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An orchard uses a histogram each year to track the number of apples produced per apple tree. The number of apples harvested this year are [tex]$41, 43, 45, 46, 48, 49, 50, 51, 53, 54, 55,$[/tex] and [tex]$56$[/tex].

For this situation, which is the appropriate way to label the number of apple intervals on the x-axis?

A. [tex]$41-46 ; 46-49 ; 49-52 ; 53-56$[/tex]
B. [tex]$41-45 ; 46-50 ; 51-55 ; 56-60$[/tex]
C. [tex]$40-44 ; 45-49 ; 50-55$[/tex]
D. [tex]$40-50 ; 50-55$[/tex]

Sagot :

GinnyAnswer
Let's look at the problem step-by-step to determine the appropriate way to label the number of apple intervals on the x-axis:

We have the following production data for apples: 41, 43, 45, 46, 48, 49, 50, 51, 53, 54, 55, and 56.

Given the four options for the intervals:

Option A: 41-46 ; 46-49 ; 49-52 ; 53-56

Let's distribute the data into these intervals:
- 41-46: Contains 41, 43, 45, 46 (4 values)
- 46-49: Contains 48, 49 (2 values)
- 49-52: Contains 50, 51 (2 values)
- 53-56: Contains 53, 54, 55, 56 (4 values)

Option B: 41-45 ; 46-50 ; 51-55 ; 56-60

Let's distribute the data into these intervals:
- 41-45: Contains 41, 43, 45 (3 values)
- 46-50: Contains 46, 48, 49, 50 (4 values)
- 51-55: Contains 51, 53, 54, 55 (4 values)
- 56-60: Contains 56 (1 value)

Option C: 40-44 ; 45-49 ; 50-55

Let's distribute the data into these intervals:
- 40-44: Contains 41, 43 (2 values)
- 45-49: Contains 45, 46, 48, 49 (4 values)
- 50-55: Contains 50, 51, 53, 54, 55 (5 values)

Option D: 40-50 ; 50-55

Let's distribute the data into these intervals:
- 40-50: Contains 41, 43, 45, 46, 48, 49, 50 (7 values)
- 50-55: Contains 51, 53, 54, 55 (4 values)

Analyzing these distributions, we see:

- Option A contains one interval with just 2 values (46-49) and another with only 2 values (49-52), which may not be ideal for visualization.
- Option B and Option D both end up with a single interval containing only one value (56 and 56, respectively), which might not be the most effective way to distribute the data.
- Option C does a good job of spreading the data evenly across the intervals, without leaving any interval too sparse or too crowded.

Therefore, by evaluating the given intervals and how the data is distributed, Option C: "40-44 ; 45-49 ; 50-55" is the most appropriate way to label the number of apple intervals on the x-axis.
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