{"id":9650,"date":"2023-06-01T16:11:30","date_gmt":"2023-06-01T10:41:30","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=9650"},"modified":"2023-06-02T17:38:08","modified_gmt":"2023-06-02T12:08:08","slug":"ap-ssc-10th-class-maths-notes-chapter-14","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-ssc-10th-class-maths-notes-chapter-14\/","title":{"rendered":"AP SSC 10th Class Maths Notes Chapter 14 Statistics"},"content":{"rendered":"

Students can go through AP SSC 10th Class Maths Notes<\/a> Chapter 14 Statistics to understand and remember the concepts easily.<\/p>\n

AP State Syllabus SSC 10th Class Maths Notes Chapter 14 Statistics<\/h2>\n

\u2192 Statistics is a branch of mathematics which deals with collection, organisation, presentation, analysis and interpretation of numerical data.<\/p>\n

\u2192 Data is a collection of actual information which is used to make logical inferences.<\/p>\n

\u2192 Arithmetic Mean of raw data:
\nThe Arithmetic Mean (A.M.) of a raw data viz. x1<\/sub>, x2<\/sub>, x3<\/sub>, ……., xn<\/sub> is the sum of values of all observations divided by the number of observations.
\nArithmetic Mean (A.M.) = \"AP
\nEg.: Sita secured 23, 24, 24, 22 and 20 marks in a test. Her mean marks are
\nA.M. = \\(\\frac{23+24+24+22+20}{5}\\) = \\(\\frac{113}{5}\\) = 22.6<\/p>\n

\"AP<\/p>\n

\u2192 A.M. by direct method:
\nLet x1<\/sub>, x2<\/sub>, x3<\/sub>, ……., xn<\/sub> be observations with respective frequencies f1<\/sub>, f2<\/sub>, ……, fn<\/sub>
\ni.e., x1<\/sub> occurs for f1<\/sub> times, x2<\/sub> occurs for f2<\/sub> times, ….., xn<\/sub> occurs for fn<\/sub> times.
\n\"AP<\/p>\n

\u2192 For a grouped data, it is assumed that the frequency of each class interval is centered around its mid-point and the A.M. is given by A.M. = \\(\\frac{\\Sigma \\mathrm{f}_{\\mathrm{i}} \\mathrm{x}_{\\mathrm{i}}}{\\Sigma \\mathrm{f}_{\\mathrm{i}}}\\)<\/p>\n

\u2192 A.M. by deviation method, \\(\\overline{\\mathbf{x}}=\\mathbf{a}+\\frac{\\Sigma \\mathbf{f}_{\\mathbf{i}} \\mathbf{d}_{\\mathbf{i}}}{\\Sigma \\mathbf{f}_{\\mathbf{i}}}\\)
\nwhere, a – assumed mean
\ndi<\/sub> – deviation = xi<\/sub> – a.
\nStep – 1: Choose \u2018a\u2019 from the central values.
\nStep – 2: Obtain di<\/sub> by subtracting a from xi<\/sub>.
\nStep – 3: Multiply fi<\/sub> and di<\/sub>.
\nStep – 4: Find \u2211fi<\/sub>di<\/sub> and \u2211fi<\/sub> .
\nStep – 5: Find \\(\\overline{\\mathbf{x}}=\\mathbf{a}+\\frac{\\Sigma \\mathbf{f}_{\\mathbf{i}} \\mathbf{d}_{\\mathbf{i}}}{\\Sigma \\mathbf{f}_{\\mathbf{i}}}\\)<\/p>\n

\u2192 A.M. by step-deviation method:
\n\"AP
\nStep – 1: Choose \u2018a\u2019 from mid values.
\nStep – 2: Obtain ui<\/sub> = \\(\\frac{x_{i}-a}{h}\\).
\nStep – 3: Multiply fi<\/sub> and ui<\/sub>.
\nStep – 4: Find Efi<\/sub>ui<\/sub> and Sfi<\/sub>.
\nStep – 5: Find \\(\\overline{\\mathrm{x}}=\\mathrm{a}+\\left(\\frac{\\Sigma \\mathrm{f}_{\\mathrm{i}} \\mathrm{u}_{\\mathrm{i}}}{\\Sigma \\mathrm{f}_{\\mathrm{i}}}\\right) \\times \\mathrm{h}\\)<\/p>\n

\"AP<\/p>\n

\u2192 Mode : Mode is the size of variable which occurs most frequently.<\/p>\n

\u2192 Mode of a grouped data:
\n\"AP
\nWhere, l – lower boundary of the modal class,
\nh – size of the modal class interval,
\nf1<\/sub> – frequency of modal class.
\nf0<\/sub> – frequency of the class preceding the modal class.
\nf2<\/sub> – frequency of the class succeeding the modal class.<\/p>\n

\u2192 Median: Median is defined as the measure of the central items when they are in descending or ascending order of magnitude.<\/p>\n

\u2192 Median for a grouped data:
\n\"AP
\nwhere,
\nl – lower boundary of median class,
\nn – number of observations.
\ncf – cumulative frequency of class preceding the median class.
\nf – frequency of median class.
\nh – size of the median class.<\/p>\n

\u2192 Cumulative frequency curve or an ogive:
\nFirst we prepare the cumulative frequency table, then the cumulative frequencies are plotted against the upper or lower limits of the corresponding class intervals. By joining the points the curve so obtained is called a cumulative frequency or ogive.
\nOgives are of two types.<\/p>\n

    \n
  1. Less than ogive: Plot the points with the upper limits of the classes as abscissa and the corresponding less than cumulative frequencies as ordinates. The points are joined by free hand smooth curve to give less than cumulative frequency curve or the less than ogive. It is a rising curve.<\/li>\n
  2. Greater than ogive: Plot the points with the lower limits of the classes as abscissa and the corresponding greater than cumulative frequencies as ordinates. Join the points by a free hand smooth curve to get the greater than ogive. It is a falling curve.<\/li>\n<\/ol>\n

    When the points are joined by straight lines, the figure obtained is called cumulative frequency polygon.<\/p>\n

    \"AP<\/p>\n

    \u2192 Median can be obtained from cumulative frequency curve: From \\(\\frac{n}{2}\\) frequency draw a line parallel to X-axis cutting the curve at a point. From this point draw a perpendicular to the axis. The point at which the perpendicular meets the X – axis determines the median.<\/p>\n

    Less than type and greater than type curves intersects at a point. From this point of intersection if we draw a perpendicular on the X-axis then this cuts X-axis at some point. This point gives the median.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Students can go through AP SSC 10th Class Maths Notes Chapter 14 Statistics to understand and remember the concepts easily. AP State Syllabus SSC 10th Class Maths Notes Chapter 14 Statistics \u2192 Statistics is a branch of mathematics which deals with collection, organisation, presentation, analysis and interpretation of numerical data. \u2192 Data is a collection … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/9650"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=9650"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/9650\/revisions"}],"predecessor-version":[{"id":40887,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/9650\/revisions\/40887"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=9650"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=9650"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=9650"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}