Statistics: Mean and Median from Frequency Table

Overview

This lecture explains how to find the mean and median scores from a frequency table of student quiz results.

Calculating the Mean

• The mean (average) is found by dividing the sum of all data values by the number of values.
• Use the formula: mean (x̄) = (sum of x) / n, where x are data values and n is their count.
• The total number of test scores is found by summing the frequency column, which is 19.
• To sum the data efficiently, multiply each score by its frequency (e.g., 2 × 3 for two scores of 3).
• The total sum is: (2×3) + (4×4) + (2×5) + (1×6) + (1×7) + (3×8) + (5×9) + (1×10).
• Calculating, this sum is: 6 + 16 + 10 + 6 + 7 + 24 + 45 + 10 = 124.
• The mean is 124 ÷ 19 ≈ 6.5 (rounded to one decimal place).

Calculating the Median

• The median is the middle value when data is ordered from smallest to largest.
• If the data count n is odd, the median is at position (n ÷ 2), rounded up to the next whole number.
• For n = 19, 19 ÷ 2 = 9.5, rounded up to 10; the median is the 10th score.
• Count cumulative frequencies to find the 10th score:
  • 2 (score 3) + 4 (score 4) = 6
  • +2 (score 5) = 8
  • +1 (score 6) = 9
  • +1 (score 7) = 10 (so the 10th score is 7)
• There are 9 scores below 7 and 9 above, confirming 7 is the median.

Key Terms & Definitions

• Mean (x̄) — The sum of all data values divided by the number of values.
• Median — The value in the middle of an ordered data set.
• Frequency Table — A table displaying data values and how often each occurs.

Action Items / Next Steps

• Practice finding mean and median from different frequency tables.
• Review chapter on measures of central tendency in your textbook.