The reported high temperatures (in degrees Fahrenheit) for selected world cities on an October day are shown below. Which measure of central tendency do you think best describes these data? 62, 72, 66, 79, 83, 61, 62, 85, 72, 64, 74, 71, 42, 38, 91, 66, 77, 90, 74, 63, 64, 68, 42
The measures of central tendency that are commonly used are the mean, median, and mode.
The mean is the average of all the data values.
The median is the middle value when the data is arranged in ascending order.
The mode is the value that appears most frequently in the data set.
In this case, the data set contains 23 values.
Mean: (Sum of all values) / (Total number of values)
Median: Middle value when data is arranged in ascending order
Mode: Value that appears most frequently
To find the mean, we add up all the values:
62 + 72 + 66 + 79 + 83 + 61 + 62 + 85 + 72 + 64 + 74 + 71 + 42 + 38 + 91 + 66 + 77 + 90 + 74 + 63 + 64 + 68 + 42 = 1,446.
The mean is then 1,446 / 23 = 62.87.
To find the median, we need to arrange the data set in ascending order:
38, 42, 42, 61, 62, 62, 63, 64, 64, 66, 66, 68, 71, 72, 72, 74, 74, 77, 79, 83, 85, 90, 91.
The median is the middle value, which in this case is the 12th value (72).
To find the mode, we look for the value that appears most frequently. In this case, there are two values that appear twice (42 and 62), while all other values appear only once. Therefore, there is no single mode in this data set.
Based on these calculations, it can be concluded that the measure of central tendency that best describes these data is the mean (62.87).