you multiply each value in the data set below by 3, what are the mean, median, mode, and range of the resulting data set? 0,3,9,5,4,2,2 The mean (Type an integer or decimal rounded to the nearest hundredth as needed )
6.00
To find the mean, you add up all the values in the data set and divide by the total number of values.
0 + 3 + 9 + 5 + 4 + 2 + 2= 25
25 (the sum) / 7 (the total number of values) = 3.57 (the original mean)
Now, if we multiply each value in the data set by 3, we get:
0, 9, 27, 15, 12, 6, 6
To find the new mean, we add up all the new values and divide by the total number of values:
0 + 9 + 27 + 15 + 12 + 6 + 6 = 75
75 (the new sum) / 7 (the total number of values) = 10.71
Therefore, the new mean is 10.71.
The median is (Type an integer)
4
To find the median, we first need to put the values in order from least to greatest:
0, 6, 6, 9, 12, 15, 27
Since there are an odd number of values, the median is simply the middle value, which is 9.
However, this was the original median. To find the new median, we need to find the middle value of the new data set:
0, 9, 27, 15, 12, 6, 6
Again, we put the values in order from least to greatest:
0, 6, 6, 9, 12, 15, 27
Now we can see that the new median is also 9.
The mode is (Type "There is no mode" if applicable)
There is no mode
The mode is the value that appears most frequently in a data set. In this case, there is no value that appears more than once, so there is no mode.
When we multiply each value by 3, there are still no values that appear more than once, so there is still no mode.
The range is (Type an integer or decimal rounded to the nearest hundredth as needed)
27
The range is the difference between the highest value and the lowest value in a data set.
The highest value in the original data set is 9 and the lowest value is 0, so the range is:
9 - 0 = 9
When we multiply each value by 3, the highest value becomes 27 and the lowest value is still 0, so the range is:
27 - 0 = 27
To find the mean of the resulting data set, we first multiply each value in the original data set by 3. The resulting data set will be:
0*3 = 0
3*3 = 9
9*3 = 27
5*3 = 15
4*3 = 12
2*3 = 6
2*3 = 6
The resulting data set is 0, 9, 27, 15, 12, 6, 6.
To find the mean, we sum up all the values and divide by the number of values.
Mean = (0 + 9 + 27 + 15 + 12 + 6 + 6) / 7
Mean = 75 / 7
Mean ≈ 10.71