Question

Examine the data from a survey of farmers
about their different soil types and the crops
they prefer to grow. Using relative frequencies
what is the percentage change that farmers with
sandy soil prefer to grow carrots? Round your
answers o the nearest tenth.

Sandy Soil: 120, 50, 170
Rocky Soil: 100, 150, 250
Totals: 220, 200, 420

Answer 1

To find the percentage change that farmers with sandy soil prefer to grow carrots, we first need to determine the relative frequency of farmers with sandy soil who prefer to grow carrots.

Relative Frequency = Number of farmers with sandy soil who prefer to grow carrots / Total number of farmers with sandy soil

Number of farmers with sandy soil who prefer to grow carrots = 120
Total number of farmers with sandy soil = 120 + 50 + 170 = 340

Relative Frequency = 120 / 340 ≈ 0.3529

Next, we find the relative frequency of farmers with sandy soil who prefer to grow carrots in the second year.

Relative Frequency = Number of farmers with sandy soil who prefer to grow carrots / Total number of farmers with sandy soil

Number of farmers with sandy soil who prefer to grow carrots = 50
Total number of farmers with sandy soil = 120 + 50 + 170 = 340

Relative Frequency = 50 / 340 ≈ 0.1471

Now, we calculate the percentage change:

Percentage Change = [(New Value - Old Value) / Old Value] * 100
Percentage Change = [(0.1471 - 0.3529) / 0.3529] * 100
Percentage Change ≈ -58.3%

Therefore, the percentage change that farmers with sandy soil prefer to grow carrots is approximately -58.3%.