Pick a city in Maryland and determine the average high temperatures for each month. 75% of the temperatures are below what value? How do you know?
City: Baltimore, Maryland
Average high temperatures for each month:
- January: 43°F
- February: 46°F
- March: 55°F
- April: 66°F
- May: 75°F
- June: 84°F
- July: 88°F
- August: 86°F
- September: 79°F
- October: 68°F
- November: 57°F
- December: 47°F
To determine the value that 75% of the temperatures are below, we first need to organize the data set in ascending order:
43°F, 46°F, 55°F, 57°F, 66°F, 68°F, 75°F, 79°F, 84°F, 86°F, 88°F
Next, we need to find the percentile rank of the 75th percentile. We can use the following formula:
Percentile rank = (number of values below the desired percentile / total number of values) x 100
Using this formula, we can find the percentile rank as follows:
Percentile rank = (9 / 11) x 100 = 81.82%
This tells us that 75% of temperatures are below the value that corresponds to the 81.82nd percentile. To find this value, we can use the following formula:
Desired value = (percentile rank / 100) x (n + 1)
Where n is the total number of values in the dataset.
Using this formula, we can find the desired value as follows:
Desired value = (81.82 / 100) x 12 = 9.8184
Rounding to the nearest whole number, we get:
Desired value = 10°F
Therefore, 75% of the temperatures in Baltimore, Maryland are below 10°F, and we know this because we have calculated the 75th percentile of the dataset.