Find the mean, median, mode, and range of the data set.
Daily temperature in degrees Celsius: 24, 24, 25, 27, 31, 32, 38, 39
A.) mean = 24, median = 30, mode = 29, range = 16
B.) mean = 29, median = 30, mode = 24, range = 15
C.) mean = 30, median = 29, mode = 24, range = 15
D.) mean = 30, median = 24, mode = 29, range = 16
C. mean = 30, median = 29, mode = 24, range = 15
To find the mean, median, mode, and range of the given data set, follow these steps:
Step 1: Arrange the data in ascending order:
24, 24, 25, 27, 31, 32, 38, 39
Step 2: Calculate the mean:
Mean is the average of all the values in the dataset.
Mean = (24 + 24 + 25 + 27 + 31 + 32 + 38 + 39) / 8
Mean = 256 / 8
Mean = 32
Step 3: Find the median:
Median is the middle value when the data is arranged in ascending order.
Since there are 8 values, the middle two values are 27 and 31.
Median = (27 + 31) / 2
Median = 58 / 2
Median = 29
Step 4: Calculate the mode:
Mode is the value that appears most frequently in the dataset.
In the given data set, both 24 and 29 appear twice, while all the other values appear only once.
Therefore, the mode is 24 and 29.
Step 5: Calculate the range:
Range is the difference between the highest and lowest values in the dataset.
Range = 39 - 24
Range = 15
So, the correct answer is:
B.) mean = 29, median = 30, mode = 24, range = 15
To find the mean, median, mode, and range of a data set, follow these steps:
1. Mean: To find the mean, add up all the values in the data set and divide the sum by the number of values. In this case, the sum of the temperatures is 24 + 24 + 25 + 27 + 31 + 32 + 38 + 39 = 240. Since there are 8 values, the mean is 240 / 8 = 30.
2. Median: To find the median, arrange the data set in ascending order and find the middle value. If there is an even number of values, take the average of the two middle values. In this case, when arranged in ascending order, the data set becomes 24, 24, 25, 27, 31, 32, 38, 39. Since there are 8 values, the middle two values are 27 and 31. Taking their average, the median is (27 + 31) / 2 = 29.
3. Mode: The mode is the value that occurs most frequently in the data set. In this case, the value 24 occurs twice, while all other values occur only once. Therefore, the mode is 24.
4. Range: To find the range, subtract the smallest value from the largest value in the data set. In this case, the smallest value is 24 and the largest value is 39. So, the range is 39 - 24 = 15.
Based on these calculations, the correct answer is:
B.) mean = 29, median = 30, mode = 24, range = 15.