Question 17 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard [Term I] - Solutions of Sample Papers for Class 10 Boards

Transcript

Question 17 The median of a set of 9 distinct observation is 20.5. If each of the observations of a set is increased by 2,then the median of a new set (A) is increased by 2 (B) is decreased by 2 (C) is two times the original number (D) Remains same as that of original observationsTo find Median, We put all observations in ascending (or descending order) And choose the middle observation If total observations is odd, Median = ((𝑛+1)/2)^𝑡ℎ term If total observations is even, Median = ((𝑛/2)^𝑡ℎ 𝑡𝑒𝑟𝑚 + (𝑛/2 + 1)^𝑡ℎ 𝑡𝑒𝑟𝑚)/2 Given that we have 9 distinct observations Let 9 distinct observations in ascending order be 𝒙_𝟏,𝒙_𝟐,𝒙_𝟑,𝒙_𝟒,𝒙_𝟓,𝒙_𝟔,𝒙_𝟕,𝒙_𝟖, 𝒙_𝟗 Now, Since n is odd Median =((9 + 1)/2)^𝑡ℎ 𝑡𝑒𝑟𝑚 = 5th term. Also, Median is given as 20.5 Thus, 5th term = 𝒙_𝟓 = 20.5 So, the correct answer is (a) Now, each observations is increased by 2 . So, New observations are 𝑥_1+2,𝑥_2+2,𝑥_3+2,𝑥_4+2,𝑥_5+2,𝑥_6+2,𝑥_7+2,𝑥_8+2, 𝑥_9+2 Since all observations have increased, our ascending order remains the same Thus, New Median will be the new 5th term New Median = New 5th term = 𝑥_5+2 = 20.5 + 2 = 22.5 Thus, New Median is increased by 2