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  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the similar image and create bar graph in place of line graph. <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text and formula in different colour <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show a boy writing on a notepad. <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text and formula. <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the table first and then given text. <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text and headings one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show the given text one by one <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show question first then table and after that options one by one. <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show question first then table. <br /> Show sentence ‘Write the mean literacy rate’ at last <br />
  • Guidance for animator: <br /> On Screen Text: <br /> All body text <br /> Show question first then options one by one. <br />

Statistics Statistics Presentation Transcript

  • Statistics
  • Learning Objectives: In this lesson, you will learn about : Mean of Ungrouped data Mean of Grouped Data •Direct method •Assumed mean method •Step deviation method Mode of Grouped Data Median of Grouped Data
  • Mean of Ungrouped Data The mean or average of observations, is the sum of the values of all the observations divided by the total number of observations. Formula to find out mean We use x So, the mean x= for indicating mean. x of the data is given by: f1 x1 + f 2 x2 + ........ + f n xn f1 + f 2 + ........ + f n
  • We can also write this in short form by using capital sigma ∑ . x= ∑ f i xi fi Note: Here, i varies from 1 to n.
  • Let’s understand this formula by an example.
  • Example 1 The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Marks obtained (xi) 10 20 36 40 50 56 60 70 72 Number of students (fi) 1 1 3 4 3 2 4 4 1 Now, we have to find out the mean of the marks obtained by the students.
  • Solution Recall the formula. x= ∑ f i xi fi So, it is clear that we require the product of each xi with the corresponding frequency fi .
  • Marks Obtained (xi) Number of students (fi) fi x i 10 1 10 20 1 20 36 3 108 40 4 160 50 3 150 56 2 112 60 4 240 70 4 280 72 1 72 Total ∑fi = 23 ∑fi xi = 1152 Now, put the values ∑fi = 23 and ∑fi xi = 23 in the given formula. We get
  • x= ∑ f i xi fi 1152 x= 23 x = 50.09 Therefore, the mean marks obtained is 50.09
  • Mean of Grouped Data (Direct method) Useful terms associated with Grouped frequency distribution. Class interval It is a group of numbers in which items are placed such as 10 – 20, 20 – 30 etc. Class frequency The number of observations falling within a class. It is denoted by f.
  • Class mark It is the average value of the upper limit and lower limit. Upper class lim it + Lower class lim it Class mark = 2
  • Example 2 Let’s find the mean of the grouped data by direct method. Class Interval Number of students 10 – 25 2 25 – 40 3 40 – 55 7 55 – 70 6 70 – 85 6 85 – 100 6
  • Solution Class Interval Number of students (fi) 10 – 25 2 25 – 40 3 40 – 55 7 55 – 70 6 70 – 85 6 85 – 100 6 Total ∑fi = 30 Class mark (xi) 10 + 25 = 2 fi xi 17.5 35.0 25 + 40 = 2 40 + 55 = 2 55 + 70 = 2 32.5 97.5 47.5 332.5 62.5 375.0 70 + 85 = 2 85 + 100 = 2 77.5 465.0 92.5 555.0 ∑fi xi = 1860.0 Now, put the values ∑fi = 30 and ∑fi xi = 1860.0 in the given formula, we get
  • x= ∑ f i xi fi 1860.0 x= 30 x = 62 Therefore, the mean is 62
  • Question type – Multiple choice Choose the correct mean daily wages of the workers of a factory by using an appropriate method. Daily wages (in Rs.) Number of workers 40 – 50 7 50 – 60 12 60 – 70 8 70 – 80 6 80 – 90 2 A. B. C. Rs. 60.43 Rs. 50 Rs. 75.05
  • Question type – Numeric The given table gives the literacy rate (in %) of 35 cities. Literacy rate (in %) Number of cities 45 – 55 3 55 – 65 10 65 – 75 11 75 – 85 8 85 – 95 3 Write the mean literacy rate.
  • Question type – Likert Scale Which method you like the most to find out the mean? A. B. C. Direct method Assumed mean method Step deviation method