Respuesta :
Answer:
Mode: 8 and 11
Mean: 9.4375
Range: 10
Median: 9.5
MAD: 1.09375
Step-by-step explanation:
Data set: 8, 14, 15, 9, 6, 12, 9, 13, 11, 11, 7, 5, 12, 6, 10, 8
Mode: The mode represents the value(s) that appear most frequently in the data set. In this case, we can observe that the numbers 8 and 11 both appear twice, which is more than any other number. Therefore, the mode is 8 and 11.
Mean: The mean is the average of all the values in the data set. To find the mean, we sum up all the values and divide by the total count. Adding up all the numbers yields 8 + 14 + 15 + 9 + 6 + 12 + 9 + 13 + 11 + 11 + 7 + 5 + 12 + 6 + 10 + 8 = 151. Since there are 16 numbers in the data set, we divide the sum by 16 to get the mean: 151 / 16 = 9.4375.
Range: The range is the difference between the largest and smallest values in the data set. The largest number in the data set is 15, and the smallest is 5. Therefore, the range is 15 - 5 = 10.
Median: The median is the middle value when the data set is arranged in ascending or descending order. First, let's sort the numbers in ascending order: 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 15. Since there are 16 numbers, the median is the average of the two middle values, which are the 8th and 9th numbers: (9 + 10) / 2 = 9.5.
MAD (Mean Absolute Deviation): The mean absolute deviation measures the average distance between each data point and the mean. To calculate the MAD, we find the absolute difference between each number and the mean, sum them up, and divide by the total count. Here are the absolute differences from the mean (9.4375) for each number: |8 - 9.4375|, |14 - 9.4375|, |15 - 9.4375|, |9 - 9.4375|, |6 - 9.4375|, |12 - 9.4375|, |9 - 9.4375|, |13 - 9.4375|, |11 - 9.4375|, |11 - 9.4375|, |7 - 9.4375|, |5 - 9.4375|, |12 - 9.4375|, |6 - 9.4375|, |10 - 9.4375|, |8 - 9.4375|. Summing up these absolute differences gives us 17.5. Dividing this sum by the total count (16) gives us the MAD: 17.5 / 16 = 1.09375.
