Question

a nutritionist compares the amount of sodium in strawberry yogurt and vanilla yogurt. she gathers data on the amount of sodium (in milligrams) per container of strawberry yogurt and vanilla yogurt from many different brands. the summary statistics are shown in the table:

amount of sodium in yogurt

	strawberry	vanilla
q1	130	120
median	185	165
q3	210	195
maximum	220	230

which flavor has the greatest variation in sodium levels?

a. vanilla, because the range is larger
b. vanilla, because the minimum is smaller
c. strawberry, because the median is larger
d. strawberry, because the maximum is smaller

Explanation:

To determine which flavor has the greatest variation in sodium levels, we calculate the range (a measure of variation) for each flavor. The range is calculated as \( \text{Range} = \text{Maximum} - \text{Minimum} \).

Step 1: Calculate the range for Strawberry yogurt

For Strawberry yogurt, the maximum is 220 and the minimum is 100. So the range is \( 220 - 100 = 120 \).

Step 2: Calculate the range for Vanilla yogurt

For Vanilla yogurt, the maximum is 230 and the minimum is 80. So the range is \( 230 - 80 = 150 \).

Step 3: Compare the ranges

Since \( 150 > 120 \), Vanilla yogurt has a larger range, indicating a greater variation in sodium levels. Now we analyze the options:

• Option A: Says vanilla because the range is larger. This matches our calculation.
• Option B: A smaller minimum does not indicate greater variation. Variation is about spread, not the lowest value. Eliminate B.
• Option C: A larger median indicates a higher central tendency, not variation. Eliminate C.
• Option D: A smaller maximum does not indicate greater variation. Eliminate D.

Answer:

A. vanilla, because the range is larger