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The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.

A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.

A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.

Which class lost the most pencils overall based on the data displayed?

Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data



Answer :

semsee45

Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

  • Minimum value = The value at the end of the left whisker.
  • Lower quartile (Q₁) = The left side of the box.
  • Median (Q₂) = The vertical line inside the box.
  • Upper quartile (Q₃) = The right side of the box
  • Maximum = The value at the end of the right whisker.

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

  • Median = 11
  • IQR = Q₃ - Q₁ = 14 - 8 = 6
  • Range = max - min = 45 - 7 = 38

Mr Simpson's class:

  • Median = 14.5
  • IQR = Q₃ - Q₁ = 21 - 12 = 9
  • Range = max - min = 50 - 0 = 50

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

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