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    "## Data Analysis III\n",
    "\n",
    "### February 6, 2024\n",
    "\n",
    "Goals for Today\n",
    "* Loading data from text files\n",
    "* Computing weighted averages\n",
    "* Plotting with errorbars\n",
    "* Compute the Chi-Squared"
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   "source": [
    "#Download the  file 'hdata.dat' from the course website. Open it in a text editor to get a sense of what it contains"
   ]
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    "Look at the syntax of np.loadtxt, and use it to open the file.\n",
    "\n",
    "Before you run any code, answer the following questions\n",
    "* What kind of delimiter is used? Is it space, comma, tab?\n",
    "* How many header lines are used? Headers often provide relevant information such as units, instrument settings used for the data included. \n",
    "* When running np.loadtext, you have to specify optional arguments for delimiter, as well as number of rows to skip\n",
    "\n"
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    "#run data = np.loadtext(...) to store the contents of the file into an array called data\n",
    "#split up data into two arrays: yvalues and yunc. You may find it useful to use the transpose operation (np.transpose())"
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    "#Make a plot of Measurement number vs value with properly labeled axes\n",
    "#Calculate the mean of the values using np.mean() or some other method you like\n"
   ]
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    "### Recall from last week:  \n",
    "Average: $\\bar{x} = \\frac{1}{N}\\Sigma_ix_i$\n",
    "\n",
    "Weighted average: $\\bar{x}_{weighted} = \\frac{\\Sigma_iw_ix_i}{\\Sigma_iw_i}$,  where the weights are given by $w_i = \\frac{1}{\\alpha_i^2}$ \n",
    "\n",
    "In this notation, $\\alpha_i$ represents the uncertainty of data point $i$."
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    "calculate the weighted mean. (Hint: a dot product makes the numerator easy. you can take the dot product of two matrices a and b either with numpy.dot -- i.e., np.dot(a,b) -- or by using the @ sign -- i.e., a @ b.) \n",
    "\n",
    "\n"
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    "Make a plot of Measurement number vs value with properly labeled axes\n",
    "\n",
    "Use ```np.hlines``` to draw horizontal lines for the mean, and the weighted means.\n",
    "\n"
   ]
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    "Look up the syntax of the function ```np.errorbar()```\n",
    "\n",
    "For example, if given three arrrs, xval,yval,yerr, then the following code snippet plots errorbar plots with circular indicators\n",
    "``` errorbarplot(xval,yval,yerr,fmt = 'o') ```"
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    "Next, plot the residuals $x_i - \\bar{x}$"
   ]
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    "And then plot the normalized residuals ($(x_i - \\bar{x})/\\alpha_i$)"
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    "Now square the residuals and add them up. This gives the chi-squared."
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