Answer :
Answer:
Let's find the mean, median, and mode for the given data set:
\[ 13, 16, 12, 14, 19, 12, 14, 13, 14 \]
### Mean:
The mean (average) is calculated by adding up all the numbers in the data set and then dividing by the total number of values.
Mean = \(\frac{13 + 16 + 12 + 14 + 19 + 12 + 14 + 13 + 14}{9}\)
Mean = \(\frac{127}{9}\)
Mean = 14.11 (rounded to two decimal places)
### Median:
To find the median, we first arrange the data set in ascending order:
\[ 12, 12, 13, 13, 14, 14, 14, 16, 19 \]
Since there are 9 numbers, the median will be the middle value. In this case, the middle value is the 5th number (since \( \frac{9+1}{2} = 5 \)).
So, the median is 14.
### Mode:
The mode is the number that appears most frequently in the data set.
From the given data set:
- 12 appears twice
- 13 appears twice
- 14 appears three times
- 16 appears once
- 19 appears once
The mode is 14 since it appears more frequently than any other number in the data set.
### Summary:
- Mean = 14.11 (rounded to two decimal places)
- Median = 14
- Mode = 14
So, the mean, median, and mode for the given data set are 14.11, 14, and 14 respectively.