Question

The weights of two varieties of apples are measured at a grocery store and recorded in tables.

The weights and numbers of McIntosh apples are as follows:

Weight in pounds 0.37 0.38 0.39 0.40 0.41 0.42 0.43
Number of apples 8 20 35 40 35 20 8
The weights and numbers of Honeycrisp apples are as follows:

Weight in pounds 0.27 0.28 0.29 030 0.31 0.32 0.33
Number of apples 4 17 26 34 26 17 4
Which variety of apple has a greater percentage of apples below the median?

(1 point)
Responses

The McIntosh apples have 2% more apples below the median than the Honeycrisp apples.
The McIntosh apples have 2% more apples below the median than the Honeycrisp apples.

The Honeycrisp apples have 1% more apples below the median than the McIntosh apples.
The Honeycrisp apples have 1% more apples below the median than the McIntosh apples.

The McIntosh apples have 1% more apples below the median than the Honeycrisp apples.
The McIntosh apples have 1% more apples below the median than the Honeycrisp apples.

The Honeycrisp apples have 2% more apples below the median than the McIntosh apples.

Answers

GPT-4o mini
To determine which variety of apple has a greater percentage of apples below the median, we first need to calculate the median weight for both McIntosh and Honeycrisp apples.

### McIntosh Apples
- **Weights (in pounds)**: 0.37, 0.38, 0.39, 0.40, 0.41, 0.42, 0.43
- **Number of apples**: 8, 20, 35, 40, 35, 20, 8

**Cumulative counts of apples:**
- 0.37: 8
- 0.38: 8 + 20 = 28
- 0.39: 28 + 35 = 63
- 0.40: 63 + 40 = 103
- 0.41: 103 + 35 = 138
- 0.42: 138 + 20 = 158
- 0.43: 158 + 8 = 166

**Total number of apples:** 166

**Finding the Median:**
The median is the middle value. For 166 apples, the median will be the average of the 83rd and 84th values.
- The 83rd apple is in the weight range of 0.40 (as the cumulative total by 0.39 is 63 and by 0.40 is 103).

Thus, the median weight for the McIntosh apples is 0.40 pounds.

**Counting apples below the median (0.40):**
- Number of apples below 0.40: apples with weights 0.37, 0.38, 0.39
- 8 + 20 + 35 = 63 apples below the median.

**Percentage of apples below the median:**
\[
\text{Percentage} = \left( \frac{63}{166} \right) \times 100 \approx 37.95\%
\]

### Honeycrisp Apples
- **Weights (in pounds)**: 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33
- **Number of apples**: 4, 17, 26, 34, 26, 17, 4

**Cumulative counts of apples:**
- 0.27: 4
- 0.28: 4 + 17 = 21
- 0.29: 21 + 26 = 47
- 0.30: 47 + 34 = 81
- 0.31: 81 + 26 = 107
- 0.32: 107 + 17 = 124
- 0.33: 124 + 4 = 128

**Total number of apples:** 128

**Finding the Median:**
For 128 apples, the median will be the average of the 64th and 65th values.
- The 64th and 65th apples fall within the weight range of 0.30 (as the cumulative total by 0.30 is 81).

Thus, the median weight for the Honeycrisp apples is 0.30 pounds.

**Counting apples below the median (0.30):**
- Number of apples below 0.30: apples with weights 0.27, 0.28, and 0.29
- 4 + 17 + 26 = 47 apples below the median.

**Percentage of apples below the median:**
\[
\text{Percentage} = \left( \frac{47}{128} \right) \times 100 \approx 36.72\%
\]

### Comparison of Percentages
- **McIntosh apples:** Approximately 37.95%
- **Honeycrisp apples:** Approximately 36.72%

### Conclusion
The McIntosh apples have about \(37.95\% - 36.72\% = 1.23\%\) more apples below the median than the Honeycrisp apples.

Thus, the correct answer is:
**The McIntosh apples have 1% more apples below the median than the Honeycrisp apples.**

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