Final answer:
The function that returns the number in the middle of a set of numbers is MEDIAN. The median is found by ordering the data and choosing the middle value. In the case of the given data set, the median is 5. Functions such as MEAN, COUNTA, and AVERAGE have different uses in data analysis.
Step-by-step explanation:
Identifying the Function for Finding the Middle Number in a Data Set
The function that returns the number in the middle of a set of numbers from the given options is 1) MEDIAN. The median is a measure of central tendency that divides a data set into two equal halves. To find the median, the data values are first arranged in ascending order and then the middle value is selected. If the total number of data values (n) is odd, the median is the value in the middle position. If n is even, the median is the average of the two middle values.
To compute the median for the data set provided (1; 1; 2; 3; 4; 4; 5; 5; 6; 7; 7; 8; 9), we arrange it in order and find the middle value. Since there are 13 values (an odd number), the median is the 7th value when arranged in ascending order, which is 5.
The MEAN, also known as the average, is the sum of all the data values divided by the number of values, and it can be skewed by outliers. The other functions mentioned, COUNTA and AVERAGE, serve different purposes: COUNTA counts non-empty cells in a range and AVERAGE computes the mean of a group of numbers. However, as stated earlier, mean and average are often used interchangeably in common practice.