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The table below shows height in cm of form 4 students in Westlands Secondary School.

 Height(cm)   150-154  155-159  160-164  165-169  170-174 
 Frequency(f)      18     16     24     28     14
  1. Using an assumed mean of 162, calculate;
    1. mean height  
    2. Standard deviation    
  2. if the heights of each student increases by 5cm. Write down
    1. The new mean   
    2. The new standard deviation  
  3. Calculate the 30th percentile

1 Answer

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  1.  
    1. Mean height
       x  d  fd  fd2  c.f 
      152
      157
      162
      167
      172
      −10
      −5
        0 
        5
        10
      −180
      −80
       0
      140
      140 
      1800
      400
      0
      700
      1400
      18
      34
      58
      86
      100 
      x̄ =Σfd + A
            Σf
      =20/100 + 162 =162.2
    2. Standard deviation

      √42.96 = 6.554
  2.   
    1. New mean
      162.2 + 5
       = 167.2
    2. new standard deviation
      = 6.554
  3. 30th percentile
    154.5 + 12/16 × 5
    154.5 + 3.75
    =158.25
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