Question

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

Height	130 -139	140 -149	150-159	160-169	170-179	180-189	190-199
Frequency	8	10	11	18	14	12	7

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

Answer 1

Class	x	d=x-A	f	fd	fd2	cf
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

median = ½ x 80 =40
From cumulative frequency 
curve, median = 165.5

Answer 2

30