Question

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 30^th percentile

Answer 1

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. 30^th percentile
   154.5 + ¹²/₁₆ × 5
   154.5 + 3.75
   =158.25