{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "# Linear Algebra\n", "##Addition of vectors and matrices" ], "metadata": { "id": "76yOpI0S212X" } }, { "cell_type": "markdown", "source": [ "Pure Python" ], "metadata": { "id": "-cZ03wkr4k2k" } }, { "cell_type": "code", "source": [ "def add_lists(x, y):\n", " res = []\n", " for i in range(len(x)):\n", " res.append(x[i] + y[i])\n", " return res\n", "a = [1, 2, 3]\n", "b = [1, 1, 1]\n", "add_lists(a, b)" ], "metadata": { "id": "sSih7Q734sSn", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "ffaaa369-6afa-4003-ed05-23aade351c26" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[2, 3, 4]" ] }, "metadata": {}, "execution_count": 2 } ] }, { "cell_type": "code", "source": [ "a + b" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "RaRb0jkj5l5h", "outputId": "f43ffb87-0bdd-49eb-fc89-c163d10fca43" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[1, 2, 3, 1, 1, 1]" ] }, "metadata": {}, "execution_count": 3 } ] }, { "cell_type": "markdown", "source": [ "Uning Numpy" ], "metadata": { "id": "wNYfjDO45dGi" } }, { "cell_type": "code", "source": [ "import numpy as np\n", "a_vec = np.array(a)\n", "b_vec = np.array(b)\n", "a_plus_b = a_vec + b_vec\n", "a_min_b = a_vec - b_vec\n", "a_plus_b" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "0-ggYTqr376b", "outputId": "478592ad-a831-45ae-f364-dc48ba7a5aae" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([2, 3, 4])" ] }, "metadata": {}, "execution_count": 4 } ] }, { "cell_type": "code", "source": [ "a_min_b" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "5BFhntZM4hnI", "outputId": "1c762976-c26f-4df2-eb38-ac5f0248e784" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([0, 1, 2])" ] }, "metadata": {}, "execution_count": 5 } ] }, { "cell_type": "code", "source": [ "#not recommended\n", "a = np.matrix([\n", " [11, 12],\n", " [21, 22]\n", "])\n", "a" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "f_TSLMCe6Gur", "outputId": "af46d6b9-5b72-4c7f-c418-d9e3bbdb6ac9" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "matrix([[11, 12],\n", " [21, 22]])" ] }, "metadata": {}, "execution_count": 6 } ] }, { "cell_type": "code", "source": [ "a = np.array([\n", " [1, 2],\n", " [3, 4]\n", "])\n", "a" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "pEeZzVLD6qz9", "outputId": "9de28d44-5e9d-4349-fcae-43755c6ecf75" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[1, 2],\n", " [3, 4]])" ] }, "metadata": {}, "execution_count": 7 } ] }, { "cell_type": "code", "source": [ "b = np.array([\n", " [11, 12],\n", " [13, 14]\n", "])\n", "a + b" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "4ZX72n_z62GD", "outputId": "2b5b6b58-d20e-4bee-cd04-192c3767663d" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[12, 14],\n", " [16, 18]])" ] }, "metadata": {}, "execution_count": 8 } ] }, { "cell_type": "markdown", "source": [ "##Multiplication of vectors and matrices" ], "metadata": { "id": "b1n4vCaU51YK" } }, { "cell_type": "code", "source": [ "np.matmul(a, b)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "22Lh9_Q17ZLf", "outputId": "e6928af0-aeb1-40b6-9ea8-66a4423c0236" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[37, 40],\n", " [85, 92]])" ] }, "metadata": {}, "execution_count": 9 } ] }, { "cell_type": "code", "source": [ "# matmul is matrix multiplication, but \"*\" is element-wise product\n", "a * b" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "6xlKZtsm82eG", "outputId": "d484f265-c90d-4139-fd45-227144537ab3" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[11, 24],\n", " [39, 56]])" ] }, "metadata": {}, "execution_count": 10 } ] }, { "cell_type": "code", "source": [ "#dot product or scalar product\n", "np.dot(a, b)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "Z1cYuDwQ9a63", "outputId": "099f8085-9228-4392-fd43-b810444007ba" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[37, 40],\n", " [85, 92]])" ] }, "metadata": {}, "execution_count": 11 } ] }, { "cell_type": "code", "source": [ "np.dot(np.array([1, 2]), np.array([2, 2]))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "_Te420yX9xxj", "outputId": "5c8f89ae-db16-445f-e05d-745cfdf8e9c1" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "6" ] }, "metadata": {}, "execution_count": 12 } ] }, { "cell_type": "code", "source": [ "np.dot(3, 4)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "9nTUZuRs-Aul", "outputId": "721c9c41-c6e2-4c2b-9208-8d6f0ef51122" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "12" ] }, "metadata": {}, "execution_count": 13 } ] }, { "cell_type": "code", "source": [ "np.matmul(2, 3)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 159 }, "id": "i0Zi8_i19gPS", "outputId": "0ede6588-f84c-41cf-c977-05cbbc8df9a7" }, "execution_count": null, "outputs": [ { "output_type": "error", "ename": "ValueError", "evalue": "matmul: Input operand 0 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mValueError\u001b[0m: matmul: Input operand 0 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)" ] } ] }, { "cell_type": "code", "source": [ "a = np.array([\n", " [1, 2],\n", " [3, 4]\n", "])\n", "b = np.ones((3,3))\n", "a.shape" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "d1V-PfdY8HY_", "outputId": "0de5cd76-2f52-4fcb-a89b-8d9f128cb70a" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "(2, 2)" ] }, "metadata": {}, "execution_count": 15 } ] }, { "cell_type": "code", "source": [ "b.shape" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "lrHD4rXE8Zur", "outputId": "6f8f79f6-13bf-452c-ccd5-48f628008441" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "(3, 3)" ] }, "metadata": {}, "execution_count": 16 } ] }, { "cell_type": "code", "source": [ "np.matmul(a, b)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 159 }, "id": "d5CTJ6rU8cR1", "outputId": "b6b84228-b272-4f9e-9384-17282efbc901" }, "execution_count": null, "outputs": [ { "output_type": "error", "ename": "ValueError", "evalue": "matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 3 is different from 2)", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mValueError\u001b[0m: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 3 is different from 2)" ] } ] }, { "cell_type": "markdown", "source": [ "## Transposed matrix" ], "metadata": { "id": "VukHwNCS-XGg" } }, { "cell_type": "code", "source": [ "a" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "uqkhMU1p-fdR", "outputId": "975aa97f-95d8-4079-c4cf-c12d718a142e" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[1, 2],\n", " [3, 4]])" ] }, "metadata": {}, "execution_count": 18 } ] }, { "cell_type": "code", "source": [ "a.transpose()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "zxjL-isU-p_Z", "outputId": "e84ed0ff-b784-4359-e287-a63bbfea60af" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[1, 3],\n", " [2, 4]])" ] }, "metadata": {}, "execution_count": 19 } ] }, { "cell_type": "code", "source": [ "b" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "IWkrpHdy-uhW", "outputId": "fe8beb7a-37fa-4086-8228-27ee6df36523" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[1., 1., 1.],\n", " [1., 1., 1.],\n", " [1., 1., 1.]])" ] }, "metadata": {}, "execution_count": 20 } ] }, { "cell_type": "code", "source": [ "b.transpose()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "lEtry8aB-wBT", "outputId": "b5e09189-8633-4048-bd16-f9688eb54f5b" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[1., 1., 1.],\n", " [1., 1., 1.],\n", " [1., 1., 1.]])" ] }, "metadata": {}, "execution_count": 21 } ] }, { "cell_type": "markdown", "source": [ "## Vector norm" ], "metadata": { "id": "rZzCcAqj_OQU" } }, { "cell_type": "code", "source": [ "a = np.array([1, 2, 3])\n", "np.linalg.norm(a)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "pV5WVCfL_SQF", "outputId": "acb92906-e8ba-4b42-9234-df7292561107" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "3.7416573867739413" ] }, "metadata": {}, "execution_count": 22 } ] }, { "cell_type": "code", "source": [ "a" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "P1aBd8ygZ6rh", "outputId": "ecd1ea1c-4ebc-40db-c0de-d328b58a22d6" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([1, 2, 3])" ] }, "metadata": {}, "execution_count": 23 } ] }, { "cell_type": "code", "source": [ "import math\n", "def vec_norm(x):\n", " res = math.sqrt(sum([el**2 for el in x]))\n", " return res\n", "vec_norm(a)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "qrt81EBg_f9S", "outputId": "6ff5fb93-5cda-4c06-cf6e-9a69e6d6143e" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "3.7416573867739413" ] }, "metadata": {}, "execution_count": 24 } ] }, { "cell_type": "markdown", "source": [ "# Descriptive statistics" ], "metadata": { "id": "72uuUliYAkfB" } }, { "cell_type": "markdown", "source": [ "## Mean" ], "metadata": { "id": "_g9YfZCwC3gg" } }, { "cell_type": "code", "source": [ "a_list = [1000, 2000, 2300, 2300, 2300, 3500, 3600, 10000]\n", "a_mean = sum(a_list)/len(a_list)\n", "a_mean" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "QNQ-1aW-AnAk", "outputId": "55784105-d506-4272-ec03-1817891a94b6" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "3375.0" ] }, "metadata": {}, "execution_count": 25 } ] }, { "cell_type": "code", "source": [ "np.mean(a_list)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "LPSae4WOB_Nh", "outputId": "603253fc-731c-4555-97d3-2c5bf07d28fd" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "3375.0" ] }, "metadata": {}, "execution_count": 26 } ] }, { "cell_type": "code", "source": [ "a_array = np.array(a_list)\n", "a_array.mean()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "nSfOFLIACFza", "outputId": "426dc000-43bf-4998-eb39-2ba6903cdd47" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "3375.0" ] }, "metadata": {}, "execution_count": 27 } ] }, { "cell_type": "code", "source": [ "a_list.mean()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 141 }, "id": "1IG5WJq9CbsW", "outputId": "bae48f4e-93bc-4f68-d57c-50ed02db3ae5" }, "execution_count": null, "outputs": [ { "output_type": "error", "ename": "AttributeError", "evalue": "'list' object has no attribute 'mean'", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma_list\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m: 'list' object has no attribute 'mean'" ] } ] }, { "cell_type": "code", "source": [ "a = np.array([1000, 2000, 2300, 2300, 2300, 3500, 3600, 10000, np.nan])\n", "a" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "GWKJ7rvCH5QU", "outputId": "bce71d9a-b0fa-4164-f302-ba5cd3be017f" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([ 1000., 2000., 2300., 2300., 2300., 3500., 3600., 10000.,\n", " nan])" ] }, "metadata": {}, "execution_count": 29 } ] }, { "cell_type": "code", "source": [ "a.mean()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "eD_FRpPMIXQk", "outputId": "cd0c19f2-bcf4-4165-b5ed-d21d031e5008" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "nan" ] }, "metadata": {}, "execution_count": 30 } ] }, { "cell_type": "code", "source": [ "np.nanmean(a)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "collapsed": true, "id": "vcEMlBR-IaDt", "outputId": "0f9015ed-38fe-440b-ae57-920b1419b7a3" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "3375.0" ] }, "metadata": {}, "execution_count": 31 } ] }, { "cell_type": "code", "source": [ "a_m = np.array([\n", " [1, 2],\n", " [3, 4]\n", "])\n", "a_m.mean()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "hC7THLCDGxLB", "outputId": "ac25186f-8c92-4458-ff6a-76d76ea93796" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2.5" ] }, "metadata": {}, "execution_count": 32 } ] }, { "cell_type": "markdown", "source": [ "## Mode" ], "metadata": { "id": "E9T3O56iC-zo" } }, { "cell_type": "code", "source": [ "import statistics\n", "statistics.mode(a_list)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "KqrplI2qDEST", "outputId": "77eb151c-c76a-44d6-a8e7-2699cf174507" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2300" ] }, "metadata": {}, "execution_count": 33 } ] }, { "cell_type": "code", "source": [ "statistics.mode(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "ekGfs0XiDPtV", "outputId": "356268a9-b8b1-46cb-dfa5-d2f84b06bf9c" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2300" ] }, "metadata": {}, "execution_count": 34 } ] }, { "cell_type": "code", "source": [ "from scipy import stats\n", "stats.mode(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "EajQ4XXCDaPJ", "outputId": "0141d9c0-5d1e-4d28-e66a-c657446acd07" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "ModeResult(mode=2300, count=3)" ] }, "metadata": {}, "execution_count": 35 } ] }, { "cell_type": "code", "source": [ "#array because multimode is possible\n", "stats.mode(a_array).mode" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "UQUHvzdoEBhw", "outputId": "75604af3-6d5e-41de-9816-0ec1d6fb6477" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2300" ] }, "metadata": {}, "execution_count": 36 } ] }, { "cell_type": "markdown", "source": [ "## Median" ], "metadata": { "id": "2x3pOhRyEbmP" } }, { "cell_type": "code", "source": [ "np.median(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "OmlAmIZ_EdnX", "outputId": "dc9790cd-0663-46b9-8a1e-2bc816f52da4" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2300.0" ] }, "metadata": {}, "execution_count": 37 } ] }, { "cell_type": "code", "source": [ "statistics.median(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "NStDoxeDE256", "outputId": "fe517297-b4b8-4adc-afe4-e94d0b81bd62" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2300.0" ] }, "metadata": {}, "execution_count": 38 } ] }, { "cell_type": "markdown", "source": [ "## Standard deviation" ], "metadata": { "id": "94Nc-m6cFbpV" } }, { "cell_type": "markdown", "source": [ "Numpy.std ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculations is N - ddof, where N represents the number of elements. By default ddof is zero." ], "metadata": { "id": "WlvntBS-FeDq" } }, { "cell_type": "code", "source": [ "np.std(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "8pyVpqPzFllQ", "outputId": "a5e26b5e-7c4e-4b6e-876e-3c52a4221f02" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2620.9492555179318" ] }, "metadata": {}, "execution_count": 39 } ] }, { "cell_type": "code", "source": [ "np.std(a_array, ddof = 1)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "G2RTQGwmFrfc", "outputId": "eaaca768-eb0c-4711-9245-742edba957e6" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2801.912612076666" ] }, "metadata": {}, "execution_count": 40 } ] }, { "cell_type": "code", "source": [ "statistics.stdev(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "pGdHRPxtF18s", "outputId": "18a6c1af-bd81-4b91-cd5f-5a0eb29badd8" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2801.9125610910846" ] }, "metadata": {}, "execution_count": 41 } ] }, { "cell_type": "code", "source": [ "statistics.pstdev(a_array)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "6B4y6MbJF6zB", "outputId": "56a47948-e565-4c30-818b-7df698249c24" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2620.9492555179318" ] }, "metadata": {}, "execution_count": 42 } ] }, { "cell_type": "markdown", "source": [ "## Percentiles" ], "metadata": { "id": "6E5pIwd9GIu8" } }, { "cell_type": "code", "source": [ "np.percentile(a_array, 25)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "NhjRwQtxGZuU", "outputId": "4ef732ee-dbde-4436-b898-4c3b54fcfb0d" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2225.0" ] }, "metadata": {}, "execution_count": 43 } ] }, { "cell_type": "code", "source": [ "np.percentile(a_array, 95)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "y4RhDHynGiKz", "outputId": "af7504aa-6612-4e78-dcbc-268aaa4fe54d" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "7759.999999999996" ] }, "metadata": {}, "execution_count": 44 } ] }, { "cell_type": "code", "source": [ "np.percentile(a_array, [25, 50, 75])" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "e8EtTefdHOUB", "outputId": "30cf4e6c-aaa0-4ef6-fdfb-09cf3083835a" }, "execution_count": null, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([2225., 2300., 3525.])" ] }, "metadata": {}, "execution_count": 45 } ] } ] }