How many values of x make the mean and median of a set of numbers equal?

Thread starter math_grl
Start date Aug 9, 2011
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Average Median

In summary, the median and average are two measures of central tendency in a set of numbers. The median is the middle value while the average is the sum of all values divided by the number of values. The median is more appropriate to use when there are extreme values or outliers, while the average is more commonly used and takes into account all values. To calculate the median, arrange the numbers and find the middle value, while the average is found by adding all values and dividing by the number of values. In some cases, the median and average may be equal in a symmetrical distribution, but this is not always the case.

Aug 9, 2011

math_grl

Let f(x) be the mean of five numbers: 4, 5, 7, 9 and x. Let g(x) be the median of the same numbers.
For how many values of x, a real number, is f(x) = g(x)?

I only got 2. x = 0, 10

There are 3 though. Perhaps someone can help me find the other one.

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Aug 9, 2011

math_grl

nevermind i found it. 25/4 was the last one.

1. What is the difference between median and average?

The median is the middle value in a set of numbers when they are arranged in ascending or descending order. The average, also known as the mean, is the sum of all the values in a set divided by the number of values.

2. When should I use median instead of average?

The median is more appropriate to use when there are extreme values or outliers in a set of data, as it is not affected by these values. The average is more sensitive to outliers and may not accurately represent the central tendency of the data in these cases.

3. How do I calculate the median and average?

To calculate the median, first arrange the numbers in order from smallest to largest. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers. To calculate the average, add up all the values and divide by the number of values.

4. Which measure of central tendency is more commonly used?

The average is more commonly used as a measure of central tendency as it takes into account all the values in a set of data. However, the median is also frequently used, especially when dealing with skewed data or data with outliers.

5. Can the median and average be equal?

Yes, if the set of data has a symmetrical distribution, the median and average may be equal. This is because the middle value in a symmetrical distribution is also the average of all the values. However, this is not always the case and the median and average can differ in other distributions.