Answer:
A. Bay Side: mean = 17.1, median = 16; Seaside: mean = 19.5, median = 18
B. Bay Side: σ = 8.96, IQR = 12, range = 37; Seaside: σ = 9.03, IQR = 16, range = 31
C. Bay Side has lower center values and less variation.
Explanation:
Given stem and leaf plots for 15 class sizes at each of two schools, you want to know (a) their measures of center, (b) their measures of variation, and (c) which would be preferred for lower class size.
A. Center
The first attachment shows the statistics for Bay Side School. It tells you the measures of center for Bay Side are ...
The second attachment shows the statistics for Seaside School. The measures of center there are ...
We note the measures of center indicate smaller classes at Bay Side.
B. Variation
For Bay Side School, the measures of variation are ...
- Standard deviation: 8.96
- IQR: 22 -10 = 12
- Range: 42 -5 = 37; with outlier removed, 25 -5 = 20
For Seaside School, the measures of variation are ...
- Standard deviation: 9.03
- IQR = 27 -11 = 16
- Range: 36 -5 = 31
The measures of variation are generally smaller for Bay Side.
C. Smaller Classes
The measures of center and the measures of variation both favor Bay Side School as the school of choice for smaller classes.
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Additional comment
The arithmetic for these descriptive statistics can be tedious and error-prone. It is convenient to let a calculator do it. The lists of data points are given as L1 and L2 for the calculator screens attached. L1 is Bay Side data, and the result of the 1-Var Stats calculation is shown in the first attachment. Seaside data was put in L2, which was used for the calculations shown in the second attachment.
The Q1 and Q3 data values are the 4th lowest and 4th highest data values in each of the lists. The median is the 8th data value, counted from either end.
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