heights, in inches, for the 200 graduating seniors from washington high school are summarized in the…

heights, in inches, for the 200 graduating seniors from washington high school are summarized in the frequency table below.\n| height | frequency |\n|--|--|\n| height < 60 inches | 22 |\n| 60 inches ≤ height < 66 inches | 84 |\n| 66 inches ≤ height < 72 inches | 62 |\n| 72 inches ≤ height < 78 inches | 24 |\n| height ≥ 78 inches | 8 |\nwhich of the following statements about the median height is true?\na it is greater than or equal to 78 inches.\nb it is greater than or equal to 72 inches but less than 78 inches.\nc it is greater than or equal to 66 inches but less than 72 inches.\nd it is greater than or equal to 60 inches but less than 66 inches.\ne it is less than 60 inches.

heights, in inches, for the 200 graduating seniors from washington high school are summarized in the frequency table below.\n| height | frequency |\n|--|--|\n| height < 60 inches | 22 |\n| 60 inches ≤ height < 66 inches | 84 |\n| 66 inches ≤ height < 72 inches | 62 |\n| 72 inches ≤ height < 78 inches | 24 |\n| height ≥ 78 inches | 8 |\nwhich of the following statements about the median height is true?\na it is greater than or equal to 78 inches.\nb it is greater than or equal to 72 inches but less than 78 inches.\nc it is greater than or equal to 66 inches but less than 72 inches.\nd it is greater than or equal to 60 inches but less than 66 inches.\ne it is less than 60 inches.

Answer

Explanation:

Step1: Calculate cumulative frequencies

Height Frequency Cumulative Frequency
Height < 60 inches 22 22
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.