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The data below shows the heights of students in a class.

Height 130 -139140 -149150-159 160-169170-179180-189190-199
 Frequency 8 10 11 18 1412 

  1. Using assumed mean of 164.5, calculate the mean and the standard deviation
  2. Draw a cumulative frequency curve on a grid and use it to estimate the median

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Class d=x-A fd fd2cf 
 130-139 134.5 -30 8 -240 7200 8
 140-149 144.5 -20 10 -200 4000 18
 150-159 154.5 -10 11 -110 1100 29
 160-169 164.5 0 18 0 0 47
 170-179 174.5 10 14 140 1400 61
 180-189 184.5 20 12 240 4800 73
 190-199 194.5 30 7 210 6300 80

∑f = 80
∑fd=40
∑fd2 = 24,800
mean = A + ∑fd/∑f

164.5 + 40/80 =165
standard dev = √(∑fd2/∑f) - (∑fd/∑f)2  
=√(24800/80) - (40/80)2
= 17.160
sukmathsp2ans18
median = ½ x 80 =40
From cumulative frequency 
curve, median = 165.5

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