Question

aring data sets
shana is fostering two kittens, janet and mr. paws. the box plots represent the amount of food each kitten eats, in ounces, per day during one week.
janets food (in ounces)
mr. paws food (in ounces)
complete the statements to compare the amounts of food eaten by janet and mr. paws.
the median amount of janet’s food is the median amount of mr. paws’ food.
the range of janet’s food is the range of mr. paws’ food.
which measure for the amount of food eaten is the same for both kittens?

Explanation:

To solve this, we analyze the box - plots:

1. Comparing the medians

• In a box - plot, the median is represented by the line inside the box. For Janet's food box - plot, the median line is at a lower value on the number line compared to Mr. Paws' food box - plot. So, the median amount of Janet’s food is less than the median amount of Mr. Paws’ food.

2. Comparing the ranges

• The range of a data set is calculated as the maximum value minus the minimum value. For Janet's food, the distance between the minimum (the left end of the whisker) and the maximum (the right end of the whisker) on the number line is smaller than the distance between the minimum and maximum for Mr. Paws' food. So, the range of Janet’s food is less than the range of Mr. Paws’ food.

3. Identifying the same measure

• We look at the whiskers (the ends of the lines extending from the boxes) for both kittens. The maximum value (the right - most end of the whisker) for both Janet and Mr. Paws seems to be the same when we observe the number line. So, the maximum amount of food eaten (or we can also say the upper extreme) is the same for both kittens. If we consider the options (even though not fully shown, from the context of box - plot analysis), the measure that is the same is likely the maximum (or the upper whisker end value).

Answer:

s:

• The median amount of Janet’s food is $\boldsymbol{\text{less than}}$ the median amount of Mr. Paws’ food.
• The range of Janet’s food is $\boldsymbol{\text{less than}}$ the range of Mr. Paws’ food.
• The measure for the amount of food eaten that is the same for both kittens is $\boldsymbol{\text{Maximum (or the upper extreme value)}}$ (assuming from the box - plot analysis of whiskers). If we consider the general box - plot terms, it's the upper whisker end (maximum) that is the same.