what are the mean median mode and range of the following data set given the altitude of lakes in feet. -11 -28 -17 -25 -28 -39 -6 -46
To find the mean, median, mode, and range of a data set, follow these steps:
1. Mean: Add up all the values in the data set and divide the sum by the total number of values.
- For the given data set (-11, -28, -17, -25, -28, -39, -6, -46):
Sum = -11 + (-28) + (-17) + (-25) + (-28) + (-39) + (-6) + (-46) = -200
Number of values = 8
Mean = -200 / 8 = -25
2. Median: Arrange the values in ascending order and find the middle value. If there is an even number of values, take the average of the two middle values.
- For the given data set (-11, -28, -17, -25, -28, -39, -6, -46):
Arrange in ascending order: -46, -39, -28, -28, -25, -17, -11, -6
Median = -25
3. Mode: Identify the value(s) that appear(s) most frequently in the data set.
- For the given data set (-11, -28, -17, -25, -28, -39, -6, -46):
The mode is -28 because it appears twice, more than any other value.
4. Range: Calculate the difference between the highest and lowest values in the data set.
- For the given data set (-11, -28, -17, -25, -28, -39, -6, -46):
Highest value = -6
Lowest value = -46
Range = Highest value - Lowest value = -6 - (-46) = 40
Therefore, the mean is -25, the median is -25, the mode is -28, and the range is 40 feet.
To find the mean, median, mode, and range of the given data set: -11, -28, -17, -25, -28, -39, -6, -46.
Step 1: Calculate the mean:
- Add up all the numbers: -11 + -28 + -17 + -25 + -28 + -39 + -6 + -46 = -190
- Divide the sum by the total number of values (which is 8): -190 / 8 = -23.75
- Therefore, the mean of the data set is -23.75.
Step 2: Arrange the numbers in ascending order:
-46, -39, -28, -28, -25, -17, -11, -6
Step 3: Calculate the median:
- Since there are 8 numbers, the median is the average of the two middle values.
- The two middle values are -28 and -25.
- (-28 + -25) / 2 = -53 / 2 = -26.5
- Therefore, the median of the data set is -26.5.
Step 4: Calculate the mode:
- The mode is the value that appears most frequently in the data set.
- In this case, there is no value that appears more than once.
- Therefore, the data set has no mode.
Step 5: Calculate the range:
- The range is the difference between the largest and smallest values.
- The smallest value in the data set is -46, and the largest value is -6.
- The range is -6 - (-46) = -6 + 46 = 40
- Therefore, the range of the data set is 40.
In summary:
- Mean: -23.75
- Median: -26.5
- Mode: None
- Range: 40
First, let's order the data set:
-46, -39, -28, -28, -25, -17, -11, -6
Mean: To find the mean, we add up all the numbers in the data set and divide by the total number of values.
Mean = (-46 + -39 + -28 + -28 + -25 + -17 + -11 + -6) / 8
Mean = -200 / 8
Mean = -25
Median: To find the median, we need to first order the data set from lowest to highest. In this case, we have already done that. The median is the middle value in the data set. If there are an even number of values, we take the average of the two middle values.
Median = (-28 + -25) / 2
Median = -26.5
Mode: The mode is the value that appears most frequently in the data set. In this case, there is no value that appears more than once, so there is no mode.
Range: To find the range, we subtract the lowest value from the highest value in the data set.
Range = -6 - (-46)
Range = 40
So, the mean is -25, the median is -26.5, there is no mode, and the range is 40.