Given the following data: 18,12,18,20,16,20,18,36,16,18, 14,20,24,20,5,18,10,15,24. Determine the mean, median and mode of this data
I'll use an example. Hopefully, this will help you with your problem.
Suppose we had these scores: 3, 4, 5, 5, 5, 10, 10.
To find the mean, add up all the scores and divide by the total number of scores. The total number of scores is 7. Therefore, the mean is 42/7 = 6.
The median is the middle score, which is 5. (If you have an even number of scores, the median is the average of the two middle scores.)
The mode is the score that occurs most frequently, which is 5.
Be sure to list your data in order before determining the mean, median, and mode. This will help you see the median and mode more clearly.
To find the mean, median, and mode of a set of data, follow these steps:
1. Mean:
- Add up all the numbers in the data set.
- Divide the sum by the total number of values.
Let's calculate the mean of the given data:
Sum = 18 + 12 + 18 + 20 + 16 + 20 + 18 + 36 + 16 + 18 + 14 + 20 + 24 + 20 + 5 + 18 + 10 + 15 + 24 = 349
Number of values = 19
Mean = Sum / Number of values = 349 / 19 ≈ 18.37
Therefore, the mean of the data set is approximately 18.37.
2. Median:
- Arrange the numbers in ascending order.
- If the total number of values is odd, the median is the middle value.
- If the total number of values is even, the median is the average of the two middle values.
Let's find the median of the given data:
Arranged in ascending order: 5, 10, 12, 14, 15, 16, 16, 18, 18, 18, 18, 20, 20, 20, 24, 24, 36
Total number of values = 19 (odd)
Median = Middle value = 18
Therefore, the median of the data set is 18.
3. Mode:
- The mode is the number(s) that appear most frequently in the data set.
- A data set can have one mode, more than one mode (multimodal), or no mode (no value repeats).
Let's find the mode(s) of the given data:
Frequencies:
- 5 appears once
- 10 appears once
- 12 appears once
- 14 appears once
- 15 appears once
- 16 appears twice
- 18 appears four times
- 20 appears three times
- 24 appears twice
- 36 appears once
The number 18 has the highest frequency (appears four times). Therefore, the mode of the data set is 18.
In summary, the mean of the data set is approximately 18.37, the median is 18, and the mode is 18.