The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in a particular statistics course. Compute the mean, median, and mode time. 66.2, 71.7, 92.5, 109.4, 128.4, 94.1, 94.7, 117.8
To find the mean, median, and mode of the given data, let's organize the data in ascending order first:
66.2, 71.7, 92.5, 94.1, 94.7, 109.4, 117.8, 128.4
Mean:
To find the mean, we sum up all the numbers and divide by the total count. Adding the numbers:
66.2 + 71.7 + 92.5 + 94.1 + 94.7 + 109.4 + 117.8 + 128.4 = 775.8
Dividing by the count (8):
Mean = 775.8/8 = 96.975
Median:
To find the median, we locate the middle value in the data set. Since there are 8 numbers, the middle is between the 4th and 5th numbers.
94.1, 94.7, 92.5, [71.7, 109.4], 117.8, 128.4
The median is the average of the two middle numbers:
Median = (71.7 + 109.4)/2 = 180.8/2 = 90.4
Mode:
The mode is the value that appears most frequently in the data set. In this case, there are no repeating values, so there is no mode.
Mean: 96.975
Median: 90.4
Mode: No mode
To calculate the mean, median, and mode of the given data set, follow these steps:
1. Arrange the data in ascending order:
66.2, 71.7, 92.5, 94.1, 94.7, 109.4, 117.8, 128.4
2. Calculate the mean by summing up all the values and dividing by the total number of values:
Mean = (66.2 + 71.7 + 92.5 + 94.1 + 94.7 + 109.4 + 117.8 + 128.4) / 8 = 546.8 / 8 = 68.35
3. Calculate the median, which is the middle value of the data set:
Median = (94.1 + 94.7) / 2 = 188.8 / 2 = 94.4
4. Calculate the mode, which is the value that appears most frequently in the data set:
There is no mode in this data set since none of the values appear more than once.
So, the mean time is 68.35 minutes, the median time is 94.4 minutes, and there is no mode.