High School

A researcher collected data on the heights (in inches) of 50 individuals. The data is as follows:
{64, 67, 70, 68, 65, 63, 71, 69, 72, 66, 68, 64, 70, 67, 69, 65, 71, 68, 66, 63, 70, 67, 69, 65, 68, 64, 71, 69, 67, 69, 66, 63, 70, 68, 72, 67, 69, 65, 63, 71, 68, 66, 64, 70, 67, 69, 66, 63, 70, 68}.
Construct a frequency distribution table for this data taking at least five class intervals and determine the mode.

Answer :

To create a frequency distribution table, we first need to determine suitable class intervals for the heights. Since we have data ranging from 63 to 72 inches, and we want at least five class intervals, we can choose a class width of 2 inches.

Frequency Distribution Table:

  • Class Interval: 63-64
    • Frequency: 8
  • Class Interval: 65-66
    • Frequency: 10
  • Class Interval: 67-68
    • Frequency: 13
  • Class Interval: 69-70
    • Frequency: 13
  • Class Interval: 71-72
    • Frequency: 6

Explanation:

  1. Choose Class Intervals:

    • We divided the data into 5 class intervals: 63-64, 65-66, 67-68, 69-70, 71-72.
    • The class width is 2, which means each class interval spans 2 inches.

  2. Count the Frequency:

    • For each class interval, count how many heights fall within that range.
    • The frequency is the count of data points within each interval.

Determine the Mode:

  • The mode is the value or class interval with the highest frequency.
  • From the frequency distribution table, the highest frequency is 13, occurring in both the 67-68 and 69-70 intervals.
  • Therefore, this data set is bi-modal with modes at 67-68 and 69-70.

By organizing the data in this manner, it becomes easier to analyze and understand the distribution of heights within this sample cohort.

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