Question

suppose a class obtained the following scores on a test.
score\tfrequency
90\t1
80\t6
70\t10
60\t3
50\t2
40\t3
what is the median?

Explanation:

Step1: Calculate total number of data points

To find the total number of scores (n), we sum the frequencies. So, \( n = 1 + 6 + 10 + 3 + 2 + 3 \). Let's compute that: \( 1+6 = 7 \), \( 7+10 = 17 \), \( 17+3 = 20 \), \( 20+2 = 22 \), \( 22+3 = 25 \). So, \( n = 25 \).

Step2: Determine the position of the median

For a dataset with \( n \) values, if \( n \) is odd, the median is the value at the position \( \frac{n + 1}{2} \). Here, \( n = 25 \), so the position is \( \frac{25 + 1}{2} = 13 \)th value (when the data is ordered from least to greatest).

Step3: Find the cumulative frequencies

We'll create a cumulative frequency table:

• Score 40: Frequency = 3, Cumulative Frequency (CF) = 3
• Score 50: Frequency = 2, CF = \( 3 + 2 = 5 \)
• Score 60: Frequency = 3, CF = \( 5 + 3 = 8 \)
• Score 70: Frequency = 10, CF = \( 8 + 10 = 18 \)
• Score 80: Frequency = 6, CF = \( 18 + 6 = 24 \)
• Score 90: Frequency = 1, CF = \( 24 + 1 = 25 \)

We need to find the score where the cumulative frequency first reaches or exceeds the 13th position. Let's check:

• For score 40, CF = 3 (less than 13)
• For score 50, CF = 5 (less than 13)
• For score 60, CF = 8 (less than 13)
• For score 70, CF = 18 (which is greater than or equal to 13). So, the 13th value falls within the score of 70.

Answer:

70