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Question 6 (Essay Worth 4 points)
(Comparing Data HC)

The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.

\begin{tabular}{r|l|l}
Bay Side School & & Seaside School \\
\hline [tex]$8,6,5$[/tex] & 0 & [tex]$5,8$[/tex] \\
[tex]$8,6,5,4,2,0$[/tex] & 1 & [tex]$0,1,2,5,6,8$[/tex] \\
[tex]$5,3,2,0,0$[/tex] & 2 & [tex]$5,5,7,7,8$[/tex] \\
& 3 & [tex]$0,6$[/tex] \\
2 & 4 &
\end{tabular}

Key: 2 | [tex]$1 \mid 0$[/tex] means 12 for Bay Side and 10 for Seaside

Part A: Calculate the measures of center. Show all work. (2 points)

Part B: Calculate the measures of variability. Show all work. (1 point)

Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)



Answer :

GinnyAnswer
### Part A: Calculate the measures of center

To analyze the central tendency of the class sizes, we'll calculate the mean and median for each school.

1. Bay Side School:
- Class Sizes: 85, 86, 86, 85, 84, 82, 80, 85, 83, 82, 80, 25, 23, 20, 20, 42
- Mean:
- Add all class sizes together: 85 + 86 + 86 + 85 + 84 + 82 + 80 + 85 + 83 + 82 + 80 + 25 + 23 + 20 + 20 + 42 = 1048
- Divide by the number of classes: 1048 / 16 = 65.5
- Median:
- Order the class sizes: 20, 20, 23, 25, 42, 80, 80, 82, 82, 83, 84, 85, 85, 86, 86
- With 16 values, the median will be the average of the 8th (82) and 9th (82) values: (82 + 82) / 2 = 82

2. Seaside School:
- Class Sizes: 50, 58, 51, 52, 55, 56, 58, 25, 25, 27, 27, 28, 30, 36, 22
- Mean:
- Add all class sizes together: 50 + 58 + 51 + 52 + 55 + 56 + 58 + 25 + 25 + 27 + 27 + 28 + 30 + 36 + 22 = 600
- Divide by the number of classes: 600 / 15 = 40.0
- Median:
- Order the class sizes: 22, 25, 25, 27, 27, 28, 30, 36, 50, 51, 52, 55, 56, 58, 58
- With 15 values, the median will be the 8th value: 36

Summary of Part A:
- Bay Side School:
- Mean: 65.5
- Median: 82
- Seaside School:
- Mean: 40.0
- Median: 36

### Part B: Calculate the measures of variability

To measure the spread or variability, we calculate the standard deviation for each school.

Standard Deviation (SD):
1. Bay Side School:
- SD: 27.97

2. Seaside School:
- SD: 14.31

Summary of Part B:
- Bay Side School SD: 27.97
- Seaside School SD: 14.31

### Part C: Choosing the school with smaller class size

When comparing which school is better for smaller class sizes, it's essential to compare their means and the variability.

- The mean class size for Seaside School is 40.0, which is significantly smaller than Bay Side School’s mean class size of 65.5.
- Additionally, Seaside School’s standard deviation of 14.31 indicates that the class sizes are more consistent and vary less from the mean compared to Bay Side School’s standard deviation of 27.97.

Based on these factors, Seaside School is the better choice for smaller and more consistent class sizes.

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