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                                  "value": "functiona user-defined function which takes a 1D array of     values, and outputs a single numerical statistic. This function     will be called on the values in each bin.  Empty bins will be     represented by function([]), or NaN if this returns an error."
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        "value": "import numpy as np\nfrom scipy import stats\nimport matplotlib.pyplot as plt\n",
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        "value": "\nFirst some basic examples:\n\nCreate two evenly spaced bins in the range of the given sample, and sum the\ncorresponding values in each of those bins:\n\n"
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        "value": "values = [1.0, 1.0, 2.0, 1.5, 3.0]\n",
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        "value": "stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)\n",
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        "value": "\nMultiple arrays of values can also be passed.  The statistic is calculated\non each set independently:\n\n"
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        "value": "values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]]\n",
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        "value": "stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',\n                       bins=3)\n",
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        "value": "\nAs a second example, we now generate some random data of sailing boat speed\nas a function of wind speed, and then determine how fast our boat is for\ncertain wind speeds:\n\n"
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        "value": "rng = np.random.default_rng()\nwindspeed = 8 * rng.random(500)\nboatspeed = .3 * windspeed**.5 + .2 * rng.random(500)\nbin_means, bin_edges, binnumber = stats.binned_statistic(windspeed,\n                boatspeed, statistic='median', bins=[1,2,3,4,5,6,7])\n",
        "execution_status": "success"
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        "value": "plt.figure()\nplt.plot(windspeed, boatspeed, 'b.', label='raw data')\nplt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5,\n           label='binned statistic of data')\nplt.legend()\n",
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        "value": "\nNow we can use ``binnumber`` to select all datapoints with a windspeed\nbelow 1:\n\n"
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        "value": "low_boatspeed = boatspeed[binnumber == 0]\n",
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        "value": "\nAs a final example, we will use ``bin_edges`` and ``binnumber`` to make a\nplot of a distribution that shows the mean and distribution around that\nmean per bin, on top of a regular histogram and the probability\ndistribution function:\n\n"
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        "value": "x = np.linspace(0, 5, num=500)\nx_pdf = stats.maxwell.pdf(x)\nsamples = stats.maxwell.rvs(size=10000)\n",
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