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.
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.