Ex 14.3, 2 - If median is 28.5, find values of x and y. - Ex 14.3

  1. Chapter 14 Class 10 Statistics
  2. Serial order wise

Transcript

Ex 14.3, 2 - Chapter 14 Class 10 Statistics - NCERT Book If the median of the distribution given below is 28.5, find the values of x and y. Since Median = 28.5 given So, 20 - 30 is the median class Class interval Frequency Cumulative frequency 0 – 10 5 5 10 – 20 x 5 + x 20 – 30 20 5 + x + 20 = 25 + x 30 – 40 15 25 + x + 15= 40 + x 40 – 50 y 40 + x + y 50 – 60 5 40 + x + y + 5= 45 + x + y Totalβˆ‘β–’π‘“π‘– =60 Median = l + (𝑛/2 βˆ’π‘π‘“)/𝑓 Γ— h Where l = lower limit of median class=20 h = class-interval= 10 βˆ’ 0 = 10 n = βˆ‘β–’π‘“π‘–=60 𝑛/2=60/2 = 30 cf = cumulative frequency of the class before median class= 5 + x f = frequency of the median class=20 Median = l + (𝑛/2 βˆ’π‘π‘“)/𝑓 Γ— h 28.5 = 20 + (30 βˆ’ (5+ π‘₯))/20 Γ— 10 28.5 = 20 + (25 βˆ’ π‘₯)/2 28.5 – 20 = (25 βˆ’ π‘₯)/2 8.5 = (25 βˆ’π‘₯)/2 8.5 Γ— 2 = 25 – x 17 = 25 – x x = 25 – 17 x = 8 Also, βˆ‘β–’π‘“π‘– = 5 + x + 20 + 15 + y + 5 60 = 45 + x + y 60 = 45 + 8 + y 60 = 53 + y 60 – 53 = y 7 = y y = 7 Hence, x = 8, y = 7

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