Question 3 - Figure it out - Page 127-132 - Chapter 5 Class 8 - Tales by Dots and Lines (Ganita Prakash II)

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Question 3 Fill in the blanks such that the median of the collection is 13: 5, 21, 14, _____, ______, ______. How many possibilities exist if only counting numbers are allowed?Our data is 5 , 21, 14, _____, ______, ______ Number of observations = 6 Since Number of observations is even Median is the average of middle two terms Since we are given 14 as a term, but median is lesser than 14 So, 14 can be our 4th term Thus, Median = (𝟑^𝒓𝒅 𝒕𝒆𝒓𝒎 + 𝟒^𝒕𝒉 𝒕𝒆𝒓𝒎)/𝟐 Putting 4th term = 14, Median = 13 13 = (𝟑^𝒓𝒅 𝒕𝒆𝒓𝒎 + 𝟏𝟒)/𝟐 13 × 2 = 3rd term + 14 26 = 3rd term + 14 26 – 14 = 3rd term 12 = 3rd term 3rd term = 12 Given terms were 5, 21, 14 And 3rd term = 13 Let 5th term = 21 Arranging data in ascending order, our data becomes 5 , ____ , 12, 14, 21, _____ Thus, 2nd term can be can be any number from 5 to 12 i.e. 2nd term can be 5, 6, 7, 8, 9, 10, 11, 12 And, 6th term can be any number greater than 21 But, there are infinitely many terms greater than 21, like 22, 100, 100000, 99, 99000000 So, we can say that Infinitely many possibilities exist