The professors at Wilfred Laurier University are required to submit their final exams to the registrar’s office 10 days before the end of the semester. The exam coordinator sampled 20 professors and recorded the number of days before the final exam that each submitted his or her exam. The results are.
14, 8, 3, 2, 6, 4, 9, 13, 10, 12
7, 4, 9, 13, 15, 8, 11, 12, 4, 0
a) Compute the mean, media and Mode
mean = Σscores/number of scores
For median, arrange scores in order of value. Median is between 10th and 11th score.
Mode(s) is(are) most frequently observed score(s).
To compute the mean, median, and mode of the given data, follow these steps:
1. Mean:
The mean is calculated by adding up all the values and then dividing the sum by the total number of values.
Adding up the values:
14 + 8 + 3 + 2 + 6 + 4 + 9 + 13 + 10 + 12 +
7 + 4 + 9 + 13 + 15 + 8 + 11 + 12 + 4 + 0 = 189
Dividing the sum by the total number of values:
Mean = 189 / 20 = 9.45
Therefore, the mean of the data is 9.45.
2. Median:
To find the median, the data needs to be arranged in ascending order. Once the data is sorted, the middle value represents the median. If there are an even number of values, the median is the average of the two middle values.
The data arranged in ascending order:
0 2 3 4 4 4 6 7 8 8
9 9 10 11 12 12 13 13 14 15
As there are 20 values, the middle two values are the 10th and 11th terms: 9 and 9.
Therefore, the median is the average of 9 and 9, which is 9.
3. Mode:
The mode refers to the value(s) that appear the most frequently in the dataset.
The values and their frequencies:
0 (1 time), 2 (1 time), 3 (1 time), 4 (3 times), 6 (1 time), 7 (1 time), 8 (2 times), 9 (2 times),
10 (1 time), 11 (1 time), 12 (2 times), 13 (2 times), 14 (1 time), 15 (1 time)
The mode of this dataset is 4 because it appears more frequently than any other number.
Therefore, the mean is 9.45, the median is 9, and the mode is 4 for the given data.