Answer to Question #270364 in Statistics and Probability for Angelo

Question

A group of 40 students in a University has been asked to measure their heights. The data collected are as follows:

 

Height (cm) f

135 - 139 5

140 - 144 4

145 - 149 2

150 - 154 12

155 - 159 15

160 - 164 2

 

1. What is the class' mean height?

2. Determine the mode.

3. What is the median height of the students?

Answer 1

1.

x is midpoint of class, f is frequency of class

then:

mean = $\sum x_i f_i/n=\frac{137\cdot5+142\cdot4+147\cdot2+152\cdot12+157\cdot15+162\cdot2}{5+4+2+12+15+2}=151.25$

2.

mode = $L+\frac{f_m-f_{m-1}}{( f_m-f_{m-1})+(f_m-f_{m+1})}w$

where

• L is the lower class boundary of the modal group
• f_m-1 is the frequency of the group before the modal group
• f_m is the frequency of the modal group
• f_m+1 is the frequency of the group after the modal group
• w is the group width

modal group is 155-159

mode =$155+\frac{15-12}{( 15-12)+(15-2)}\cdot4=155.75$

3.

median = $L+\frac{n/2-B}{G}w$

where:

• L is the lower class boundary of the group containing the median
• n is the total number of values
• B is the cumulative frequency of the groups before the median group
• G is the frequency of the median group
• w is the group width

median group is 145-149

median = $145+\frac{20-9}{2}\cdot4=123$