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The median of the following data is 50. Find the values of ‘p’ and ‘q’, if the sum of all frequencies is 90. Also find the mode of the data.

Marks obtained

Number of students

20 - 30

p

30 - 40

15

40 - 50

25

50 - 60

20

60 - 70

q

70 - 80

8

80 - 90

10

 

This question is similar to Ex 13.3, 2 – Chapter 13 Class 10

Please check https://www.teachoo.com/1947/559/Ex-14.3--2---If-median-is-28.5--find-values-of-x-and-y./category/Ex-14.3/

 

 

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Transcript

Now, Median = l + (š‘µ/šŸ āˆ’š’„š’‡)/š’‡ Ɨ h Since Median = 50 50 ā€“ 60 is Median Class Where N = āˆ‘ā–’š‘“š‘– l = h = cf = f = Putting values in formula Median = l + (š‘µ/šŸ āˆ’š’„š’‡)/š’‡ Ɨ h 50 = 50 + (šŸ’šŸ“ āˆ’ (š’‘ + šŸ’šŸŽ))/šŸšŸŽ Ɨ 10 50 = 50 + (5 āˆ’š‘)/2 50 ā€“ 50 = (5 āˆ’š‘)/2 0 = (5 āˆ’š‘)/2 5āˆ’š‘ = 0 p = 5 Also, āˆ‘ā–’š’‡š’Š = 78 + p + q Putting values 90 = 78 + 5 + q 90 = 83 + y 90 ā€“ 83 = q 7 = q q = 7 Hence p = 5, q = 7 Finding Mode Mode = l + (š’‡šŸ āˆ’š’‡šŸŽ)/(šŸš’‡šŸ āˆ’š’‡šŸŽ āˆ’š’‡šŸ) Ɨ h Modal class = Interval with highest frequency = 40 ā€“ 50 Here l = lower limit of modal class = 40 h = class-interval = 50 āˆ’ 40 = 10 f1 = frequency of the modal class = 25 f0 = frequency of the class before modal class = 15 f2 = frequency of the class after modal class = 20 Putting these values in formula āˆ“ Mode = l + ((š’‡_šŸ āˆ’ š’‡_šŸŽ)/(šŸš’‡_šŸ āˆ’ š’‡_šŸŽ āˆ’ š’‡_šŸ )) Ɨ h = 40 + {(šŸšŸ“ āˆ’šŸšŸ“)/(šŸ ƗšŸšŸ“ āˆ’šŸšŸ“ āˆ’šŸšŸŽ)} Ɨ 10 = 40 + 10/(50āˆ’35) Ɨ 10 = 40 + 100/15 = 40 + 6.67 = 46.67

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.