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Problem of the Week
Problem B
Measuring Feet - A Great Feat!

While reading an article in Teen Feat Magazine, Sundip learned that the mean (average) length of an \(11\)-year-old’s foot is \(22.9\,\)cm. He wondered how many of his \(11\)-year-old friends had “average” feet. Here is the information of the foot lengths, in cm, that he gathered from himself and \(11\) of his friends: \[19.1,~23.3,~21.7, ~24.3, ~22.1,~22.4,~20.7,~21.9,~22.5,~24.1,~26.4,~24.7\]

  1. Complete the frequency table below to reveal the number of students with foot lengths within each interval.

    Foot Length Tally Frequency Relative Frequency
    \(18.0\) - \(19.9\)
    \(20.0\) - \(21.9\)
    \(22.0\) - \(23.9\)
    \(24.0\) - \(25.9\)
    \(26.0\) - \(27.9\)

  2. What is the mean (average) foot length for Sundip and his friends? How does it compare to the average for \(11\)-year-olds?

  3. Does the information in the table reveal any similarities or differences among the students as to foot length?

  4. Sundip’s article also stated that fifty years ago, the average foot length an \(11\)-year-old was about \(21.9\,\)cm. How do his friends’ sizes compare to those of fifty years ago?

Theme: Data Management