Question

heights, in inches, for the 200 graduating seniors from washington high school are summarized in the frequency table below.

height	frequency
60 inches ≤ height < 66 inches	84
66 inches ≤ height < 72 inches	62
72 inches ≤ height < 78 inches	24
height ≥ 78 inches	8

which of the following statements about the median height is true?
a it is greater than or equal to 78 inches.
b it is greater than or equal to 72 inches but less than 78 inches.
c it is greater than or equal to 66 inches but less than 72 inches.
d it is greater than or equal to 60 inches but less than 66 inches.
e it is less than 60 inches.

Explanation:

Step1: Calculate cumulative frequencies

Height	Frequency	Cumulative Frequency
60 inches ≤ height < 66 inches	84	22 + 84=106
66 inches ≤ height < 72 inches	62	106+62 = 168
72 inches ≤ height < 78 inches	24	168+24 = 192
Height ≥ 78 inches	8	192 + 8=200

Step2: Determine position of median

There are \(n = 200\) data - points. For a set of \(n\) data - points (where \(n\) is even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data - points. Here, \(\frac{n}{2}=\frac{200}{2}=100\) and \(\frac{n}{2}+1 = 101\).

Step3: Locate median class

The 100th and 101st ordered data - points fall within the class "60 inches ≤ height < 66 inches" since the cumulative frequency up to the class "60 inches ≤ height < 66 inches" is 106 which includes the 100th and 101st values.

Answer:

D. It is greater than or equal to 60 inches but less than 66 inches.