What are the mean, median, mode, and range of the data set given the altitude of lakes in feet:
–11, –28, –17, –25, –28, –39, –6, and –46?
A. mean = –25; median = –26.5; mode = –28; range = 40
B. mean = –25; median = –40; mode = –26.5; range = 28
C. mean = –26.5; median = –25; mode = –28; range = 28
D. mean = –26.5; median = –28; mode = –25; range = 40
First, let’s order the data set from smallest to largest:
–46, –39, –28, –28, –25, –17, –11, –6
Mean:
To find the mean, we add all the values and divide the sum by the 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 find the middle value.
Median = (-28 -25) ÷ 2
Median = -26.5
Mode:
The mode is the most frequent value in the data set. Here, -28 occurs twice, which is more than any other value.
Mode = -28
Range:
To find the range, we subtract the smallest value from the largest value.
Range = Largest Value - Smallest Value
Range = (-6) - (-46)
Range = 40
Therefore, the answer is A. mean = –25; median = –26.5; mode = –28; range = 40.
To find the mean of a data set, you need to sum up all the values and divide by the number of values.
The provided data set is:
–11, –28, –17, –25, –28, –39, –6, –46
To find the mean, we sum up all the values:
–11 + –28 + –17 + –25 + –28 + –39 + –6 + –46 = –200
Now, we divide the sum by the number of values, which is 8:
–200 / 8 = –25
So, the mean of the data set is –25.
To find the median, you need to arrange the values in ascending order and find the middle value.
Arranging the values in ascending order gives us:
–46, –39, –28, –28, –25, –17, –11, –6
Since the data set has an even number of values, the median is the average of the two middle values. The two middle values are –28 and –25. Thus, the median is:
(–28 + –25) / 2 = –26.5
So, the median of the data set is –26.5.
To find the mode, you need to determine the value that appears most frequently in the data set.
In this case, the value –28 appears twice, which is more than any other value. So, the mode of the data set is –28.
Finally, to find the range, you need to subtract the lowest value from the highest value in the data set.
The lowest value is –46, and the highest value is –6. So, the range is:
–6 - (–46) = 40
Therefore, the mean is –25, the median is –26.5, the mode is –28, and the range is 40.
The correct answer is:
A. mean = –25; median = –26.5; mode = –28; range = 40
To find the mean, median, mode, and range of a dataset, you need to follow these steps:
1. Mean: Add up all the values in the dataset and then divide the sum by the number of values in the dataset.
2. Median: Arrange the values in the dataset in ascending order and then find the middle value. If there is an even number of values, you need to find the average of the two middle values.
3. Mode: Identify the value(s) that appear most frequently in the dataset. If there is no value that repeats, then there is no mode.
4. Range: Find the difference between the maximum value and the minimum value in the dataset.
Now, let's apply these steps to the given dataset of altitudes:
Altitude of lakes in feet: –11, –28, –17, –25, –28, –39, –6, and –46
1. Mean:
Sum of all values = -11 + -28 + -17 + -25 + -28 + -39 + -6 + -46 = -200
Number of values = 8
Mean = (-200) / 8 = -25
2. Median:
Arranging the values in ascending order: -46, -39, -28, -28, -25, -17, -11, -6
Since there are 8 values, the middle two values are -28 and -25. Thus, the median is the average of -28 and -25.
Median = (-28 + -25) / 2 = -26.5
3. Mode:
The mode is the value that appears most frequently in the dataset. In this case, -28 appears twice, which is more than any other value.
Mode = -28
4. Range:
The maximum value in the dataset is -6, and the minimum value is -46.
Range = Maximum value - Minimum value
= -6 - (-46)
= -6 + 46
= 40
Now that we have calculated the mean, median, mode, and range, let's compare the results to the options provided:
A. mean = –25; median = –26.5; mode = –28; range = 40
B. mean = –25; median = –40; mode = –26.5; range = 28
C. mean = –26.5; median = –25; mode = –28; range = 28
D. mean = –26.5; median = –28; mode = –25; range = 40
By comparing the calculated values to the options, we can see that the correct answer is:
C. mean = –26.5; median = –25; mode = –28; range = 28