Find the mean, median, mode, and range of each data set below. If there is no mode, write “no mode”; if there is more than one mode, write all the numbers that happen most often.
33, 33, 38, 39, 38, 34, 33, 30, 33, 32, 31, 34, 38, 40, 42
for mean: add them up, then divide by the number of data values
for median: put them in order from smallest to largest, the number in the middle is the median
mode: the data value which appears most often. (I see a lot of 33s)
range = largest minus smallest
To find the mean, you need to add up all the numbers in the data set and then divide the sum by the total count of numbers. Let's calculate the mean for the given data set:
Sum of all numbers = 33 + 33 + 38 + 39 + 38 + 34 + 33 + 30 + 33 + 32 + 31 + 34 + 38 + 40 + 42 = 512
Total count of numbers = 15
Mean = Sum of all numbers / Total count of numbers = 512 / 15 ≈ 34.13
So, the mean of the given data set is approximately 34.13.
To find the median, you need to arrange the numbers in ascending order and then find the middle value. If there is an even number of values, you take the average of the two middle values. Let's find the median for the given data set:
Arranging the numbers in ascending order: 30, 31, 32, 33, 33, 33, 33, 34, 34, 38, 38, 38, 39, 40, 42
Counting from the left and right, the two middle values are 34 and 38. To find the median, we take their average:
Median = (34 + 38) / 2 = 72 / 2 = 36
So, the median of the given data set is 36.
To find the mode, you need to determine the number(s) that occur most frequently. Let's find the mode for the given data set:
The numbers that occur most frequently are 33 and 38 since each appears 4 times.
So, the mode of the given data set is both 33 and 38.
To find the range, you need to subtract the minimum value from the maximum value. Let's find the range for the given data set:
Minimum value = 30
Maximum value = 42
Range = Maximum value - Minimum value = 42 - 30 = 12
So, the range of the given data set is 12.
In summary:
Mean ≈ 34.13
Median = 36
Mode = 33, 38
Range = 12