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

[tex]\[
\begin{array}{r|l|l}
\text{Riverside School} & & \text{South Lake School} \\
\hline
9,6,5 & 0 & 5,8 \\
7,6,5,4,2,0 & 1 & 0,1,2,6,6,8 \\
5,3,2,0,0 & 2 & 5,5,6,7,8 \\
& 3 & 0,6 \\
2 & 4 & \\
\end{array}
\][/tex]

Key: [tex]\(2|1|0\)[/tex] means 12 for Riverside and 10 for South Lake.

Part A: Calculate the measures of center. Show all work. (5 points)

Part B: Calculate the measures of variability. Show all work. (5 points)

Part C: If you are interested in a smaller class size, which school is a better choice?

Sagot :

GinnyAnswer
Certainly! Let's go through the problem step by step, calculating the necessary statistics for each school.

### Part A: Measures of Center (5 points)

To find the measures of center, we'll calculate the mean and median for the class sizes at each school.

#### Riverside School:

1. Data: [9, 6, 5, 17, 16, 15, 14, 12, 10, 25, 23, 22, 20, 20, 42]

2. Mean:
Mean is calculated by summing all the values and dividing by the number of values.
[tex]\[ \text{Mean} = \frac{9 + 6 + 5 + 17 + 16 + 15 + 14 + 12 + 10 + 25 + 23 + 22 + 20 + 20 + 42}{15} \][/tex]
[tex]\[ \text{Mean} \approx 17.07 \][/tex]

3. Median:
The median is the middle value in the ordered list. Ordering the data: [5, 6, 9, 10, 12, 14, 15, 16, 17, 20, 20, 22, 23, 25, 42]
The middle value (8th value in the list):
[tex]\[ \text{Median} = 16 \][/tex]

#### South Lake School:

1. Data: [5, 8, 10, 11, 12, 16, 16, 18, 25, 25, 26, 27, 28, 30, 36]

2. Mean:
[tex]\[ \text{Mean} = \frac{5 + 8 + 10 + 11 + 12 + 16 + 16 + 18 + 25 + 25 + 26 + 27 + 28 + 30 + 36}{15} \][/tex]
[tex]\[ \text{Mean} \approx 19.53 \][/tex]

3. Median:
Ordering the data: [5, 8, 10, 11, 12, 16, 16, 18, 25, 25, 26, 27, 28, 30, 36]
The middle value (8th value in the list):
[tex]\[ \text{Median} = 18 \][/tex]

### Part B: Measures of Variability (5 points)

#### Riverside School:

1. Standard Deviation:
[tex]\[ \text{Standard Deviation} \approx 8.89 \][/tex]

#### South Lake School:

1. Standard Deviation:
[tex]\[ \text{Standard Deviation} \approx 8.95 \][/tex]

### Part C: School Choice Based on Smaller Class Size

To determine which school is better for smaller class sizes, we compare the median and mean values.

- Mean:
- Riverside: 17.07
- South Lake: 19.53
- Median:
- Riverside: 16
- South Lake: 18

Both the mean and median class sizes are smaller at Riverside School (17.07 mean vs 19.53 mean and 16 median vs 18 median).

Therefore, if you are interested in a smaller class size, Riverside School is a better choice.
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