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

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

Key: 2|1|0 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 go through the problem step by step.

### Part A: Calculate the measures of center (mean and median)

#### Bay Side School
Bay Side class sizes: [tex]\(8, 6, 5, 18, 16, 15, 14, 12, 10, 25, 23, 22, 20, 20, 42\)[/tex].

Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} = \frac{8 + 6 + 5 + 18 + 16 + 15 + 14 + 12 + 10 + 25 + 23 + 22 + 20 + 20 + 42}{15} = 17.07 \][/tex]

Median:
Arrange the data in ascending order: [tex]\(5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 20, 22, 23, 25, 42\)[/tex]. As there are 15 data points, the median will be the 8th data point:
[tex]\[ \text{Median} = 16.0 \][/tex]

#### Seaside School
Seaside class sizes: [tex]\(5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36\)[/tex].

Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} = \frac{5 + 8 + 10 + 11 + 12 + 15 + 16 + 18 + 25 + 25 + 27 + 27 + 28 + 30 + 36}{15} = 19.53 \][/tex]

Median:
Arrange the data in ascending order: [tex]\(5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36\)[/tex]. As there are 15 data points, the median will be the 8th data point:
[tex]\[ \text{Median} = 18.0 \][/tex]

### Part B: Calculate the measures of variability (standard deviation and range)

#### Bay Side School
Standard Deviation:
[tex]\[ \text{Standard Deviation} = 8.96 \][/tex]

Range:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 42 - 5 = 37 \][/tex]

#### Seaside School
Standard Deviation:
[tex]\[ \text{Standard Deviation} = 9.03 \][/tex]

Range:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 36 - 5 = 31 \][/tex]

### Part C: School choice for smaller class size

If you are interested in smaller class sizes, you should consider the mean class size of each school. A lower mean value indicates smaller average class sizes.

Bay Side School:
Mean = 17.07

Seaside School:
Mean = 19.53

Better choice:
Since [tex]\( 17.07 < 19.53 \)[/tex], the better choice for smaller class sizes is Bay Side School.
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