{"id":2815,"date":"2023-10-03T13:49:22","date_gmt":"2023-10-03T13:49:22","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2815"},"modified":"2023-10-03T13:53:39","modified_gmt":"2023-10-03T13:53:39","slug":"week-2-ss2-first-term-economics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-2-ss2-first-term-economics-notes\/","title":{"rendered":"Week 2 &#8211; SS2 First Term Economics Notes"},"content":{"rendered":"<p>\u00a0<strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n<\/strong><strong>WEEK TWO<br \/>\n<\/strong><strong>MEASURES OF DISPERSION  OF A GROUPED FREQUENCY DISTRIBUTION<br \/>\n<\/strong><strong>CONTENT<br \/>\n<\/strong><\/p>\n<ul>\n<li>Range\n<\/li>\n<li>Mean Deviation\n<\/li>\n<li>Variance\n<\/li>\n<li>Standard Deviation\n<\/li>\n<\/ul>\n<p><strong> MEASURES OF DISPERSION: <\/strong> also known as measures of spread or variation describes how the data given in any distribution are spread about the &#8216;Mean&#8217;, or the overall spread of the data. These measures are the range, mean \u2013 deviation, standard deviation, variance, coefficient of variation, etc.<strong><br \/>\n\t\t\t<\/strong><br \/>\n\u00a0<strong>The Range<\/strong>: The range of a data is the difference between the highest and the lowest value in the data. The formula for calculation of range is:<br \/>\nRange = Highest value \u2013 Lowest value<\/p>\n<p>\u00a0<strong>The Mean Deviation<\/strong>: This measures the dispersions around the arithmetic mean. It tells us how far, on the average, the individual observations are from the mean.  For a grouped frequency distribution<br \/>\n           Mean Deviation = \u2211f\/x- x\/<br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0                                 \u2211f<br \/>\n<strong>Variance<\/strong>: This is the average of the square about the deviations of the measurement about their mean.<br \/>\nVariance = \u2211f(X \u2013 X)<sup>2<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0             \u2211f                 <\/p>\n<p>\u00a0<strong>Standard Deviation<\/strong>: This is the square root of the average of the square of the deviations of the measurement about their mean.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi1.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi2.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi3.png\" alt=\"\"\/>  Standard Deviation =         <\/p>\n<p>\t\t\t\u2211f(X \u2013 X )<sup>2<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0                                                \u01a9f             \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>Example:<\/strong><br \/>\n\t\tThe data below shows the weight of 50 students to the nearest kg.<br \/>\n65 58 51 36 23 40 53 59 70 51 46 59 50 67 46 39 61 62 73 60 71 51 47 32 48 40 40 51 58 67 60 69 43 52 37 26 38 50 59 40 44 54 42 68 74 45 39 48 55.<\/p>\n<ol>\n<li>\n<div>Prepare a grouped frequency table\n<\/div>\n<\/li>\n<li>\n<div>Calculate:\n<\/div>\n<ol>\n<li>\n<div>The range\n<\/div>\n<\/li>\n<li>\n<div>The mean deviation\n<\/div>\n<\/li>\n<li>\n<div>The variance\n<\/div>\n<\/li>\n<li>\n<div>The standard deviation\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><strong>NB:<\/strong> Note that the standard Deviation is the positive square root of the variance.<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>\n\u00a0<strong>Class <\/strong>\u00a0<\/td>\n<td>\n\u00a0<strong>F<\/strong>\u00a0<\/td>\n<td>\n\u00a0<strong>Mid-point<br \/>\n<\/strong><strong>      X<\/strong>\u00a0<\/td>\n<td>\n\u00a0<strong>FX <\/strong>\u00a0<\/td>\n<td><strong>       _<br \/>\n<\/strong><strong>\/X- X\/ <\/strong><\/td>\n<td><strong>         _<br \/>\n<\/strong><strong>F\/X-X\/<\/strong><\/td>\n<td><strong>      _<br \/>\n<\/strong><strong>(X-X )<sup>2<\/sup><\/strong><\/td>\n<td><strong>         _ <sup><br \/>\n\t\t\t\t\t\t\t\t\t<\/sup><\/strong><strong>F(X-X)<sup>2<\/sup><br \/>\n\t\t\t\t\t\t\t\t<\/strong><strong><br \/>\n\t\t\t\t\t\t\t\t<\/strong>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>21-30\u00a0<\/td>\n<td>2\u00a0<\/td>\n<td>25.5\u00a0<\/td>\n<td>51\u00a0<\/td>\n<td>25.5\u00a0<\/td>\n<td>50.4<\/td>\n<td>635.04\u00a0<\/td>\n<td>1270.08\u00a0<\/td>\n<\/tr>\n<tr>\n<td>31-40\u00a0<\/td>\n<td>10\u00a0<\/td>\n<td>35.5\u00a0<\/td>\n<td>355\u00a0<\/td>\n<td>15.2\u00a0<\/td>\n<td>152\u00a0<\/td>\n<td>231.04\u00a0<\/td>\n<td>2310.40\u00a0<\/td>\n<\/tr>\n<tr>\n<td>41-40\u00a0<\/td>\n<td>12\u00a0<\/td>\n<td>45.5\u00a0<\/td>\n<td>546\u00a0<\/td>\n<td>5.2\u00a0<\/td>\n<td>62.4\u00a0<\/td>\n<td>27.04\u00a0<\/td>\n<td>324.48\u00a0<\/td>\n<\/tr>\n<tr>\n<td>51-60\u00a0<\/td>\n<td>15\u00a0<\/td>\n<td>55.5\u00a0<\/td>\n<td>832.5\u00a0<\/td>\n<td>4.8\u00a0<\/td>\n<td>72\u00a0<\/td>\n<td>23.04\u00a0<\/td>\n<td>345.60\u00a0<\/td>\n<\/tr>\n<tr>\n<td>61-70\u00a0<\/td>\n<td>8\u00a0<\/td>\n<td>65.5\u00a0<\/td>\n<td>524\u00a0<\/td>\n<td>14.8\u00a0<\/td>\n<td>118.4\u00a0<\/td>\n<td>219.04\u00a0<\/td>\n<td>1752.32\u00a0<\/td>\n<\/tr>\n<tr>\n<td>71-80\u00a0<\/td>\n<td>3\u00a0<\/td>\n<td>75.5\u00a0<\/td>\n<td>226.5\u00a0<\/td>\n<td>24.8\u00a0<\/td>\n<td>74.4\u00a0<\/td>\n<td>615.04\u00a0<\/td>\n<td>1845.12\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td><strong>50<\/strong>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td><strong>2535<\/strong>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td><strong>529.60<\/strong>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td><strong>7848<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u2211fx = 2535 = 50.7<br \/>\n\t\t\t\u00a0\u00a0\u00a0\u00a0 \u2211f        50<\/p>\n<ol>\n<li>\n<div>Range = Highest score \u2013Lowest score\n<\/div>\n<\/li>\n<\/ol>\n<p>\u00a0\u00a0\u00a0\u00a0                =        74             &#8211;        23<br \/>\n                            =                   51kg<\/p>\n<ol>\n<li>\n<div> Mean Deviation\n<\/div>\n<\/li>\n<\/ol>\n<p>                                     =\u2211f\/ X \u2013X\/           =         529.60 = 10.59kg<br \/>\n\u00a0\u00a0\u00a0\u00a0                                \u2211f                               50<br \/>\n(iii) Variance = \u2211f\/X \u2013 X \/<sup>2<\/sup><br \/>\n\t\t                            \u00a0\u00a0\u00a0\u00a0            \u2211f<br \/>\n                                     = 7848 = 156.9kg<br \/>\n                                                         50<br \/>\n(iv)\u00a0\u00a0\u00a0\u00a0Standard Deviation<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi4.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi5.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi6.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi7.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi8.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi9.png\" alt=\"\"\/><br \/>\n\t\t\t\u2211f\/X \u2013 X \/<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0                            156.96<br \/>\n       \u2211f                          =                                                         =12.53kg<br \/>\n<strong>EVALUATION QUESTION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>How is the mid-point (X) ascertained in a grouped frequency table?\n<\/div>\n<\/li>\n<li>\n<div>State two advantages of the mean over other measures of central tendency (i.e median and mode)\n<\/div>\n<\/li>\n<li>\n<div>The table below shows the income of forty Workers in a factory in N\n\t\t\t\t<\/div>\n<\/li>\n<\/ol>\n<p>61 78 70 83 92 67 66 83<br \/>\n76 68 79 84 82 86 81 60<br \/>\n78 77 86 77 81 92 80 70<br \/>\n70 40 75 60 74 82 77 87<br \/>\n63 94 76 87 81 77 87 84.<\/p>\n<h2>Using a class interval of 40-49, 50-59 etc<br \/>\n<\/h2>\n<ol>\n<li>\n<div>Construct a grouped frequency table of the distribution.\n<\/div>\n<\/li>\n<li>\n<div>Calculate the mean of the distribution.\n<\/div>\n<\/li>\n<\/ol>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>Fundamentals of Economics for SSS by R.A I. Ayanwuocha Page 97-101\n<\/div>\n<\/li>\n<li>\n<div>Comprehensive Economics for SSS by J.U Anyaele page 36 \u201338\n<\/div>\n<\/li>\n<\/ol>\n<p>\u00a0<strong>GENERAL EVALUATION QUESTIONS<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>Give five reasons why government participates in business enterprises.\n<\/div>\n<\/li>\n<li>\n<div>Define ageing population.\n<\/div>\n<\/li>\n<li>\n<div>Explain the sources of finance available to a public limited liability business.\n<\/div>\n<\/li>\n<li>\n<div>Explain any three weapons that can be used by a trade union during trade      dispute.\n<\/div>\n<\/li>\n<li>\n<div>What is occupational mobility?\n<\/div>\n<\/li>\n<\/ol>\n<p>\u00a0<strong>WEEKEND ASSIGNMET<br \/>\n<\/strong>1. \u00a0\u00a0\u00a0\u00a0In a class of 5 students the following scores were obtained in a mathematics test 10,2,6,7,12. What is the median score (A) 2 (B) 4(C) 6 (D) 7<br \/>\n2. \u00a0\u00a0\u00a0\u00a0Which measure of central tendency can be applied to find the highest goal scorer in a football match (A) mean (b) Mode (C) Median (D) range<br \/>\n3. \u00a0\u00a0\u00a0\u00a0If the following scores 2, 4, 6, and 10 with frequencies 3,5,7, and 10 respectively makes up a distribution, then the  mean score is (A) 5.7 (B) 6.7 (C) 7.5 (D) 5.4<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1349_Week2SS2Fi10.png\" alt=\"\"\/>4. \u00a0\u00a0\u00a0\u00a0In the formula X = \u2211fx<br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0    \u2211f<br \/>\n\u2211fX stands for (A) total number of observations (B) Sum of frequencies times observations (C) Sum of frequencies (D) number of elements times frequencies<br \/>\n5.\u00a0\u00a0\u00a0\u00a0The most reliable measure of central tendency is (a) Mode (b) median (c) Histogram (d) mean<\/p>\n<p>\u00a0<strong>SECTION B<br \/>\n<\/strong><\/p>\n<ol>\n<li>Give the definition of the mean deviation and the standard deviation\n<\/li>\n<li>Explain the difference between continuous data and discrete data.\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\t\t\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 WEEK TWO MEASURES OF DISPERSION OF A GROUPED FREQUENCY DISTRIBUTION CONTENT Range Mean Deviation&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,229],"tags":[],"class_list":["post-2815","post","type-post","status-publish","format-standard","hentry","category-posts","category-first-term-ss2-economics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2815","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2815"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2815\/revisions"}],"predecessor-version":[{"id":2816,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2815\/revisions\/2816"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}