4. For Questions 4-7, use the following data:

The number of file conversions performed by a processor per day for 10 days was:

15, 27, 25, 28, 30, 31, 22, 25, 27, 29

What is the arithmetic mean of the data?

(Points: 5)
20.7
25.9
27
29

5. What is the trimmed mean of the data? (Points: 5)
22.875
26.625
31.525
34.375

6. What is the median of the data? (Points: 5)
26
26.5
27
There is no median for this data set.

7. What is the mode of the data? (Points: 5)
25
26
There is no mode for the data set.
The data set is bimodal, with modes of 25 and 27.

What are your answers to 4 and 5?

6. Half the scores are above and half below the median. There is a median.

7. Since the distribution is bimodal, there are modes.

To find the arithmetic mean of the data, we need to sum up all the values and then divide by the total number of values.

Step 1: Add up all the values:
15 + 27 + 25 + 28 + 30 + 31 + 22 + 25 + 27 + 29 = 259

Step 2: Divide the sum by the total number of values:
259 / 10 = 25.9

Therefore, the arithmetic mean of the data is 25.9. The correct answer to question 4 is "25.9".

To find the trimmed mean of the data, we need to remove a certain percentage of outliers from the data and then calculate the mean of the remaining values.

Step 1: Arrange the data in ascending order:
15, 22, 25, 25, 27, 27, 28, 29, 30, 31

Step 2: Remove the highest and lowest values. In this case, we will remove the first and last value since we are looking for a trimmed mean.
22, 25, 25, 27, 27, 28, 29, 30

Step 3: Add up the remaining values:
22 + 25 + 25 + 27 + 27 + 28 + 29 + 30 = 213

Step 4: Divide the sum by the number of remaining values (8 in this case):
213 / 8 = 26.625

Therefore, the trimmed mean of the data is 26.625. The correct answer to question 5 is "26.625".

To find the median of the data, we need to arrange the values in ascending order and find the middle value. If there is an even number of values, we find the average of the two middle values.

Step 1: Arrange the data in ascending order:
15, 22, 25, 25, 27, 27, 28, 29, 30, 31

Step 2: Since there are 10 values, we need to find the average of the 5th and 6th values:
(27 + 27) / 2 = 26.5

Therefore, the median of the data is 26.5. The correct answer to question 6 is "26.5".

To find the mode of the data, we need to identify the value(s) that occur(s) most frequently.

Step 1: Count the frequency of each value:
15: 1
22: 1
25: 2
27: 2
28: 1
29: 1
30: 1
31: 1

Step 2: Identify the value(s) with the highest frequency. In this case, both 25 and 27 occur most frequently.

Therefore, the mode of the data is bimodal with modes of 25 and 27. The correct answer to question 7 is "The data set is bimodal, with modes of 25 and 27."