Question

suppose a class obtained the following scores on a test.
score | frequency
90 | 2
80 | 4
70 | 11
60 | 5
50 | 3
what is the median?

Explanation:

Step1: Calculate total number of data points

First, we sum up the frequencies. The frequencies are 2, 4, 11, 5, and 3. So, \(2 + 4+11 + 5+3=25\). The total number of data points \(n = 25\), which is odd.

Step2: Find the position of the median

For a set with \(n\) data points (where \(n\) is odd), the median is the \(\frac{n + 1}{2}\)-th value when the data is ordered. So, \(\frac{25+ 1}{2}=13\)-th value.

Step3: Cumulative frequency to find the median

Now, we calculate cumulative frequencies:

• For score 90: cumulative frequency \(= 2\)
• For score 80: cumulative frequency \(=2 + 4=6\)
• For score 70: cumulative frequency \(=6+ 11 = 17\)
• For score 60: cumulative frequency \(=17+5 = 22\)
• For score 50: cumulative frequency \(=22 + 3=25\)

We need to find the 13 - th value. Since the cumulative frequency for 70 is 17 (which is greater than 13) and the cumulative frequency for 80 is 6 (which is less than 13), the 13 - th value falls in the score of 70.

Answer:

70