Let's calculate the values required step-by-step for the given data set: [tex]\(5, 28, 16, 32, 5, 16, 48, 29, 5, 35\)[/tex].
1. Mean:
- To calculate the mean, sum all the numbers and divide by the total count of numbers.
- Sum of the numbers: [tex]\(5 + 28 + 16 + 32 + 5 + 16 + 48 + 29 + 5 + 35 = 219\)[/tex]
- Number of elements: [tex]\(10\)[/tex]
- Mean: [tex]\(\frac{219}{10} = 21.9\)[/tex]
2. Median:
- To find the median, arrange the numbers in ascending order and find the middle value. If the number of observations is even, the median is the average of the two middle numbers.
- Sorted data: [tex]\(5, 5, 5, 16, 16, 28, 29, 32, 35, 48\)[/tex]
- Since there are [tex]\(10\)[/tex] numbers (an even count), the median is the average of the 5th and 6th values.
- The 5th and 6th values in sorted data: [tex]\(16\)[/tex] and [tex]\(28\)[/tex]
- Median: [tex]\(\frac{16 + 28}{2} = \frac{44}{2} = 22.0\)[/tex]
3. Mode:
- The mode is the number that appears most frequently in the data set.
- Observing the data set: [tex]\(5\)[/tex] appears [tex]\(3\)[/tex] times, [tex]\(28\)[/tex] appears [tex]\(1\)[/tex] time, [tex]\(16\)[/tex] appears [tex]\(2\)[/tex] times, [tex]\(32\)[/tex] appears [tex]\(1\)[/tex] time, [tex]\(48\)[/tex] appears [tex]\(1\)[/tex] time, [tex]\(29\)[/tex] appears [tex]\(1\)[/tex] time, [tex]\(35\)[/tex] appears [tex]\(1\)[/tex] time.
- Mode: [tex]\(5\)[/tex] (since it appears the most frequently)
4. Range:
- The range is the difference between the largest and smallest numbers in the data set.
- Smallest number: [tex]\(5\)[/tex]
- Largest number: [tex]\(48\)[/tex]
- Range: [tex]\(48 - 5 = 43\)[/tex]
Final results:
- Mean: [tex]\(21.9\)[/tex]
- Median: [tex]\(22.0\)[/tex]
- Mode: [tex]\(5\)[/tex]
- Range: [tex]\(43\)[/tex]
