Question

Find the median for the data items in the given frequency distribution.

Score, x
Frequency, f
1
1
2
3
The median is
(Type an integer or a decimal.)
3
1
4
01.
5
01
5
5
6
7
7
51
8
51
97
7
10
3
...

Answer 1

The median of a frequency distribution is found by listing out all values in order according to their frequencies, then choosing the middle value. If the total number of values is odd, the median is the value at position (n+1)/2.

If even, it is the average of the values at positions n/2 and (n/2)+1.

Step-by-step explanation:

To find the median for the data items in a frequency distribution, you would list out all the values in order as if you had a list of individual data points. Since we are not provided all the specific frequencies or the entire dataset in this case, we will use the information given to explain the process of finding the median.

Let's assume that scores are given with their corresponding frequencies, which means that a score with a frequency of 1 occurs once, a score with a frequency of 2 occurs twice, and so on. We would create a list of the scores repeating each score as many times as its frequency refers to.

Then you would count the total number of data points, which is the sum of all frequencies. If the total number of data points, n, is odd, the median is the value at position (n+1)/2. If n is even, the median is the average of the values at positions n/2 and (n/2)+1.

For example, if we had a data list of 1; 2; 2; 3; 4; 4; 5; 5; 6; 7; 7 based on the given frequencies, and there are 11 total data points (odd), the median would be the 6th value when listed in order. In our example, the 6th value is 4.