Jake recorded the average temperatures for his hometown over a period of 20 days as shown in the chart. He used the data to determine the mean temperature. In a report, he stated, “The typical temperature in my hometown is about 61°.” How is this statement misleading?
50° 58° 45° 51° 54°
49° 46° 49° 48° 56°
56° 55° 51° 59° 56°
48° 94° 99° 95° 96°
A. There is not enough data to decide what the typical temperature is.
B. The mean of the data is not about 61°.
C. The mean is not misleading. The typical temperature is about 61°.
D. The mean is not a good measure of the typical temperature because a few higher temperatures pull the mean higher than most of the daily temperatures.
D
Yes, that is correct.
D. The mean is not a good measure of the typical temperature because a few higher temperatures pull the mean higher than most of the daily temperatures.
The statement made by Jake, "The typical temperature in my hometown is about 61°," can be misleading because he used the mean temperature to determine the "typical" temperature. While the mean is a measure of central tendency, it may not accurately represent the typical temperature in this case due to the presence of a few higher temperatures.
To explain this further, let's look at the data provided in the chart. There are 20 days of recorded temperatures, ranging from 45°F to 99°F. Among these temperatures, there are two outliers - 94°F and 99°F - which are significantly higher than the majority of the other temperatures.
When calculating the mean, all temperatures are added together and divided by the number of days (20 in this case). The presence of these higher temperatures will increase the value of the mean. In this specific dataset, if we calculate the mean, it will be skewed higher than the majority of the daily temperatures.
Therefore, the statement made by Jake is misleading because the mean temperature is not about 61°. Choosing the mean as a measure of the typical temperature can be influenced by extreme values and may not accurately represent the majority of the temperatures recorded.
So, the correct answer is D. The mean is not a good measure of the typical temperature because a few higher temperatures pull the mean higher than most of the daily temperatures.