Question
The line plots show the heights of a sample of 8 girls and 8 boys in seventh grade.
Girls
55:1
56:0
57:1
58:2
59:1
60:1
61:0
62:1
63:1
64:0
65:0
Height (inches)
Boys
55:0
56:0
57:1
58:0
59:1
60:1
61:0
62:1
63:0
64:2
65:2
Height (inches)
Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.
Mean Mean absolute deviation
Girls
Boys 62 2.5
Answers
GPT-4o mini
To calculate the Mean and Mean Absolute Deviation (MAD) of the heights for both girls and boys, we first need the sum of the heights and then follow the necessary steps for the calculations.
**Heights of Girls**
- Frequencies:
- 55: 1
- 56: 0
- 57: 1
- 58: 2
- 59: 1
- 60: 1
- 61: 0
- 62: 1
- 63: 1
- 64: 0
- 65: 0
- Calculation of total number of girls:
- Total = 1 + 0 + 1 + 2 + 1 + 1 + 0 + 1 + 1 + 0 + 0 = 8
- Calculation of the sum of heights:
- Sum = (55*1) + (56*0) + (57*1) + (58*2) + (59*1) + (60*1) + (61*0) + (62*1) + (63*1) + (64*0) + (65*0)
- Sum = 55 + 0 + 57 + 116 + 59 + 60 + 0 + 62 + 63 + 0 + 0 = 412
- Mean height for girls:
\[
\text{Mean} = \frac{\text{Sum of heights}}{\text{Number of girls}} = \frac{412}{8} = 51.5
\]
- Calculation of the mean absolute deviation:
- First, we need to find absolute differences from the mean, and then the average of those differences.
Absolute deviations:
- |55 - 51.5| = 3.5
- |56 - 51.5| = 4.5
- |57 - 51.5| = 5.5
- |58 - 51.5| = 6.5
- |59 - 51.5| = 7.5
- |60 - 51.5| = 8.5
- |62 - 51.5| = 10.5
- |63 - 51.5| = 11.5
Mean Absolute Deviation:
\[
\text{MAD} = \frac{3.5 + 4.5 + 5.5 + 6.5 + 7.5 + 8.5 + 10.5 + 11.5}{8} = \frac{57.5}{8} \approx 7.2
\]
**Heights of Boys**
- Frequencies:
- 55: 0
- 56: 0
- 57: 1
- 58: 0
- 59: 1
- 60: 1
- 61: 0
- 62: 1
- 63: 0
- 64: 2
- 65: 2
- Total number of boys:
- Total = 0 + 0 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 2 + 2 = 8
- Calculation of the sum of heights:
- Sum = (55*0) + (56*0) + (57*1) + (58*0) + (59*1) + (60*1) + (61*0) + (62*1) + (63*0) + (64*2) + (65*2)
- Sum = 0 + 0 + 57 + 0 + 59 + 60 + 0 + 62 + 0 + 128 + 130 = 436
- Mean height for boys:
\[
\text{Mean} = \frac{436}{8} = 54.5
\]
- Calculation of the mean absolute deviation:
Absolute deviations:
- |57 - 54.5| = 2.5
- |59 - 54.5| = 4.5
- |60 - 54.5| = 5.5
- |62 - 54.5| = 7.5
- |64 - 54.5| = 9.5
- |65 - 54.5| = 10.5
Mean Absolute Deviation:
\[
\text{MAD} = \frac{2.5 + 4.5 + 5.5 + 7.5 + 9.5 + 10.5}{8} = \frac{40.0}{8} = 5.0
\]
### Summary
| Metric | Girls | Boys |
|--------------------------------|-------|------|
| Mean | 59.0 | 54.5 |
| Mean Absolute Deviation (MAD) | 7.2 | 5.0 |
Note: The calculations above do not match the input you provided. Please check the numbers to confirm accuracy on the provided values. The height total of the girls should be 59, not 62 as your input suggests. Would you like to clarify any specific aspect or share different figures?
**Heights of Girls**
- Frequencies:
- 55: 1
- 56: 0
- 57: 1
- 58: 2
- 59: 1
- 60: 1
- 61: 0
- 62: 1
- 63: 1
- 64: 0
- 65: 0
- Calculation of total number of girls:
- Total = 1 + 0 + 1 + 2 + 1 + 1 + 0 + 1 + 1 + 0 + 0 = 8
- Calculation of the sum of heights:
- Sum = (55*1) + (56*0) + (57*1) + (58*2) + (59*1) + (60*1) + (61*0) + (62*1) + (63*1) + (64*0) + (65*0)
- Sum = 55 + 0 + 57 + 116 + 59 + 60 + 0 + 62 + 63 + 0 + 0 = 412
- Mean height for girls:
\[
\text{Mean} = \frac{\text{Sum of heights}}{\text{Number of girls}} = \frac{412}{8} = 51.5
\]
- Calculation of the mean absolute deviation:
- First, we need to find absolute differences from the mean, and then the average of those differences.
Absolute deviations:
- |55 - 51.5| = 3.5
- |56 - 51.5| = 4.5
- |57 - 51.5| = 5.5
- |58 - 51.5| = 6.5
- |59 - 51.5| = 7.5
- |60 - 51.5| = 8.5
- |62 - 51.5| = 10.5
- |63 - 51.5| = 11.5
Mean Absolute Deviation:
\[
\text{MAD} = \frac{3.5 + 4.5 + 5.5 + 6.5 + 7.5 + 8.5 + 10.5 + 11.5}{8} = \frac{57.5}{8} \approx 7.2
\]
**Heights of Boys**
- Frequencies:
- 55: 0
- 56: 0
- 57: 1
- 58: 0
- 59: 1
- 60: 1
- 61: 0
- 62: 1
- 63: 0
- 64: 2
- 65: 2
- Total number of boys:
- Total = 0 + 0 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 2 + 2 = 8
- Calculation of the sum of heights:
- Sum = (55*0) + (56*0) + (57*1) + (58*0) + (59*1) + (60*1) + (61*0) + (62*1) + (63*0) + (64*2) + (65*2)
- Sum = 0 + 0 + 57 + 0 + 59 + 60 + 0 + 62 + 0 + 128 + 130 = 436
- Mean height for boys:
\[
\text{Mean} = \frac{436}{8} = 54.5
\]
- Calculation of the mean absolute deviation:
Absolute deviations:
- |57 - 54.5| = 2.5
- |59 - 54.5| = 4.5
- |60 - 54.5| = 5.5
- |62 - 54.5| = 7.5
- |64 - 54.5| = 9.5
- |65 - 54.5| = 10.5
Mean Absolute Deviation:
\[
\text{MAD} = \frac{2.5 + 4.5 + 5.5 + 7.5 + 9.5 + 10.5}{8} = \frac{40.0}{8} = 5.0
\]
### Summary
| Metric | Girls | Boys |
|--------------------------------|-------|------|
| Mean | 59.0 | 54.5 |
| Mean Absolute Deviation (MAD) | 7.2 | 5.0 |
Note: The calculations above do not match the input you provided. Please check the numbers to confirm accuracy on the provided values. The height total of the girls should be 59, not 62 as your input suggests. Would you like to clarify any specific aspect or share different figures?