Final answer:
To find the mean of a data set with a missing value, sum the known values, add the missing value (m), and divide by the total number of values. If the desired mean is known, rearrange the formula to solve for m. For grouped data, use midpoints of intervals multiplied by frequencies to estimate the mean.
Step-by-step explanation:
Finding the Mean with a Missing Value
To find the mean of a data set with a missing value, you must first sum all the known values. Next, if you know the number of data values in the set, you can use the formula for the mean which is the sum of all data values divided by the number of values. Representing the mean with the symbol x bar and the missing value as 'm', the formula will look like this:
mean = (sum of known values + m) / total number of values
If the total number of values and the desired average are known, you can rearrange the formula to solve for 'm'. Assume the data set has a total of 10 values and the desired mean is 5. With the sum of 9 known values being 40, the equation to find 'm' would be:
5 = (40 + m) / 10
After multiplying both sides by 10 and subtracting 40 from both sides, the missing value 'm' is calculated to be 10. This is a simplified example for a single missing value
Grouped Frequency Tables
When working with grouped data, calculating an approximated mean is necessary. For grouped frequency tables, you can estimate the mean by using midpoints of intervals multiplied by their frequencies, and then dividing by the total number of data values.
when a data set has an even number of data values, the median is the average of the two middle values once the data is arranged in ascending order. When the data set has an odd number of data values, the median is the value in the middle.