLAZeNOE9RH52o3y8+oZjAzkvr1LcAXAbSYFbO1JwZZyEAiSlOfQvAZRA2i+lfJig++CExxalvAbgMXIN5eIdozHeFIDHFqW8BAKBh6lsAAGiY+hYAABqmvgUAgIapbwEAoGGqZm+8nw4AaA7z/+48gnaMujuzUOKcZTaJuTa9DSrWdq/wGgfDyQ+H4+R4iulZ1VRFnfxjhp+aU98hCO9vcr7S1fh8k4/wq4/qtaxdKafV1ZiY//fv1FtDtMg5y7wSc26GvtkM54mG3zOi2QZ/ApAY/3q2Xv85fL+LOZhrvzrkP3LkfD2uRuXrqg0XXX+jjv941XNkXY0OVez9dqd5Hnze7Z/nJDG2B1ZNU5gm6ZsNZ7EC0Op5tT70nSTi7L/8sqKInK/DqoR85dpwEtL59ZRz2jwCVGFU5xSb7fv+zvC4pXuK19rMdCxkH9M0X6jVallIWcQlMcodg+kH52aDxARAvVu0iJEYa5D0HSmsIeR8qat58pVrgzfGOxct5aw2jwBT8t7v1uJ+/7bbnN1w9SVUtjCsNYiGOVzNNjCEPCBlscHIdZCy6LVf2Dcd5U+1taYGo9fBEqN51eydMK23x7idkQCJyZSvXBsUgY6v1JTz2jwCVDPs77o/dpu7Xdck/KTOKLBVL2qLWtEbxLmikLKFud1LNl4/RWKXSIORkBgvzD0vozlCJab//tmD5OAl25c4iUnPV64N9su7jdZvWcXRU85p8ygQzdCpwNfvz4fjM+39XIW7ZK8P6U94EQlYrCqzGNbh4Lk5jTQpv2eQGM86F3YroyRG9VA7psSk5SvXBkW/XTB0RcfWr3Ipn80jYfyvTDTUuZw22q0nxMzWBuXWTP+m+YlPynwDa77smccKR9NFgPVlSIx3hbM+4iIlZqt5wL4ea6GUK98Qj3nEBi3Z8YiUM9k8Hsb/TCS6QQusdqLmGrSmOiTGK2WpjfWHfHopzjs7xj3BFrW0Yw6XgWt/MXK7V+8zEVofud2bmG/MbiuxF0NsANMp56mr8TD+FyTmbbfhHtHLcxOuWnUHpT4ps5BPlIbOpM1CHcFMJ91aU8BjRElDndkRI/fpQh/EhktMcr7O2mDKawuKaQmfcpa6Gg+X9R2DOmiHSk7PmKk45Fwb97+93h67MFT6034pZQGrwfrTVooDd6WNiRPMeg1AYjj8nNEJQ/3sjttsWf1pY1wrREhMUr4eteFZXvOmKKeco67GQ/+f2ys192VOS4k+Rrq5a8WvOAaH76c5kXVAjknZ3bfsmH7v2/s+R2qLl0586g1WFdNfv36CiVl16pXJPtczOkBAE8j5elgVma9cG4HltRc+csqRNlegvgUAgIapbwEAoGHqWwAAaJj6FgAAGqa+BQCAhqlvAQCgYepbAABomPoWAAAapr4FAICGqZo9IhAA0Drm/4hA4H0im3nVINCh2dxABIKw2vAtL/dyAPkCgf2FqXpyuEUEAqLsvn2Fcb/a8tQMEQhCakPEcFTkcsqp389m1cfM/xGBwPs1SMYP0KyaPxFEIGBrw6O82iSa9da4uLWdzM6qj1HVhAgEfvci3vOWV11ZV4vNFouBCAQetUFidTNJYqyb4pwlBhEI4iTmbqc5u/CqK+3W5HCUNVEQgcCjNgRjDC8ognvsEKfXE4MqOSIQ+EtMV0BlHU57DiZKZGZkVdfkQQQCr9qQv/+8Xck+0qj1uLEUmPadiSgPIhB4SozqC/6w3x4sv/BiieYuMYhA4Fkb7l9JP3TuDYVK2+gY/yMCQYTEXG+Pz9vV3e58RzJcwzMlIhZK03ZfZlY4IhB41QaD7fuVmw+6jAnZA6qA8T8iECg4B3xvYb+cvN+/Hb5fK2V3lMjcGp+NviACQVBtUNhdlLzHqDLkqr0wgRsR439EIAjpYZ2F37fDcvK43u61JRtbotme0EMEgqDaoMtriwIhMb5KHbJrWQHjf0QgCJGY01MqfbpLH8CxSjRLP+SIQBBYG1x5DQf11FaO39xE7MyTQP8fEQhiJMbsKEMFyiUizolPd9POaD7KbEQgIBqRL6/xc6M3SnKpj7Lpzl866ltwoRCHdwJPzQMwB+pbcJlQTwEizt0DMHXqW3ChWLMYv20OAGZGfQsuF+WdhmF/qrpVAGSlvgUAgIapbwEAoGHqWwAAaJj6FgAAGqa+BQCAhqlvAQCgYayPrFPtwU9SRS+kFXD6c/+8uC3lob49ZJ/7ZTzyJ6M6MDV6puHbNLDfxpfXla8r5fn0SbKZrfdogsowNYkhsP25l/BQ3x6yz/0xPfIHoL92L76DFuYVIam8Yr5ekR7m0ifJ0trOGUIkY/ISY/mCGslDfXvIQlDOI38AYb4WI/xRxZU3LF895Zn1SbJJqPeSLWcI1oSWd+9keVqnJnhyxZ26oDI/jK1TTvWLe6hvD9nfWjGP/KEW6v1Z8tTDxMbKURsijny1lOfWJ62PCInRx54zToDQOYwJ0Wq9M5KSZ4NKXvGeblnJL+6hvj3yzWJCPPIHwdwyyf6Z6Nsp2mZnvmrKs+uTPk0ijWfuLhHehD4SY0Z0DL9jCDPSwh7q20N2TF3KI38oxqSV8rOrTI3jM41w0+2Zr57y7PokWewAiSG+75rF+PqCkmOPxEmM9KuiHurbQ/a5X8wjfwyq86fn7Ybvn/HRrOLK65OvmfLs+qT1kXOh5IwTIK+iE/ZikiVG3lQr56G+PXwiEJTwyJ8D2WtyvM/gtGkXnS+R8uz6JFlUIdKQR5wAv4066xxKeYlxPBor5aG+PeT9xYIe+XPg2PgI71d5dlupfOmU59YnyaIScaY19/1ynADvZwF6Y5NRBDJKjNOnXBEP9e2RqC8JHvmz4BiNoTu+keX1yJdPeWZ90vpIlwxr480nTgA7mPsI2erXlKpXd3zOz8WzSYz7dE9+D/XtIbvmK+uRPx3nOdLAI2AJ5XXk61PPc+mTTDMI57i94gRwx5/1z83GVq7u7/Q1c6LECFOYch7q20P2uV/UI388qr9+brMjKtOU8sr5eqQ8nz5Z3wIAQMPUtwAA0DD1LQAANEx9CwAADVPfAgBAw9S3AADQMPUtAAA0TH0LAAANU98CAEDD1LegfSL8HwPQCtZHxMH8JG+DOcngbPF0NNuzOOnxGD43JjFun/tSLIcSbeSXb4kIE6WjF7A220E1Jty76OpuVWKG11UCJCYtHkNTeHnGZ2M5FGojZ77jRJjIG73AbXO2d7hKQ9dUmxLTFy3kzdT0eAxNo3mrdcRyKNZGcr7jRZjIF73AWZPtSwwfUuvk7E+ZBA6V7hFFgJ6y+sU2cHDuTGkSY7uzYMsrVBTddUwHppMPx8X43I+WmKg28s23dISJEtELLlJidDfrpuN408+LNu9wRRHQsqbuCQmzGCWvRInRWl0sL5m7UM9EADmpNiYA43M/UmIi28g337IRJspEL2hXYtj5AjGEtN5gibE6NuQoAnQkHW0QRkuMnJHjh5KzdLG89E+0ejOnPHw4LtnjbBVYD7tREhPdRr75lokwUTZ6gSAx89jrvQ2dxVBSrQ0qI2yojrjuZe7qOSIEGvlmlxj3WCJDOBB+Rc99xac2KiM4pouQmIQ28s23cISJItELPGqyqCv1HFgfuSWG2kHIJDGO3ZYoibFMyr5QipQYrTjGJMWnNmriE4EgoNMntZFvvuUjTOSPXuBVkwlRKMfAp5pqzWIsYiSG3yr26cSOeAxpEqOos5nOtB0+u/ZEQyUmrY188y0fYSJ/9AK/mpz2U06falK2e4kdAW0CHy8xPguBPHGOk2Yxxh0jUWJO6V9vj8QO1zQ7jcczF2lg+HnkH+uJUlZv/uSOr1DexJqU850O1kcxT5SGKkiQGJ/5XsKBC8EMAUc8hmSJ+Xy9Pb4d9lvbxfo0Z78ePvflZvLzyD+exOTz5k9PJdjyJtekls4070YddE3J52JUl+5GHaVIzPkTBf/YBv6ESoxqD9lB2R6gVRSz/y/d1d21MTKyZ3yPWA5FZjFyvuUiTHhFL2DKm1STer+q3isc1LcAANAw9S0AADRMfQsAAA1T3wIAQMPUtwAA0DD1LQAANEx9CwAADVPfAgBAw9S3AADQMPUtABQJJ9kBmBLWR6367uWdgU7S5sISk/ZCqa83f/965pxXBHuEYN6lFlJO8OafFoFAb2u2uZmrk3e6eoZu7MYkpnunQynU3W60VmlMYkTP+MYbW4yzyAI1EBb5wHZgmuM1n1iPCnLEBfpqrqgJo0DXVFMSY0eQmL7N05QYD2/+ObwULm6DHBQERj4wU87mBzfKl5UccYG+mjFqwhhwZbbqbr4RCBwSE2iVb3m9bNZn2pTbt95tYpBVQhfMEsthIUhMupfCIangO7OPxMguk1OIuBPLEReYqzmjJoyB9VGDEQj6fJkfklYNJUoor8vmzVb53PCdnmKVx10u1bkXOZjNyolfKEXelj0khvYfkkFiIvxCyREXuKsZoyaMA90G7F1uphEIVPcctOcOxSrLpW5secNs1rtOilW1JObsqvp5u0pxlRTtPdcpMVTKid78oyMQyJ2fv5ohasK4yCVXGmbGEQh0A8x1gX0DGT5JK2+gzXKQkwCr6knMcIla2XmSGI9RaA5nyine/MMiEMjbK9K/OaMmjIJPM8w7AoGF4fPdHsy5yuu02d4ZESTG36p6EqM+VYkcrilB6Twca7pSTvJn6i2OcsQFn6vZoiaUx6eaZh2BgE2HXVaMNIuxxsPcZzHMPlTYNmSSM31RYjxTTjHAV2LkiAv/dsRjyBs1oTw+1dRYBAJqE5rbA0oqr2izPfxkiVHrymEV7Wu5uMTYg5OSGNF3b6L7d+fyzZ1yijf/0AgERvPJDz2NdVOuqAkjYH3UXgQC7cHNORFuMJsPNRPKK9usZXR6MpXHKjskLt2mmQdzt9VlWEXF7da+Zva9IjtEfiknefMPjEBAfM1XYvJFTRgFuqYai0BgHPQmJpkKTND7iPK6bDYOAa3WB+pxeIRVWo6nwzWWdkfUpNObv1GZxLji7+rRque0Sko5wZt/SgQCgzCJMTvPhPXlFq9BTv8mAMCsqW9BbSAxABSkvgW1gcQAUJD6FtQGEgNAQepbAABomPoWAAAapr4FAICGqW8BAKBh6lsAAGiY3Cn6eIcm3uMCALSJ/j/7Kkewo0PTo52VS36JyfWSJHCRPwKBT8q5rJJdUoX0zOIRCBS3qpLZ075bU6W1LQ5/lVOSmEJAYkagXASCsCgCIb+V/fVPNQIB8X68Z4kmBllgs8Yj9AIS0yDlIhAERhEItUp6+XaaEQgkq5qIQCB4q72V/OYP0BLjmkXLHvmZOAG5vOoDf8pFIEjxMsF6sZH89U8xAoGY1OwjENAzSU31eb/5RrHZjsIJUKBHfpfXNVCKchEIMkuM21//BCMQ0M43vEs0MbiSGx2FbXKuZmMkRkpZjl4wNAwkZhTKRSAoITGiv/4JRiDoJUabnuue22YdgeCzsVZyvSXI3ATSJSbA0aTSMJCYUSgXgaCUxHj5659IBIJetozbfF+f849AcC5wZzHnBM/l3CxKYkI88kNialI4AkFuifH31z+FCARcwB81/sScIxB8XtwqayVLC2S/+UYKQRIT6JEfElOTYhEIymz3Bvjrrx+BgHSEqmwAzz4CgVbRa/IZgc/TtWCJSfHIr6QAiRmFQhEImJRTrAr01z+NCAT2EyW1FHOPQKCWmVhRy37zB8JnMUEe+YUV3LiHcS6UMhEI2JRTrArw1z+dCATGes0YLzOPQHDidOhQPNti+c3X/bmbu/TyVTFlz+NGMfEJgDflIhA4U06xSvLXP90IBPIrAohAAAAAt5AYAEBR6lsAAGiY+hYAABqmvgUAgIbJmNaff9z++cdt/SIBAKZDxrQgMQAAk4xpQWIAACYZ04LEAABMMqYFiQEAmGRMCxIDADDJmBYkBgBgQn36cfW6eHz4GJoWJAYAYEJ+uny4evmxeHm6CUoLEgMAMGEvrD+8/Fi8vC6X3mlBYgAABv8HwDNtmD0ZsRsAAAAASUVORK5CYII=" alt="" />

summary(mtcars[vars])

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xzmEDf8LmCV9gc6JtcX2+NfNOudq7Q95Yv1e1+Pu3OjXJD/rV5sTR21lpMr1plE0mpZEHz8ZCxpLIcHBEbVo77Kg7f3j4uzU8c61StBvRlaCTe1ncnE/om1TdII7+0et1QJlXz3GreMnuFpmjePi7X22WYhzYCG+Kbt6XJXoVnjRSktBnjNouRNy7VKSh+oRbIqW81+iZjm6rVgL5MjVSadoEnEPRNrq+3Rj5peXVjnhHZnFcIVUQcRMi1ikCpfP0N/WqVHt6oqFZjkN/zd4kZRtNqVEKTEbdRxgT6mvTlzQLZVkHf5PqOcWc6LatuWHekisZ5hWHR3DbWoC6zfPK62dK1SntoixtLbrZBC5f0NiNx6Nvr2GsY0JfWl7sVzLcK+maZK0TemUrrVTfmGITOeYWlVjWFZd1rVcfRTUXh1SrHceAxatUIZ1ToB9sSb9Zcpcg13KnHGtCX0Jd/OogcExjUh76J9Q3QyJ02sm7MAucVhkojVBf30b226F+q2/1aV1fuWEPa1+2OuI1Zq2LPqBCjP8G2B/H8tLkwVCm5JBMMJKEvoa9dI70CmKPJ0+pD31T6hmhkT8uvG8Qr5fPBdcXesJWqDCIsJ5qFvdnzqUk4fCvE7aP27pVj1FLa6cYa+mKoNDoQbTb9nGW0SC3jGo4xJAhvC33V0rZrpKS1nFg1tFbQN7W+XhrZ0zqeX7k0ZjlLaMhvAQAAgHLIbwEAAIByyG8BAACAcshvAQAAgHLIbwEAAIByyG8BAACAcshvAQAAgHLIbwEAAIByyG8BAACAcshvAQAAgHJwX0E49DD6/1kM8ovvumcC5VV+r5tb04oRDdM4UVmlvmJRW7wfdh4O9ArQes/3qQAmn9UTu+Bfob5yWFDf58j17JtqTiZ9p8B9he6CqnP3Mb/c8pCDtdKuH2UfZ/wHzJpWdjGWxnvaCvXt/efs7N4PB7c2sgrN52P4Ok0h8Rr1FfFzZ8169p01pyPRIzw67iuO9f1RV2fJrdXlXF/WUqvU6KwxXr2sadlxr8bP3ar03R+ukqs7QzZbOUjJxhEljafl1emrEhXaSHr2mTWnY8GetJtatWv+3b5utqfqUe/EILTth7xVEbkoOze/QvKkoYs8/LMb226+v3V7WqIOhUR582bF+lqe7b4zUHoFeSwZhecsE/p66zuCZAY34+zIK/NcpnNe0ZXpqWpK4Vjfz6dN/2evTVdwWs98qgTZlBDevWda0RVtuiEMyz+7PF5Q2u63j8ujPjAHI460xCDUGhFlHNasrz3qTvO53CuM2E+nCLmzcn032+gBu7xOIJeqPaeJ9J0E5xV9T/tS3ZoJdXV8FZswbYptfXJkkZRKlrwoOWMNOSq3OMjqw7IzY7K70iqDC17c4FjWrK/h2db3ftReQdqQDMpOgojN69ZXmL6EP0Hys6+Wqq1XSKbvJDiveKlubbG+fVyut4sa5puoB9YRbq7YrYG0z39vUt+y98361r9XMKcVw3pcqpMhZMrYGVyrvuSzrdgs/9m2NWrYGe8cpSuHNeu72b52LXtIA60++9pXjiiNZZWDD84rhCoiDiLkWkWgLMVK386lVhGj9aZlr4RmnT8u8E6bYl8B+krPtrrgTvUKehvquWydciC5Zn1jrLLP1O29wrwnCtvwuM22sYa1+OYz1qC3kYmz3ux2wTNtkjMM69WXerYNwTv7hpLop/03M/3OSkLfaIIjQhtldZ9em2nE5gbnFZZa1RS0db5JH/gtplaZ9TNXCy2/lM2WuM3OtOLF2aK9L13f7evG4ySJ7QwSUT62uM28Q43Qdwx9RTnU0ZVFI8apQouIifWdBOcVhkojDJoMh7eG5H3Rd0fcSqlVpjMMrZ22IbxhN1LMtbwAzU47lEOSSega9e0I6BXU0qBO3RjV70sg4UByzfpaCtzxhLpGY+aaM/+JwtbdK+wNG57KVFpdnRTKWjkKvT9ci6lVrhqjYDjfbXknnqyv5rTDy7TJCmGN+hqWieiGgOq5Xf5OzOonH0hCX8MarGU2b372nTVnCROFLbzjAQAAEMlvAQAAgHLIbwEAAIByyG8BAACAcshvAQAAgHLIbwEAAIByyG8BAACAcshvAQAAgHLIbwEAAIBySP6TSaJOgmxA32UDfVcA6yI5RF+clw/fWiW9i5/sVXL51XbVF4L927gcubwpTMH69BVzbfRmM4lG0HcW+W3j7Vj9pDlrzmydafuniXT/5FOrZL9dTVucYJwi+8VU3Ubav+XkaKhMavw/PQpY+oq1fH37PO5IrzUTagR9088z/PNri6RkrTlF6DsGAWniYkrwaxXR4KZxLq1iiN3K+lZGc2ApOS/L7WtsJfruD1fJ2Rnh8XQajaBvlufXM7+WDDJqTgH6jkBoKSu+hW+HN3FdRdHA4pHRDOkV3RhmPUwDD//s9ki2oe2C2OJo9jP8vE/BevTlPdtjaQR98zy/XmGRmBdTNacUfUfAO4Eudr+K15aI7LxXbTTZYw3Kc7346yPUKpZ/9jHnCuokWkyrFOzbx+VRH9KH+luTvmSvMJVG0De5vnR+bXBj4ppiu+bXdxTYlwrjBTLylFCU4pSNjD7GEYn2VC78VqqxRrvvZNgos39rvP5S7du8yI9fe59u+LY51qlq1Rr1NXjDn0Yj6JtUX3N+bbS9gnSchDLJEfE7g76j4p+meWaErGoB0FVtpGItqla5aeuH4bb2bx33VBL2xdhXqW2WWrUifZ1xFsfUCPom15fOr422L1FmirpVtl4hs75jEJRM1s9Vq+Q6NEKtGm0GyrPBNNawf2srujaJPM9oirESqlTsxmAw69KXPkkyukbQN7m+/ncmriR3yI29QhH6RjNCKU9Tq8j1elGMyWuVfbMoZCtJD5contMgYjXnOXO1En3plms6jaBvan3970zsK5D7z8bd5iL0jSYkDbGvYl12V5csmZs/+qKhdNZNVYuc69niJ5M/Id8tuEugf9eRI3INN8PJtjXoK1hLPNuRGlliAkPfhPrS+bXeWe8DNNVMNacYfePxT6MpYatV0hzqpbrdr3V1ZdYqtaKoSoiHHNRzFIJOlrN0pjMM7d0Mjb79W+vvNp/3H6rbEvK+X86B5LL1lYwnT6ZGaWS0Cvqm1ZfOr49G9Ekqxq5JPn3HgHOR7OCBLkfLIZxegPv51IwXPN5vbIUnj1GLhtU78lRZ0FhjMFhGmPkav3X+rpJcKwrxbHiiKrU2fZX86qUdq5HNKuibWl/aWq5G0gXOmpNF3/HJbwEDchIHFgP0XTbQd2bkt4CDtHN1qubbCQMS6LtsoO+8yG8BE2EqCke+CwT6LhvoOyPyWwAAAKAc8lsAAACgHPJbAAAAoBzyWwAAAKAc8lsAAACgHPJbAAAAoBzyWwAAAKAc3FcogUe2r6R3wEXRe2VpIKOUmL71ujmR1vi2/bSZhb7Mb7VwlZ4FBX0TEKlRS+fqQ3rnTnZ6YXwdj0w7G9xX6C6ouhdS2AHIZo3dLyPPa6NcmH252Z0J785JHl3o66cvP5y94W7Qd3JiNFJLSXxCZY+qkgtYZ9o5wSudujoPpbw7Py7n2u5Ra0nYQ2f4BNZwRLZK6HFeAPr66Rve4kDfVMT3Cq00Dr+ndMx2XtqScV9xrO+Petf82+a53il+FuVJt1DbTJEoCnE7zhrpk2E3mN9KEH7eRT+RWhsREtjHH+jrp29wiwN9k+kb2yv0DbqjZddCXnukLRnnFd1Tcaqa6nKs7+fTpv+z0UAQpqk0aoXrLzDEQc0Dxz87GbKD+a0KUVkHd5JELJT6MH2EP+jrqW9oiwN90+kb1ysIy7zecwV+2pJxXtGPlV6qWzMtqo7WctcfpL7siI2vvFjGksKGlX1P2Cc7ylKyFPlZHL71AcGnjwYOfT31VXYy2epA33T6hmrUp2VFzpFjevulLRvnFS/VbWi2rreLEMDW0BsbRsRz3X5ptDdVLPu3BGJEl0t1GqIE961G32RsU7Ua0DdQX71dMAN9c+rL3URRmnJLy64G6fNJWzqsYmp7Y3URXI1i+BDbOzp81Tw3uOy7gjF7hkKRNq1GJTQZflvZgUDfKH2plWXLldA3A74aCXk0tezSLN8z7QxwXmGIozTUKi2EqWn1vK5MB7lKZ7JeQZqtm3b2pi0x6BunL/9oMvTNqi9DI0MATm2SRB0T4KadBc4rLLWqj+NqP6QxVDvTVpUjOut08KpLwIYzL0fElFN/22jinT3oG3WgwEd96FuQvkFP6GbrcXJshXOFYTYq7aB2R9zksxbKDow6D+1XLVMHaeKcUQl6i42RI+r9UqKsJq9V0Df8LUXD7qsxv9A3vb6+GhGXCRq15cNSbcG9wn7YDtU/Fw/aD9v9+8O1K2uiEKkFysLGGspkUKk39m8dORLiFBoGiWJhJqhS0NdTX1FBX/WhbxJ9ozUaoDaQCcjtlgX3CgAAANZEfgsAAACUQ34LAAAAlEN+CwAAAJRDfgsAAACUQ2T6//5n+9//bPNnAwAAwChEpkevAAAAiyIyPXoFAABYFJHp0SsAAMCiiEyPXgEAABZFZHr0CgAAsCgi06NXAACARdH978f+3+bP+w/f9OgVAABgUfT/e35/+vzafP797pUevQIAACwK6Y/Dt8+vzee/52d2evQKAACwKNS/fz3/+dp8fn37yUuPXgEAABYF9en331+bz6+n/S93evQKAACwKKhPm16BtceAXgEAABaF+jdWkAAAYM1If2C3GQAA1s3/AW/kp4T5yiToAAAAAElFTkSuQmCC" alt="" />

方法二:sapply()函数 #

 mystats<-function(x,na.omit=FALSE){
if(na.omit)
x<-x[!is.na(x)]
m<-mean(x)
n<-length(x)
s<-sd(x)
skew<-sum((x-m)^/s^)/n
kurt<-sum((x-m)^/s^)/n
return(c(n=n,mean=m,stdev=s,skew=skew,kurtosis=kurt))
}
sapply(mtcars[vars], mystats)

aaarticlea/png;base64,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" alt="" />

方法三:通过Hmisc包中的describe()函数——变量和观测的数量,缺失值和唯一值的数目、平均数,分位数,以及5个最大的值,和5个最小的值

 library(Hmisc)
describe(mtcars[vars])

方法四:通过pastecs包中的stat.desc()函数计算描述性统计量

stat.desc(x,basic=TRUE,desc=TRUE,norm=FALSE,P=0.95)

x是一个数据框或时间序列。

basic=TRUE(默认值),则计算其中所有值、空值、缺失值的数量,以及最小值、最大值、值域,还有总和。

desc=TRUE(默认值),则计算中位数、平均数、平均数的标准误、平均数置信度为95%的置信区间、方差、标准差以及变异系数。

norm=TRUE(非默认),则返回正态分布统计量,包括偏度和峰度(以及它们的统计显著程度)和Shapiro–Wilk正态检验结果。

这里使用了p值来计算平均数的置信区间(默认置信度为0.95)。

 library(pastecs)
stat.desc(mtcars[vars])

方法五:通过psych包中的describe()函数——非缺失值的数量、平均数、标准差、中位数、截尾均值、绝对中位差、最小值、最大值、值域、偏度、峰度和平均值的标准误

 library(psych)
describe(mtcars[vars])

以上方法都是为整体的数据计算描述性统计量

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