{"id":3537,"date":"2023-10-05T11:14:18","date_gmt":"2023-10-05T11:14:18","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=3537"},"modified":"2023-10-05T11:16:19","modified_gmt":"2023-10-05T11:16:19","slug":"week-4-ss2-third-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-ss2-third-term-mathematics-notes\/","title":{"rendered":"Week 4 &#8211; SS2 Third Term Mathematics Notes"},"content":{"rendered":"<p><strong>WEEK FOUR<br \/>\n<\/strong><strong>TOPIC:STATIASTICS<br \/>\n<\/strong><strong>CONTENT<\/strong><\/p>\n<ul>\n<li>Frequency Table.\u00a0\u00a0\u00a0\u00a0\n<\/li>\n<li>Cumulative Frequency Table.\n<\/li>\n<li>Histogram.\n<\/li>\n<\/ul>\n<p>\u00a0When data has a large number of values, it is cumbersome to prepare its frequency table; hence the data are organized into classes or groups to overcome this problem. E.g 0 \u2013 4, 5 \u2013 9, 10 \u2013 14 e.t.c.<br \/>\nThe range of the classes is first considered before we group the data. When data is divided into groups, it is called a grouped frequency distribution.<\/p>\n<p>\u00a0<strong>Grouped frequency distribution<\/strong>: The groups into which the data are arranged are called class intervals<br \/>\n e.g 15 \u2013 19<\/p>\n<p>\u00a0<strong><em>Class Limit<\/em><\/strong>: The number of each class intervals is called class limits of that interval.<br \/>\n Consider the class interval 20 \u2013 24,<br \/>\n20 = lower class limit,    24 = upper class limit<br \/>\n<strong><em>Class Boundaries<\/em><\/strong>: When data is given to the nearest unit, the class interval 34 \u2013 37, has a lower class boundary of 33.5 and upper class boundary of 37.5.<br \/>\nConsider the intervals below: 20 \u2013 24, 25 \u2013 29 ETC. To obtain the class boundaries of 25 \u2013 29,<br \/>\n24 + 25    = 24.5,     29 + 30 = 29.5<br \/>\n             2                                2<br \/>\n<strong><em>Class Width<\/em><\/strong>: This is the difference between the upper class boundary and the lower class boundary.<br \/>\n<strong><em>Class Marks<\/em><\/strong>: This is the centre or mid-point of any class interval. It is obtained by finding the average of the lower and upper limits. Find the class mark of the following class intervals 40 \u2013 44, 45 \u2013 49, 50 \u2013 54 etc.<\/p>\n<p>\u00a0<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td><strong>Class Interval       <\/strong><\/td>\n<td><strong>Class Mark<\/strong><\/td>\n<\/tr>\n<tr>\n<td>40 \u2013 44               <\/td>\n<td>40 + 44 = 42<br \/>\n      2<\/td>\n<\/tr>\n<tr>\n<td>45 \u2013 49 <\/td>\n<td>45 + 49 = 47<br \/>\n      2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u00a0<strong>Cumulative Frequency Table<\/strong>:<br \/>\nThis is the table that shows the cumulative frequency of each of the classes and it is the running total of the frequencies class by class, giving the total frequency.<\/p>\n<p>\u00a0<strong>EXAMPLE:<\/strong> In a mock examination for the final year Chemistry class, the following were obtained by 50 students.<br \/>\n                     71   63   70   45   59   82   61   79   37   89<br \/>\n                     33   56   39   42   64   73   59   67   72   60<br \/>\n                     46   36   61   87   91   67   54   72   39   43<br \/>\n                     57   65   45   52   35   46   64   37   95   86<br \/>\n                     76   73   67   71   74   82   61   59   58   43<br \/>\nUsing class interval 31 \u2013 40, 41 \u2013 50 \u2026 e.t.c   Construct a table showing the following columns: class interval, class boundary, class mark, frequency and cumulative frequency.<\/p>\n<p>\u00a0<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Class interval<\/td>\n<td>Frequency<\/td>\n<td>Class boundary<\/td>\n<td>Class mark<\/td>\n<td>Cumulative Frequency<\/td>\n<\/tr>\n<tr>\n<td>31 \u2013  40<\/td>\n<td>6<\/td>\n<td>30.5 \u2013 40.5<\/td>\n<td>35.5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>41 \u2013  50<\/td>\n<td>9<\/td>\n<td>40.5 \u2013 50.5<\/td>\n<td>45.5<\/td>\n<td>6 + 9     = 15<\/td>\n<\/tr>\n<tr>\n<td>51 \u2013  60<\/td>\n<td>9<\/td>\n<td>50.5 \u2013 60.5<\/td>\n<td>55.5<\/td>\n<td>9 + 15   = 24<\/td>\n<\/tr>\n<tr>\n<td>61 \u2013  70<\/td>\n<td>11<\/td>\n<td>60.5 \u2013 70.5<\/td>\n<td>65.5<\/td>\n<td>11 + 24 = 35<\/td>\n<\/tr>\n<tr>\n<td>71 \u2013  80<\/td>\n<td>9<\/td>\n<td>70.5 \u2013 80.5<\/td>\n<td>75.5<\/td>\n<td>9 + 35   = 44<\/td>\n<\/tr>\n<tr>\n<td>81 \u2013  90<\/td>\n<td>4<\/td>\n<td>80.5 \u2013 90.5<\/td>\n<td>85.5<\/td>\n<td>4 + 44   = 48<\/td>\n<\/tr>\n<tr>\n<td>91 \u2013 100<\/td>\n<td>2<\/td>\n<td>90.5 \u2013 100.5<\/td>\n<td>95.5<\/td>\n<td>2 + 48   = 50<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u00a0<strong><em>EVALUATION<br \/>\n<\/em><\/strong>The following figures show how many people visited an art gallery each day for 50 days.<br \/>\nUsing class interval 11 \u2013 20, 21 \u2013 30 \u2026 e.t.c   Construct a table showing the following columns: class interval, boundary, class mark, frequency and cumulative frequency.<br \/>\n           30   60   53   54   35   51   13   36   43   44<br \/>\n           44   38   39   52   45   39   25   27   31   44<br \/>\n           29   46   49   42   47   43   34   52   50   39<br \/>\n           53   25   28   51   54   33   35   45   51   59<br \/>\n           19   28   34   42   48   51   20   25   37   38<\/p>\n<p>\u00a0<strong>HISTOGRAM<\/strong><br \/>\n\t\tThis is a type of bar chart, each bar corresponding to one mark and with its length proportional to the frequency of that mark. The class marks or centres, class boundaries can be used on the variable scale. In histogram, the bars are joined together and must be of equal width, except when dealing with unequal class interval.<br \/>\nThe following table shows the distribution of marks scored by a class of 80 students.<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Marks<\/td>\n<td>10       &#8211;    14<\/td>\n<td>15       &#8211;    19<\/td>\n<td>20       &#8211;    24<\/td>\n<td>25        &#8211;   29<\/td>\n<td>30       &#8211;    34<\/td>\n<td>35      &#8211;     39<\/td>\n<\/tr>\n<tr>\n<td>Frequency<\/td>\n<td>            18<\/td>\n<td>            9<\/td>\n<td>           11<\/td>\n<td>             25<\/td>\n<td>            14<\/td>\n<td>           3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Draw a histogram for the distribution.   <\/p>\n<p>\u00a0<br \/>\n\u00a0<strong>Solution                                                                                                  <\/strong><\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Class Interval<\/td>\n<td>Class Mark<\/td>\n<td>Frequency<\/td>\n<\/tr>\n<tr>\n<td> 10        &#8211;      14<\/td>\n<td>          12<\/td>\n<td>18                                <\/td>\n<\/tr>\n<tr>\n<td> 15        &#8211;      19<\/td>\n<td>          17<\/td>\n<td>9<\/td>\n<\/tr>\n<tr>\n<td> 20        &#8211;      24<\/td>\n<td>          22<\/td>\n<td>11<\/td>\n<\/tr>\n<tr>\n<td> 25        &#8211;      29<\/td>\n<td>          27<\/td>\n<td>25<\/td>\n<\/tr>\n<tr>\n<td> 30        &#8211;      34<\/td>\n<td>          32<\/td>\n<td>14<\/td>\n<\/tr>\n<tr>\n<td> 35        &#8211;      39<\/td>\n<td>          37<\/td>\n<td>3                        <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100523_1114_Week4SS2Th1.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100523_1114_Week4SS2Th2.png\" alt=\"\"\/>25 \u2013 <strong><em><br \/>\n\t\t\t\t<\/em><\/strong><br \/>\n\u00a0<br \/>\n\u00a0                               20 \u2013<\/p>\n<p>\u00a0<br \/>\n\u00a015 \u2013<\/p>\n<p>\u00a0<br \/>\n\u00a010 \u2013<\/p>\n<p>\u00a0 5 \u2013<\/p>\n<p>\u00a0<br \/>\n\u00a0   0      9.5\u00a0\u00a0\u00a0\u00a0       14.5     19.5\u00a0\u00a0\u00a0\u00a0     24.5        29.5      34.5\u00a0\u00a0\u00a0\u00a039.5<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>Class boundaries<br \/>\n<\/strong><strong>EVALUATION<em><br \/>\n\t\t\t\t<\/em><\/strong>Draw a histogram to illustrate the data shown below.<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Heights(cm)<\/td>\n<td>120      &#8211; 129<\/td>\n<td>130   &#8211;    139<\/td>\n<td>140    &#8211;   149<\/td>\n<td>150   &#8211;    159<\/td>\n<td>160    &#8211;   169<\/td>\n<td>170     &#8211;  179<\/td>\n<\/tr>\n<tr>\n<td>Frequency<\/td>\n<td>           6<\/td>\n<td>             15<\/td>\n<td>              31<\/td>\n<td>             37<\/td>\n<td>         9<\/td>\n<td>            2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u00a0<strong><em>GENERAL EVALUATION<\/em><\/strong><br \/>\n\t\t1. Construct a table showing the following columns: class interval, class boundary, class mark, frequency ,and cumulative frequency for the distribution shown below.<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Shoe Sizes<\/td>\n<td>5    &#8211;  9<\/td>\n<td>10     &#8211;   14<\/td>\n<td>15    &#8211;    19<\/td>\n<td>20      &#8211;  24<\/td>\n<td>25    &#8211; 29<\/td>\n<td>30      &#8211;  34<\/td>\n<td>35      &#8211;  39<\/td>\n<\/tr>\n<tr>\n<td>No of students<\/td>\n<td>      5<\/td>\n<td>         7<\/td>\n<td>        6<\/td>\n<td>          2<\/td>\n<td>           3<\/td>\n<td>         4<\/td>\n<td>          3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>2. Draw a histogram for the distribution.<\/p>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>New General Mathematics SSS1, page 180, exercise 14e, numbers 2,3,4 and 7.<\/p>\n<p>\u00a0<strong><em>WEEKEND ASSIGNMENT<\/em><\/strong>:<br \/>\n1. The thickness of 20 samples of steel plate are measured and the results (in mm) to two significant figures are as follows:<br \/>\n 7.3     7.1        6.6       7.0     7.8      7.3     7.5       6.2      6.9      6.7<br \/>\n 6.5      6.8       7.2       7.4      6.5     6.9      7.2      7.6      7.0      6.8<br \/>\nConstruct a table showing the following columns: class interval, class boundary, class mark, frequency and cumulative frequency, using class interval 6.2 \u2013 6.4,   6.5 \u2013 6.7 e.t.c<\/p>\n<p>\u00a02. The following table shows the distribution of the masses of 120 logs of wood, correct to the nearest kg.<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Masses (kg)<\/td>\n<td>15      &#8211;   24<\/td>\n<td>25       &#8211;      34<\/td>\n<td>  35        &#8211;     44<\/td>\n<td>45      &#8211;    54<\/td>\n<td> 55    &#8211;    64<\/td>\n<\/tr>\n<tr>\n<td>Frequency<\/td>\n<td>           14<\/td>\n<td>            54<\/td>\n<td>           24<\/td>\n<td>            26<\/td>\n<td>           2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<ol>\n<li>Draw a histogram for the distribution.\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>WEEK FOUR TOPIC:STATIASTICS CONTENT Frequency Table.\u00a0\u00a0\u00a0\u00a0 Cumulative Frequency Table. Histogram. \u00a0When data has a large&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,278],"tags":[],"class_list":["post-3537","post","type-post","status-publish","format-standard","hentry","category-posts","category-third-term-ss2-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3537","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=3537"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3537\/revisions"}],"predecessor-version":[{"id":3538,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3537\/revisions\/3538"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=3537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=3537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=3537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}