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    "%matplotlib widget\n",
    "from collections.abc import Iterable\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import chi2\n",
    "import math\n",
    "from fractions import Fraction as F"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AS\n",
    "This contains automations for A-level (AS) Maths stats ordered in the same way as they are on [integral maths](https://my.integralmaths.org/)."
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "## Collecting and Interpreting Data\n",
    "### Sampling\n",
    "- Simple random sampling\n",
    "  - Random procedure\n",
    "    - e.g. drawing tickets, random number generator\n",
    "  - In a finite sample space, all candidates have an equal chance of being selected\n",
    "  - Sampling is done without replacement\n",
    "  - Selections are independent\n",
    "- Cluster sampling\n",
    "  - Only some subgroups of a sample space are selected\n",
    "  - Only appropriate when subgroups are reasonably representative of the entire sample space\n",
    "- Opportunity sampling\n",
    "  - Selection by opportunity\n",
    "    - e.g. interviewing passers by on a street\n",
    "- Stratified sampling\n",
    "  - Used when sample space can be divided into subgroups (strata)\n",
    "    - ... to ensure all strata are sampled\n",
    "  - Weighting needs to be used if numbers of samples from each strata are not proportional to the size of the strata\n",
    "- Quota sampling\n",
    "  - Same as stratified sampling with a quota for each strata\n",
    "- Self-selected sample\n",
    "  - Individuals chose to be sampled\n",
    "  - e.g. online poll\n",
    "- Systematic sampling\n",
    "  - Systematic procedure\n",
    "  - e.g. every 10th person on alphabetically sorted list"
   ]
  }
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