Question

In a greenhouse, a histogram titled 'Flower Height' has height (inches) on the x-axis and frequency on the y-axis. The histogram shows the following intervals and frequencies: 0 to 10 (4), 10 to 20 (8), 20 to 30 (10), 30 to 40 (18), 40 to 50 (12), 50 to 60 (6). The interval that contains the median height of the flowers indicates that

1) The median height of the flowers is between 0 and 10 inches
2) The median height of the flowers is between 10 and 20 inches
3) The median height of the flowers is between 20 and 30 inches
4) The median height of the flowers is between 30 and 40 inches
5) The median height of the flowers is between 40 and 50 inches
6) The median height of the flowers is between 50 and 60 inches

Answer 1

The interval that contains the median height of the flowers in a histogram with the given frequencies is between 30 and 40 inches since the cumulative frequency reaches just beyond the midpoint of the dataset within this interval.

Step-by-step explanation:

To find the interval that contains the median height of the flowers, we need to tally the cumulative frequency of the heights from the given histogram's intervals. As the data is continuous, the median will be the height below which 50 percent of the flowers fall. To calculate this, we sum the frequencies of the consecutive intervals until we reach a cumulative frequency that represents the middle of the data set.

The given frequencies are 0 to 10 inches (4), 10 to 20 inches (8), 20 to 30 inches (10), 30 to 40 inches (18), 40 to 50 inches (12), and 50 to 60 inches (6). The total count of flowers is 4+8+10+18+12+6=58. Since the median is the middle value, we look for the height that splits the dataset in half, so we want the 29th and 30th heights, considering that there is an even number of data points.

The cumulative frequencies up to each interval are as follows: up to 10 inches (4), up to 20 inches (4+8=12), up to 30 inches (12+10=22), and up to 40 inches (22+18=40). We see that the 29th and 30th heights fall in the 30 to 40 inches interval, which means this interval contains the median height.