What are the mean, median, mode, and range of the data set given the altitude of lakes in feet:
–12, –9, –14, –39, –49, –49, –18, and –43?
A. mean = –28.5, median = –29.1, mode = –49, range = 40
B. mean = –29.1, median = –49, mode = –28.5, range = 41
C. mean = –49, median = –29.1, mode = –28.5, range = 41
D. mean = –29.1, median = –28.5, mode = –49, range = 40
mean = average
In this case:
mean = [ - 12 + ( - 9 ) + ( - 14 ) + ( - 39 ) + ( - 49 ) + ( - 49 ) + ( - 18 ) + ( - 43 ) ] / 8 =
( - 12 - 9 - 14 - 39 - 49 - 49 - 18 - 43 ) / 8 = - 233 / 8 = - 29.125
The median is the "middle" value in the list of numbers.
When numbers are sorted from lowest to highest, the median is the mean value in the list of numbers.
If we find middle pair of numbers, then find the value of median is halfway between them.
In this case:
- 49 , - 49 , - 43 , - 39 , - 18 , - 14 , - 12 , - 9
median = [ - 39 + ( - 18 ) ] / 2 = ( - 39 - 18 ) / 2 = - 57 / 2 = - 28.5
The mode is the value that occurs most often.
In this case:
mode = - 49
because appeared 2 times
The range is the difference between the lowest and highest values.
In this case:
range = - 9 - ( - 49 ) = - 9 + 49 = 40
So answer is D
To find the mean, median, mode, and range of the given data set, we can follow these steps:
Step 1: Organize the data set in ascending order:
–49, –49, –43, –39, –18, –14, –12, –9
Step 2: Calculate the mean (average):
Mean = (–49 + –49 + –43 + –39 + –18 + –14 + –12 + –9) / 8 = –28.5
Step 3: Find the median (middle value):
Since we have 8 numbers in the data set, we need to find the average of the two middle values.
The middle two values are –39 and –18.
Median = (–39 + –18) / 2 = –29.1
Step 4: Determine the mode (most frequently occurring value):
The mode is the value that appears most frequently in the data set.
Here, the value –49 appears twice, while all other values appear only once.
Mode = –49
Step 5: Calculate the range (the difference between the highest and lowest values):
Range = Highest value - Lowest value
Range = –9 - (–49) = 40
Therefore, the correct answer is:
A. mean = –28.5, median = –29.1, mode = –49, range = 40
To find the mean, median, mode, and range of the given data set, follow these steps:
1. Mean: Add up all the values in the data set and divide the sum by the number of values.
Mean = (-12 - 9 - 14 - 39 - 49 - 49 - 18 - 43) / 8 = -28.5
2. Median: Arrange the values in ascending order and find the middle value. If the number of values is odd, the middle value is the median. If the number of values is even, take the average of the two middle values.
Arranging the data set in ascending order: -49, -49, -43, -39, -18, -14, -12, -9
Median = (-39 + -18) / 2 = -29.1
3. Mode: The mode is the value that appears most frequently in the data set.
In this case, the mode is -49, as it appears twice, while the other values appear only once.
4. Range: The range is the difference between the highest and lowest values in the data set.
The highest value is -9, and the lowest value is -49.
Range = -9 - (-49) = 40
Therefore, the correct answer is option A:
mean = -28.5,
median = -29.1,
mode = -49,
range = 40.