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

\begin{tabular}{r|l|l}
Mountain View School & & Bay Side School \\
\hline
& 0 & [tex]$5,6,8$[/tex] \\
[tex]$9,8,2,0$[/tex] & 1 & [tex]$0,2,4,5,6,8$[/tex] \\
[tex]$8,7,6,5,5,4,4,3,1,0$[/tex] & 2 & [tex]$0,0,2,3,5$[/tex] \\
0 & 3 & \\
& 4 & 2 \\
\end{tabular}

Key: [tex]$2|1|0$[/tex] means 12 for Mountain View and 10 for Bay Side.

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 larger class size, which school is a better choice for you? Explain your reasoning. (1 point)

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Part A:
First, I wrote out all the numbers.

For Mountain View School, I wrote: [tex]$19,18,12,10,20,21,23,24,24,25,25,26,2$[/tex].

For Bay Side School, I wrote: [tex]$5,6,8,10,12,14,15,16,18,20,20,22,23,25,42$[/tex].

Then I found the mean. To find the mean, I added up all the numbers and divided them by however many numbers there are.

For Mountain View, I got 18.92. For Bay Side School, I got 16.

For the median, I found the middle value when the numbers were listed in order.

For Mountain View, the median is 21. For Bay Side School, the median is 16.

(Note: The above mean and median calculations are just examples and may need to be rechecked for accuracy based on the data provided.)

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Part B:
To calculate the measures of variability, such as range and standard deviation, show your work here.

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Part C:
If you are interested in a larger class size, Bay Side School is a better choice because it has a higher mean class size and a higher maximum value of 42.

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Please ensure your calculations are accurate and complete.



Answer :

GinnyAnswer
### Part A: Measures of Center
1. Mean:
- To find the mean, add up all the values and divide by the number of values.

Mountain View School:
The class sizes are: 19, 18, 12, 10, 20, 21, 23, 24, 24, 25, 25, 26, 2.
Mean = [tex]\( \frac{19 + 18 + 12 + 10 + 20 + 21 + 23 + 24 + 24 + 25 + 25 + 26 + 2}{13} \approx 19.15 \)[/tex].

Bay Side School:
The class sizes are: 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 20, 22, 23, 25, 42.
Mean = [tex]\( \frac{5 + 6 + 8 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 20 + 22 + 23 + 25 + 42}{15} \approx 17.07 \)[/tex].

2. Median:
- To find the median, arrange the numbers in order and find the middle value.

Mountain View School:
Sorted class sizes: 2, 10, 12, 18, 19, 20, 21, 23, 24, 24, 25, 25, 26.
Since there are 13 numbers, the median is the 7th value.
Median = 21.

Bay Side School:
Sorted class sizes: 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 20, 22, 23, 25, 42.
Since there are 15 numbers, the median is the 8th value.
Median = 16.

### Part B: Measures of Variability
1. Range:
- The range is the difference between the maximum and minimum values.

Mountain View School:
Range = 26 - 2 = 24.

Bay Side School:
Range = 42 - 5 = 37.

2. Standard Deviation:
- The standard deviation measures how spread out the numbers are.

Mountain View School:
Standard Deviation ≈ 6.86

Bay Side School:
Standard Deviation ≈ 8.96

### Part C: Decision for Larger Class Size
If you are interested in a larger class size, Mountain View School would be a better choice. This conclusion is based on the mean class sizes, where Mountain View School has a higher mean (19.15) compared to Bay Side School (17.07). The higher average indicates that on average, the class sizes in Mountain View School are larger.

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