Starting with the data values 70 and 100, add three data values to the sample so that the mean is 81, the median is 91, and the mode is 91.
How do i do this??
To add three data values to the sample in order to achieve the desired mean, median, and mode, we need to analyze the given information and come up with a plan.
First, let's determine what the given sample currently consists of. We know that the starting values are 70 and 100.
Next, let's identify the objectives we need to achieve. We want the mean to be 81, the median to be 91, and the mode to be 91.
To start, let's work on finding the additional data values that will allow us to achieve the desired mode of 91. Since mode represents the most frequently occurring value, we know that we need to add a value of 91 to the sample at least twice.
Now, let's focus on the median. We want the median to be 91, which means it should fall right in the middle of the ordered data set. Since we currently have two values in our sample (70 and 100), we know that one of the additional values needs to be 91 so that it becomes the median value.
Finally, let's calculate the mean. The mean represents the average value of all the data points. To find the mean, we sum up all the values and divide by the total number of values.
If the mean is 81 with a sample size of 5 (we currently have 2 values and are adding 3 more), the sum of the 5 values should be 5 * 81 = 405.
Let's summarize our plan based on the information above:
1. Add the value 91 to the sample twice to achieve the desired mode.
2. Add the value 91 to the sample to make it the median value.
3. Calculate the sum of all the values (including the newly added ones) to determine the missing value required to achieve the desired mean of 81.
4. Add the calculated value to the sample to complete the task.
By following these steps, you should be able to add three data values to the sample so that the mean is 81, the median is 91, and the mode is 91.
To add three data values to the sample so that the mean is 81, the median is 91, and the mode is 91, follow these steps:
Step 1: Start with the given data values: 70 and 100.
Step 2: Calculate the current mean:
Mean = (70 + 100) / 2 = 85
Step 3: Calculate the difference between the desired mean (81) and the current mean (85):
Difference = desired mean - current mean = 81 - 85 = -4
Step 4: Take the absolute value of the difference:
Absolute Difference = |-4| = 4
Step 5: Divide the absolute difference by 2 to find out how much each additional value should increase or decrease:
Increment/Decrement = Absolute Difference / 2 = 4 / 2 = 2
Step 6: Determine which values need to be added. Since the desired median and mode are both 91, we need two values that are smaller than 91 and one value that is larger than 91.
Step 7: Calculate the values to be added:
Value 1 = 91 - Increment/Decrement = 91 - 2 = 89
Value 2 = 91
Value 3 = 91 + Increment/Decrement = 91 + 2 = 93
Step 8: Add the three calculated values to the original sample:
Final sample: 70, 89, 91, 91, 93, 100
Now, the mean of the final sample is 81, the median is 91, and the mode is 91.