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

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

Key: [tex]$2|1|0$[/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)

Sagot :

GinnyAnsweridn
Sure, let's work through this step-by-step.

### Part A: Calculate the measures of center
To find the measures of center, we'll calculate the mean and median for both schools.

#### Mean
The mean is the average of the data set. It can be found using the formula:
[tex]\[ \text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} \][/tex]

1. Bay Side School:
- Data: 8, 6, 5, 18, 16, 15, 14, 12, 10, 25, 23, 22, 20, 20, 3
- Sum of data points: [tex]\( 8 + 6 + 5 + 18 + 16 + 15 + 14 + 12 + 10 + 25 + 23 + 22 + 20 + 20 + 3 = 217 \)[/tex]
- Number of data points: 15
- Mean: [tex]\( \frac{217}{15} = 14.467 \)[/tex]

2. Seaside School:
- Data: 5, 18, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 0, 6
- Sum of data points: [tex]\( 5 + 18 + 10 + 11 + 12 + 15 + 16 + 18 + 25 + 25 + 27 + 27 + 28 + 0 + 6 = 243 \)[/tex]
- Number of data points: 15
- Mean: [tex]\( \frac{243}{15} = 16.2 \)[/tex]

#### Median
The median is the middle value when the data set is ordered from smallest to largest. If the number of data points is odd, it's the center point; if even, it's the average of the two center points.

1. Bay Side School:
- Ordered data: 3, 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 20, 22, 23, 25
- Number of data points: 15 (odd)
- Median: 15 (8th value)

2. Seaside School:
- Ordered data: 0, 5, 6, 10, 11, 12, 15, 16, 18, 18, 25, 25, 27, 27, 28
- Number of data points: 15 (odd)
- Median: 16 (8th value)

### Part B: Calculate the measures of variability
To find the measures of variability, we'll calculate the standard deviation for both schools.

1. Bay Side School:
- Given standard deviation: 6.722

2. Seaside School:
- Given standard deviation: 8.604

### Part C: School with the smaller class size
If you're interested in a smaller class size, compare the mean class sizes of the two schools. The mean class size is lower in Bay Side School (14.467) compared to Seaside School (16.2). Therefore, Bay Side School is the better choice if you prefer a smaller class size.

Explanation:
Bay Side School has a mean class size of 14.467, which is smaller than Seaside School's mean class size of 16.2. This indicates that, on average, classes at Bay Side School are smaller. Therefore, if you're looking for smaller class sizes, Bay Side School is the better choice.
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