Question

a pediatrician records the heights of all his two-year-old patients. he plans to display their heights in centimeters with a histogram, using the intervals 70–74, 75–79, 80–84, 85–89, 90–94, and 95–99. which of the following can be determined about these patients from the histogram? select all that apply. how many patients were measured how many of the patients are 99 cm tall how many patients are shorter than 85 cm the mean of the patients heights the median of the patients heights

Explanation:

To solve this, we analyze each option based on what a histogram (with intervals) can tell us:

1. "how many patients were measured": A histogram shows the frequency (number of data points) in each interval. Summing the frequencies of all intervals gives the total number of patients measured. So this can be determined.
2. "how many of the patients are 99 cm tall": A histogram uses intervals (e.g., 95–99), so it shows how many are in the 95–99 range, not the exact height of 99 cm. So this cannot be determined.
3. "how many patients are shorter than 85 cm": The intervals shorter than 85 cm are 70–74, 75–79, 80–84. Summing their frequencies gives the number of patients shorter than 85 cm. So this can be determined.
4. "the mean of the patients' heights": The mean requires knowing the exact heights (or midpoints and weights), but a histogram with intervals doesn’t provide exact values (just counts per interval). So the mean cannot be calculated precisely from a histogram.
5. "the median of the patients' heights": The median is the middle value. With interval frequencies, we can find the interval containing the median (by cumulative frequency) but not the exact median value. However, the question is about what "can be determined about these patients"—finding the interval of the median is possible, but typically, histograms don’t give the exact median. But among the options, the first and third are clear.

Answer:

• how many patients were measured
• how many patients are shorter than 85 cm