{"id":1492,"date":"2023-09-29T08:32:25","date_gmt":"2023-09-29T08:32:25","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=1492"},"modified":"2023-09-29T08:34:40","modified_gmt":"2023-09-29T08:34:40","slug":"week-8-and-9-jss-3-first-term-mathematics-lesson-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-8-and-9-jss-3-first-term-mathematics-lesson-notes\/","title":{"rendered":"Week 8 and 9 – Jss 3 First Term Mathematics Lesson Notes"},"content":{"rendered":"

WEEK 8
\n<\/strong>EVERYDAY STATISTICS
\n<\/strong>Data Presentation
\n<\/strong>Frequency Table
\n<\/strong>Example: The raw data below show the number of mobile phone calls made by a group of students in a certain day.
\n5\u00a0\u00a0\u00a0\u00a06\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a08\u00a0\u00a0\u00a0\u00a04\u00a0\u00a0\u00a0\u00a04\u00a0\u00a0\u00a0\u00a05\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a08\u00a0\u00a0\u00a0\u00a010
\n7\u00a0\u00a0\u00a0\u00a06\u00a0\u00a0\u00a0\u00a05\u00a0\u00a0\u00a0\u00a08\u00a0\u00a0\u00a0\u00a05\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a08\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a010\u00a0\u00a0\u00a0\u00a07
\n6\u00a0\u00a0\u00a0\u00a05\u00a0\u00a0\u00a0\u00a06\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a05\u00a0\u00a0\u00a0\u00a04\u00a0\u00a0\u00a0\u00a05\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a08<\/p>\n

    \n
  1. \n
    Use a tally mark to prepare a frequency table for this data\n<\/div>\n<\/li>\n
  2. \n
    What calls occur most often?\n<\/div>\n<\/li>\n
  3. \n
    What percentage of students made 8 calls?\n<\/div>\n<\/li>\n<\/ol>\n

    SOLUTION
    \n<\/strong><\/p>\n

      \n
    1. \n
      \"\"\/\"\"\/\"\"\/No of calls made\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Tally\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Frequency\n<\/div>\n

      4\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\u00a0\u00a0\u00a03\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/5\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\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/\"\"\/\"\"\/6\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\u00a0\u00a0\u00a04\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/7\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\u00a0\u00a0\u00a09
      \n\"\"\/8\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\u00a0\u00a0\u00a05
      \n\"\"\/9\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\u00a0\u00a0\u00a00
      \n10\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\u00a0\u00a0\u00a02\n<\/li>\n

    2. \n
      7 calls\n<\/div>\n<\/li>\n
    3. \n
      x 100\n<\/div>\n

      = 16%\n<\/li>\n<\/ol>\n

      \u00a0Pictogram
      \n<\/strong>Example:<\/strong> The following table shows the colour of cars in a car park one morning. Draw pictogram to illustrate this data.
      \n\"\"\/\"\"\/Colours of car\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0frequency\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
      \nBlack\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a020
      \nWhite\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a017
      \nRed\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a08\u00a0\u00a0\u00a0\u00a0
      \nYellow\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05
      \nGreen\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010<\/p>\n

      \u00a0SOLUTION
      \n<\/strong>Colour of cars
      \n<\/strong>\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/Black\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/White\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/\"\"\/\"\"\/Red\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/\"\"\/Yellow\u00a0\u00a0\u00a0\u00a0
      \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/Green
      \n\"\"\/\"\"\/Key: \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 1<\/p>\n

      \u00a0
      \n\u00a0
      \n\u00a0Bar Chart
      \n<\/strong>Bar charts consist of series of bars with equal width.
      \nExample: Draw bar chart to illustrate the data of the example above <\/p>\n

      \u00a0
      \n\u00a0Frequency \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0colour of cars of the park
      \n\"\"\/<\/p>\n

      \u00a0Compound bar chart<\/strong>
      \n\t\tIt is used to compare two or more different sets of information.
      \nExample:
      \n\"\"\/The following table shows the number of candidates who gained admission into higher institutions at a certain town over a period of years.
      \nYear\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Boys\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Girls
      \n1997\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a065\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a046
      \n1998\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a050\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a055
      \n1999\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a080\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a073
      \n2000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a070\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a092
      \n2001\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a045\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a064<\/p>\n

        \n
      1. \n
        Illustrate this information on dual bar chart\n<\/div>\n<\/li>\n
      2. \n
        Illustrate what year did girls leave the highest admission?\n<\/div>\n<\/li>\n
      3. \n
        Illustrate what year did boys have the least admission?\n<\/div>\n<\/li>\n
      4. \n
        How many more boys had admission than girls in 1999?\n<\/div>\n<\/li>\n
      5. \n
        How many more candidates gained admission in 2000 than 1998?\n<\/div>\n<\/li>\n<\/ol>\n

        SOLUTION
        \n<\/strong>No of candidates \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
        \n\"\"\/<\/p>\n

        \u00a0ASSIGNMENT
        \n<\/strong>EXERCISE 22.1; NO 1, 2, AND 3 PAGE 226.
        \n<\/strong>
        \n\u00a0Pie charts
        \n<\/strong>A pie chart is a circle divided into sectors whose angle are used to display data
        \nExample:<\/p>\n

          \n
        1. \n
          In a certain year, the expenditure of a university is shown in the table below.\n<\/div>\n

          \u00a0\"\"\/
          \n\t\t\t\t\"\"\/Items\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Expenditure in Million Naira
          \nEquipment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a020
          \nSalaries and wages\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a025
          \nBuilding projects\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a070
          \nMaintenance\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a025
          \nMiscellaneous\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010\n<\/li>\n

        2. \n
          Draw a pie chart to illustrate the information\n<\/div>\n<\/li>\n
        3. \n
          What percentage of total expenditure goes on project\n<\/div>\n<\/li>\n<\/ol>\n

          \"\"\/\"\"\/SOLUTION
          \n<\/strong>\"\"\/Items\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Expenditure in Million Naira\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Angles
          \nEquipment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a020\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 48o<\/sup>
          \n\t\t\"\"\/\"\"\/Salaries and wages\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a025\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 60o<\/sup>
          \n\t\t\"\"\/Building Project\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a070\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 168o<\/sup>
          \n\t\t\"\"\/Maintenance\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a025\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 60o<\/sup>\u00a0\u00a0\u00a0\u00a0
          \n\"\"\/Miscellaneous\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 24o<\/sup>
          \n\t\tTotal\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0150\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 360o<\/sup>
          \n\t\t\"\"\/
          \n\t\tb)\u00a0\u00a0\u00a0\u00a0x = 46.7o<\/sup><\/p>\n

          \u00a0
          \n\u00a0Example 2
          \n\"\"\/
          \n\t\tHistory 40%\u00a0\u00a0\u00a0\u00a0, Geography 30%\u00a0\u00a0\u00a0\u00a0, Further Mathematicss10% and Physics 20%
          \nThe pie chart shows the percentage of students taking Further Mathematics, Physics, History and Geography<\/p>\n

            \n
          1. What angle represented subject?\n<\/li>\n
          2. What fraction of students are taking history\n<\/li>\n
          3. \"\"\/If the total number of students is 500, how many students are taking physics?\n<\/li>\n<\/ol>\n

            \"\"\/SOLUTION
            \n<\/strong>\"\"\/Subject\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Percentage\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Angles
            \n<\/strong>\"\"\/Further Maths\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 36o<\/sup>
            \n\t\t\"\"\/Physics\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a020%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 72o<\/sup>
            \n\t\t\"\"\/History\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a040%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 144o<\/sup>
            \n\t\t\"\"\/Geography\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a030%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = 108o<\/sup>\u00a0\u00a0\u00a0\u00a0
            \nTotal\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0100%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 360o<\/sup>
            \n\t\t(b)\u00a0\u00a0\u00a0\u00a0Fraction for history = =
            \n(c) No of Physics Students = x 500 = 100 Students
            \nExercise: Ex. 22.2 No 1 and 5 page 228 and 229<\/p>\n

            \u00a0WEEK 9
            \n<\/strong>MEASURE OF CENTRAL TENDENCY (MEAN, MEDIAN, MODE)
            \n<\/strong>Example<\/p>\n

              \n
            1. \n
              In a test 10 pupils obtained the following marks 5, 7, 4, 8, 5, 7, 10, 9, 3. Find (a) The mean mark (b) Median mark (c) Modal mark.\n<\/div>\n<\/li>\n<\/ol>\n

              SOLUTION
              \n<\/strong><\/p>\n

                \n
              1. \n
                Mean = = =\n<\/div>\n

                Mean = 6.4\n<\/li>\n

              2. \n
                Arrange the marks in ascending order of magnitude 3, 4, 5, 5, 6, 7, 8, 9, 10\n<\/div>\n

                Median = = = 6.5\n<\/li>\n

              3. \n
                The mode is the value that occurs most the mode are 5 and 7 this is bimodal.\n<\/div>\n<\/li>\n<\/ol>\n

                Calculating average from frequency tables
                \n<\/strong>Examples: In a science test. The following score shown in the table below were obtained out of 10 by some students.
                \n\"\"\/\"\"\/Marks\u00a0\u00a0\u00a0\u00a0No of Students (Frequency)
                \n<\/strong>0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02
                \n1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01
                \n2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02
                \n3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04
                \n5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01
                \n6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a07
                \n7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03
                \n8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04
                \n9 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01<\/p>\n

                  \n
                1. \n
                  Find (i) the mode (ii) the median (iii) the mean of the frequency distribution\n<\/div>\n<\/li>\n
                2. \n
                  How many students scored at least 5 marks\n<\/div>\n<\/li>\n<\/ol>\n

                  \u00a0
                  \n\u00a0
                  \n\u00a0
                  \n\u00a0SOLUTION
                  \n<\/strong><\/p>\n

                    \n
                  1. \n
                    (i) Mode = 8\n<\/div>\n

                    (ii) 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9
                    \nMedian = = 5.5
                    \n(iii) Sum of values = 0 + 0 + 1 + 2 + 2 + 3 + 4 + 4 + 5 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 = 99\n<\/li>\n<\/ol>\n

                    Mean = = = 4.95<\/p>\n

                    \u00a0
                    \n\u00a0ALTERNATIVELY
                    \n<\/strong>
                    \n\u00a0\"\"\/
                    \n\t\t\t<\/strong>\"\"\/\"\"\/Scores frequency (f) frequency x score
                    \n<\/strong>\"\"\/0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02 x 0 = 0
                    \n\"\"\/1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01 x 1 = 1
                    \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02 x 2 = 4
                    \n3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01x 3 = 9
                    \n4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03 x 4 = 12
                    \n5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01 x 5= 5
                    \n6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02 x 6 = 12
                    \n7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03 x 7 = 21
                    \n8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04 x 8 = 32
                    \n\"\"\/9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01 x 9 = 99
                    \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 20 = 99
                    \nMean = = = 4.95
                    \nExercise: Ex 22.3 No 1 and 2 page 231
                    \nRange: <\/strong>It gives a measure of how spread and the values are. Range = Highest value \u2013 Lowest value
                    \nExamples<\/p>\n

                      \n
                    1. \n
                      Find the range of these numbers 9, 4, 7, 6, 12, 8, 15, 10\n<\/div>\n

                      Solution: Range = 15 \u2013 4 = 11\n<\/li>\n<\/ol>\n

                      \u00a0<\/p>\n

                        \n
                      1. \n
                        A student obtained the following marks each out of 100 in different geography test 42, 44, 50 40, 54, 48, 10 88. Find (a) The mean (b) the range (c) make a comment why the range in this case is not good to measure the spread.\n<\/div>\n<\/li>\n<\/ol>\n

                        SOLUTION
                        \n<\/strong><\/p>\n

                          \n
                        1. \n
                          Mean = =\n<\/div>\n

                          Mean = 48\n<\/li>\n

                        2. \n
                          Range = 88 \u2013 10\n<\/div>\n

                          = 78\n<\/li>\n

                        3. \n
                          The two extreme values i.e. 10 and 88 affects the range, so at it not a good measure of spread in this particular case.\n<\/div>\n<\/li>\n<\/ol>\n

                          Exercise
                          \nFind the range of the following<\/p>\n

                            \n
                          1. \n
                            35cm, 50cm, 45cm, 90cm, 30cm\n<\/div>\n<\/li>\n
                          2. \n
                            67km, 50km, 20km, 48km, 55km\n<\/div>\n<\/li>\n
                          3. \n
                            5.2, 4.7, 8.2, 9.3, 6.4, 5.5\n<\/div>\n<\/li>\n<\/ol>\n

                            ASSIGNMENT
                            \n<\/strong>EXERCISE 22.4; NO 8, 9 AND 10. PAGE 240.
                            \n<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

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