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??
If the mode (most frequently occurring score) = 91, at least 2 of the scores = 91. You only need to find one more score. Use the mean.
81 = (x+70+91+91+100)/5
Solve for x.
To check, it should still lead to a median of 91.
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81 = (x + 352)/5
81 = 352x/5
81 = 70.4x
x = 1.15??
Did i do that correctly??
No, X+352 ≠ 352x
81 = (x + 352)/5
Multiply both sides by 5, then subtract 352 from both sides.
oh....so i get x = 53??
To add three data values to the sample in order to achieve the desired mean, median, and mode, we need to understand each of these statistical measures.
1. Mean: The mean is calculated by summing up all the data values and then dividing the sum by the total number of values. In this case, the desired mean is 81.
2. Median: The median is the middle value in a sorted list of data points. If the list has an odd number of values, the median is the middle value. If the list has an even number of values, the median is the average of the two middle values. In this case, the desired median is 91.
3. Mode: The mode is the value that appears most frequently in a dataset. In this case, the desired mode is 91.
To add three data values to the sample, while ensuring the desired mean, median, and mode, we can follow these steps:
Step 1: Add a value that is less than 91 to maintain the desired mean of 81. For example, let's add 80 to the sample.
Step 2: Add two equal values that are greater than 91 to maintain the desired median and mode of 91. For example, let's add 92 twice to the sample.
The updated sample would be: 70, 80, 92, 92, 100.
By following these steps, we ensured that the mean is 81, the median is 91, and the mode is 91.