High School

The following data set shows class intervals and their corresponding frequencies:

Class Intervals: 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90
Frequencies: 5, 15, 25, 20, 7, 8, 10

Find the median.

Answer :

Final answer:

In the given data, the median lies in the 40-50 interval. This is determined by creating a cumulative frequency column and finding the interval where the cumulative frequency first exceeds half of the total frequency.

Explanation:

This is a statistics problem about finding the median of grouped data. Before proceeding, we first need to calculate the cumulative frequency. Each entry in the cumulative frequency column is the sum of all frequencies up to and including the current row.

  • 20-30: 5
  • 30-40: 20 (5+15)
  • 40-50: 45 (20+25)
  • 50-60: 65 (45+20)
  • 60-70: 72 (65+7)
  • 70-80: 80 (72+8)
  • 80-90: 90 (80+10)

Calculate the total frequency (sum of all frequencies), which is 90. Since the median is the middle number, we'll find it in the interval where the cumulative frequency first exceeds half of the total frequency. Half of 90 is 45, and the first interval where the cumulative frequency exceeds 45 is 40-50. So, the median lies in the 40-50 interval.

Learn more about Median of Grouped Data here:

https://brainly.com/question/35903228

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