phys326Lab2.ipynb

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  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np \n",
      "from matplotlib import pyplot as plt\n",
      "%matplotlib inline\n",
      "from pylab import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data=np.loadtxt(\"Magnetic+Moment+Measurements+Survey.csv\", delimiter=',')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(40, 4)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[0:3:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([[  1.32000000e+00,   5.00000000e-02,   5.36500000e+01,\n",
        "          5.00000000e-02],\n",
        "       [  1.48000000e+00,   3.00000000e-02,   5.36400000e+01,\n",
        "          1.00000000e-01],\n",
        "       [  1.20000000e+00,   1.00000000e-01,   5.36300000e+01,\n",
        "          5.00000000e-01]])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m=data[:,0]\n",
      "dm=data[:,1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the mean mass."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z=sum(m)/40\n",
      "z"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "1.4205000000000001"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "My mass is 1.2 grams with an uncertainty of .1 grams, so I would change my .3 to include the mean."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dz=(sum((m-sum(m)/40)**2)/40)**.5\n",
      "dz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "0.19679875507736319"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the standard deviation of uncertainty in the mass measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q=dz/(40**.5)\n",
      "q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.031116615336504699"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the weighted mean of our mass measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W=(sum(1/((m-z)**2)*m))/sum(1/((m-z)**2))\n",
      "W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "1.4053558594046851"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of the weighted mean."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dW=1/((sum(1/((m-z)**2))**.5))\n",
      "dW"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "0.0053649383029114308"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.histogram(m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "(array([ 9,  0, 14,  3,  5,  7,  1,  0,  0,  1]),\n",
        " array([ 1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ,  2.1]))"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the Histogram for measurements of mass. I plotted a Gaussian over it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(hist,bins,p)=plt.hist(m,bins=10,normed=True)\n",
      "plt.plot(bins,(1/(dz*(2*np.pi)**.5)*np.exp((-(bins-z)**2/(2*dz**2)))))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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37/9e5e6FVOwiFtTGvw0fTviQTYc2Eb8qns+Pf252JHEjFbuIRQU0DSDt3jQG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\n5v8DV4leebKvEW0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb3c8ac3350>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=np.array(m)\n",
      "y=np.array(dm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 119
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are our coefficients for the line of best fit, where A is the y-intercept and B is the slope."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A=(np.sum(x*x)*np.sum(y)-np.sum(x)*np.sum(x*y))/(3*np.sum(x*x)-(np.sum(x))**2)\n",
      "A"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "0.015384581898594183"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B=(3*np.sum(x*y)-np.sum(x)*np.sum(y))/(3*np.sum(x*x)-(np.sum(x))**2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is line of best fit on our data for mass."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,y,'ro')\n",
      "plt.plot(x,A+B*x)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fb3c887bad0>"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "np.polyfit(x,y,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 70,
       "text": [
        "array([ 0.60288118, -0.74026772])"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When the polyfit graph is placed on the graph it doesn't correlate to the data at all."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of the line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S=(sum((y-B*x-A)**2)/38)**.5\n",
      "S"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "0.23323167384392071"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of the coefficients."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dA=S*(sum(x**2)/(40*sum(x**2)-(sum(x))**2))**.5\n",
      "dA"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "0.26872298993887439"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dB=S*(40/(40*sum(x**2)-(sum(x)**2)))**.5\n",
      "dB"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "0.18738515687011689"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the weighted line for the mass measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w=(1/(sum((m-z)**2)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 120
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the y-intercept for the line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=((sum(w*x**2))*sum(w*y)-sum(w*x)*sum(w*x*y))/(sum(w)*sum(w*(x**2))-(((sum(w*x)))**2))\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 121,
       "text": [
        "0.014580090001736826"
       ]
      }
     ],
     "prompt_number": 121
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the slope."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b=(sum(w)*sum(w*x*y)-sum(w*x)*sum(w*y))/(sum(w)*sum(w*(x**2))-(sum(w*x))**2)\n",
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 122,
       "text": [
        "0.081492782646924652"
       ]
      }
     ],
     "prompt_number": 122
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the graph with the weighted line of the mass measurements. This changes the line too low such that it doesn't collect enough of the data points."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,y,'ro')\n",
      "plt.plot(x,a+b*x)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb3c86dc5d0>"
       ]
      }
     ],
     "prompt_number": 123
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.polyfit(x,y,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([ 0.60288118, -0.74026772])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[2:3:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "array([[  1.2 ,   0.1 ,  53.63,   0.5 ]])"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c=data[:,2]\n",
      "dD=data[:,3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 79
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because one persons measurement of the diameter was so much of an outlier I omitted it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D=c[c>50]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 124
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the mean Diameter"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v=sum(D)/39\n",
      "v"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 125,
       "text": [
        "53.656153846153863"
       ]
      }
     ],
     "prompt_number": 125
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "My diameter is 54 milimeters with an uncertainty of 1 milimeter, so I would leave my error bars as they are on the graph from Lab 1."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dv=(sum((D-sum(D)/39)**2)/39)**.5\n",
      "dv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 126,
       "text": [
        "0.12626011784012373"
       ]
      }
     ],
     "prompt_number": 126
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the Standard deviation of mean for the diameter measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s=dv/(39**.5)\n",
      "s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "0.020217799568951759"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the weighted mean of the diameter measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W=(sum(1/((D-v)**2)*D))/sum(1/((D-v)**2))\n",
      "W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "53.654310036534177"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of the weighted mean."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dW=1/((sum(1/((m-z)**2))**.5))\n",
      "dW"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "0.0053649383029114308"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the Histogram for the measurements of the diameter. I plotted the Gaussian over it.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(hist,bins,p)=plt.hist(D,bins=20,normed=True)\n",
      "plt.plot(bins,(1/(dv*(2*np.pi)**.5)*np.exp(-(bins-v)**2/(2*dv**2))))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ITDEdjRfOAgyLgPNrgKpmwDhAyrP34Lm73l7OPiyEQG55Lvbl78O+gn04VnYM9427z1z0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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb3c8b13510>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=np.array(c)\n",
      "y=np.array(dD)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 165
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are our coefficients, where A is the y-intercept and B is the slope."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A=(np.sum(x*x)*np.sum(y)-np.sum(x)*np.sum(x*y))/(3*np.sum(x*x)-(np.sum(x))**2)\n",
      "A"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 166,
       "text": [
        "0.00023094079015950763"
       ]
      }
     ],
     "prompt_number": 166
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B=(3*np.sum(x*y)-np.sum(x)*np.sum(y))/(3*np.sum(x*x)-(np.sum(x))**2)\n",
      "B"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 167,
       "text": [
        "0.010377770444942581"
       ]
      }
     ],
     "prompt_number": 167
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the line of best fit for our data for diameter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,y,'ro')\n",
      "plt.plot(x,A+B*x)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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q7bff1k033aRFixbprbfeUkVFRapSAIDHHE2tFBQUaNu2bQoGg4rFYlq1ahUhDgA5wrUL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\nDYgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb3c8ab46d0>"
       ]
      }
     ],
     "prompt_number": 171
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When we make a polyfit of the line doesn't correlate to the data at all."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.polyfit(x,y,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 169,
       "text": [
        "array([ 0.04389668, -1.79541447])"
       ]
      }
     ],
     "prompt_number": 169
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of our line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S=(sum((y-B*x-A)**2)/37)**.5\n",
      "S"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 279,
       "text": [
        "1.2383696305674723"
       ]
      }
     ],
     "prompt_number": 279
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty of the y-intercept."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dA=S*(sum(x**2)/(40*sum(x**2)-(sum(x))**2))**.5\n",
      "dA"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 280,
       "text": [
        "17.951857713768025"
       ]
      }
     ],
     "prompt_number": 280
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty of the slope."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dB=S*(40/(40*sum(x**2)-(sum(x)**2)))**.5\n",
      "dB"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 281,
       "text": [
        "0.33512318930379742"
       ]
      }
     ],
     "prompt_number": 281
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the weighted line for our diameter measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=np.array(c)\n",
      "y=np.array(dD)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 160
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w=1/((sum((D-v)**2)))\n",
      "w"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 161,
       "text": [
        "1.6084331386716859"
       ]
      }
     ],
     "prompt_number": 161
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Here are the coefficients of the weighted line."
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=((sum(w*x**2))*sum(w*y)-sum(w*x)*sum(w*x*y))/(sum(w)*sum(w*(x**2))-(((sum(w*x)))**2))\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 162,
       "text": [
        "0.00021909622748799944"
       ]
      }
     ],
     "prompt_number": 162
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b=(sum(w)*sum(w*x*y)-sum(w*x)*sum(w*y))/(sum(w)*sum(w*(x**2))-(sum(w*x))**2)\n",
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 163,
       "text": [
        "0.010377991544706413"
       ]
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the graph of weighted line for the diameter measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,y,'ro')\n",
      "plt.plot(x,a+b*x)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fb3c89ce490>"
       ]
      }
     ],
     "prompt_number": 164
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "My best estimate for magnetic moment can be calculated using this equation\n",
      "\n",
      "$\\tau$ = $\\frac{D}{2}$ $\\times$ $mg$ \n",
      "where we make the angle with between the arm and the magnetic field $90$ degrees, such that we have\n",
      "\n",
      "$\\tau$ = $\\frac{D}{2}$ $mg$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T=(v/2)*(z)*(9.81)\n",
      "T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 121,
       "text": [
        "373.85206887115402"
       ]
      }
     ],
     "prompt_number": 121
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of magnetic moment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dT=((((dz/z)**2)+((dv/v)**2))**.5)*T\n",
      "dT"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 122,
       "text": [
        "51.80164280646472"
       ]
      }
     ],
     "prompt_number": 122
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is my best estimate for the magnetic moment."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\tau$ = $374$ $\\pm$ $52$\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}