starting with the values 70 and 100, add 3 data values to the sample so that the mean is 76. the median is 82 and the mode is 82. show work

70+82+82+100+x/5=76

(There has to be at least two 82's since it is the mode.) Solve for x, and that's the third unknown.

starting with the values 70 and 100, add 3 data values to the sample so that the mean is 76. the median is 82 and the mode is 82. show work. (please help me find the 3 data values and show how was figured out. i am totally confused.

I did explain it, Mary. We already know that you have a 70 and 100. There has to be at least 82's since it's the mode (occurs the most). We can then solve for the missing number. (70+82+82+100+x)/5=76..x will be the last missing number.

70+83+83+x+100/5=76

336+x=5(76)

380-336=44

x=44 which is the third number therefore the number group will be

70+83+83+44+100

To find the additional values that need to be added to the sample, we can follow these steps:

Step 1: Find the mode
The mode is the value that appears most frequently in the sample. In this case, the mode is given as 82.

Step 2: Find the median
The median is the middle value when the data is arranged in ascending or descending order. In this case, the median is given as 82.

Step 3: Find the mean
The mean is the average of all the values in the sample. In this case, the mean is given as 76.

Now, let's work through the solution:

Step 4: Calculate the sum of the existing data values
We start with the values 70 and 100, so the sum is:
70 + 100 = 170

Step 5: Calculate the sum of all the values needed to reach the desired mean
To achieve a mean of 76, the sum of all the values should be equal to:
(76 * 5) - 170 = 380 - 170 = 210

Step 6: Find the remaining three data values
Since 82 is both the mode and the median, we need to add three instances of 82 to the sample.

Step 7: Calculate the sum of the new sample
Adding the three instances of 82 to the existing values:
170 + (82 * 3) = 170 + 246 = 416

Step 8: Check the mean of the new sample
To verify if the mean is 76, we divide the sum by the total number of values:
416 / 5 = 83.2

The mean of the new sample is 83.2, which is higher than the desired mean of 76.

Step 9: Modify the values to achieve the desired mean
To adjust the mean to 76, we need to subtract a certain value from the sum.

Step 10: Calculate the value to be subtracted
(83.2 - 76) * 5 = 37

To achieve a mean of 76, we need to subtract 37 from the sum.

Step 11: Adjust the mode and median
Since we need to subtract 37 from the sum, we can remove one instance of 82 from the sample.

Step 12: Calculate the new sum of the sample
416 - 37 = 379

Step 13: Check the adjusted mean
The new mean will be:
379 / 5 = 75.8

The mean of the adjusted sample is 75.8, which is approximately equal to 76, the desired mean.

Therefore, to obtain a sample with a mean of 76, a median of 82, and a mode of 82, you can add one more instance of 82 to the existing values of 70 and 100.