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The table gives some information

about the heights of 60 boys.

a) Complete the boxplot for this information.

b) Work out an estimate for the number of these boys with a height between

149 cm and 181 cm.

The table gives some information about the heights of 60 boys a Complete the boxplot for this information b Work out an estimate for the

Answer :

Considering the information of the distribution given in the table, it is found that:

a) The box plot is given at the end of the answer.

b) The estimate for the number of these boys with a height between 149 cm and 181 cm is of 45.

What does a box-and-whisker plot shows?

A box and whisker plot shows five things of a distribution, listed as follows:

  • The minimum value of the data-set.
  • The first quartile, which is the median of the bottom 50% of measures in the data-set, hence it is the value that 75% of the measures are greater than.
  • The median, which is the middle-value of the data-set, meaning that 50% of the data-set is less than the median and 50% is greater.
  • The thid quartile, which is the median of the upper 50% of the measures in the data-set, hence it is the value that 75% of the measures are lesser than.
  • The maximum value of the data-set.

For the data-set of the heights, these measures are given as follows:

  • Minimum: 142 cm.
  • First quartile: 149 cm.
  • Median: 156 cm.
  • Third quartile: 160 cm.
  • Maximum: 181 cm.

The box plot showing these information is given by the image at the end of the answer.

The proportion of students with a height between 149 cm and 181 cm is of 75% = 0.75, as:

  • 149 cm is the first quartile of the distribution.
  • 181 cm is the maximum value of the distribution.

75% of the values are greater than the first quartile, hence the number of students is:

Number = 0.75 x 60 = 45 students.

More can be learned about the box plot of a distribution at https://brainly.com/question/29228493

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