Starting with the data values 70 and 100, add three data values to the sample so that the mean is 96, the median is 97, and the mode is 97
For the mode to be 97, at least two of the three scores will be 97. For the third value, (70+97+97+100+x)/5 = mean (96). Solve for x.
How do you solve for X?
To find the three data values that satisfy the given conditions, we need to understand the properties of mean, median, and mode.
1. Mean: The mean is calculated by summing all the data values and dividing by the total number of values.
2. Median: The median is the middle value in a sorted set of data. If there is an even number of data values, the median is the average of the two middle values.
3. Mode: The mode is the value that appears most frequently in a set of data. A set can have multiple modes or no mode at all.
Now, let's break down the given conditions:
1. Mean = 96: We have a total of five data values (including the three additional values). To get a mean of 96, the sum of all the data values must be (96 * 5) = 480.
2. Median = 97: Since we have five data values, the median is the third value when sorted in ascending order.
3. Mode = 97: The mode is the data value that occurs most frequently.
Now, let's proceed to find the three additional data values:
Step 1: Start with the initial data values: 70 and 100.
Step 2: Calculate the sum of the initial data values: 70 + 100 = 170.
Step 3: Calculate the sum required to reach a mean of 96: 480 (sum for mean) - 170 (sum of initial values) = 310.
Step 4: Divide the remaining sum equally into three parts: 310 / 3 = 103.33 (approximately).
Since we need whole numbers for the data values, we can have two values as 103 and one as 104.
Thus, the three additional data values to achieve the given conditions are 103, 103, and 104.