Find the mean, median, and mode for the data set below. Explain which measure best describes the data 3 35 31 34 32 31 The mean is Type an integer or decimal rounded to the nearest hundredth as needed)
The mean is: 30.33
To find the median, we first need to put the data set in order from least to greatest:
3, 31, 31, 32, 34, 35
The median is the middle number, which in this case is 32.
There are two modes (the values that occur most frequently), which are both 31.
In this case, the median best describes the data as it is not affected by extreme values (like the low value of 3).
To find the mean of a data set, you need to add up all the values and divide the sum by the number of values.
Sum of the data set: 3 + 35 + 31 + 34 + 32 + 31 = 166
Number of values: 6
Mean = Sum of the data set / Number of values = 166 / 6 = 27.67
Therefore, the mean of the data set is approximately 27.67.
Now let's find the median, which is the middle value when the data set is arranged in numerical order.
Arranged data set in numerical order: 3, 31, 31, 32, 34, 35
The middle value is the average of the two middle numbers, which are 31 and 32.
Median = (31 + 32) / 2 = 63 / 2 = 31.5
So the median of the data set is 31.5.
Lastly, let's determine the mode, which is the value that appears most frequently in the data set.
In this case, the number 31 appears twice, while all the other numbers appear only once. Therefore, the mode of the data set is 31.
In conclusion, the mean is 27.67, the median is 31.5, and the mode is 31. Each measure describes different aspects of the data set. The mean gives an average value, the median represents the middle value, and the mode indicates the most frequently occurring value.