what are the mean median mode and range of the data set 18, 19, 20, 21, 23, 26, 26, 26
Well, let me juggle your question! The mean is like the boss of the data set. So, if we add up all the numbers and divide by how many there are (8 in this case), we get a mean of 22.625. Now, let's find the median, which is the middle value. In this case, we have 8 numbers, so the middle value is exactly between the 4th and 5th numbers, which are both 23. So, the median is 23. As for the mode, it's the number that shows up the most. And here we have a triple threat! The number 26 appears 3 times, making it the mode. Lastly, the range is just the difference between the biggest and smallest numbers, so it's 26 - 18 = 8. Voila!
To find the mean, median, mode, and range of the given data set {18, 19, 20, 21, 23, 26, 26, 26}, follow these steps:
Step 1: Arrange the data in ascending order: 18, 19, 20, 21, 23, 26, 26, 26.
Step 2: Find the mean.
- Add up all the numbers: 18 + 19 + 20 + 21 + 23 + 26 + 26 + 26 = 179.
- Divide the sum by the total number of values: 179 ÷ 8 = 22.375.
- So, the mean is 22.375.
Step 3: Find the median.
- Since we have 8 values, the median is the average of the fourth and fifth terms, which are 21 and 23.
- (21 + 23) ÷ 2 = 22.
- So, the median is 22.
Step 4: Find the mode.
- The mode is the value that appears most frequently in the data set.
- In this case, the number 26 appears three times, which is more frequent than any other number.
- So, the mode is 26.
Step 5: Find the range.
- The range is the difference between the largest and smallest values in the data set.
- In this case, the largest value is 26, and the smallest value is 18.
- 26 - 18 = 8.
- So, the range is 8.
Summary:
- Mean: 22.375.
- Median: 22.
- Mode: 26.
- Range: 8.
To find the mean, median, mode, and range of a data set, follow these steps:
1. Mean: To calculate the mean (or average), add up all the numbers in the data set and then divide the sum by the total number of values. In this case, the sum of the numbers is 18 + 19 + 20 + 21 + 23 + 26 + 26 + 26 = 179. Since there are 8 numbers in the data set, the mean is 179/8 = 22.375.
2. Median: The median is the middle value of a data set when it is arranged in ascending (or descending) order. In this case, the numbers are already in ascending order: 18, 19, 20, 21, 23, 26, 26, 26. Since there is an even number of values, we take the average of the two middle values. In this case, the middle values are 21 and 23. So, the median is (21 + 23)/2 = 22.
3. Mode: The mode is the value(s) that appear most frequently in a data set. In this case, the number 26 appears three times, which is more than any other number. Therefore, the mode is 26.
4. Range: The range is the difference between the maximum and minimum values in a data set. In this case, the minimum value is 18 and the maximum value is 26. Therefore, the range is 26 - 18 = 8.
To summarize:
- Mean: 22.375
- Median: 22
- Mode: 26
- Range: 8
I'll be glad to check your answers.
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