Statistics in Swim Teams

Study Notes

Swim Team Ages

Mean ages with standard deviations indicate dispersion of ages within each swim team.
Most likely assertion regarding dispersion among teams is "The ages of the Dolphins are not the most dispersed," implying a comparison where Dolphins do not have the highest variation.

Z-Score Interpretation

A z-score measures how many standard deviations a data point is from the mean.
For a data point with a mean of 12 and a standard deviation of 3, a z-score of 1.3 means the data point is 1.3 standard deviations above the mean (not from 3).

Variance Calculation

To calculate variance, the equation incorporates the deviation of each value from the mean.
For Fiona's bike miles (4, 7, 4, 10, 5) with a mean of 6, the focused formula for variance would be derived based on these distances.

Standard Deviation Errors

When calculating standard deviation, substituting n for n - 1 incorrectly affects the result as it underestimates variability.
Yuri's mistake was using n instead of n - 1 when finding the standard deviation from the dataset 12, 14, 9, and 21, where the mean was calculated as 14.

Standard Deviation of Car Sales

The standard deviation of the dataset representing cars sold (14, 23, 31, 29, 33) is calculated to be 6.9, reflecting the spread of sales figures.

Voter Age Analysis

For a computed mean (u) of 6 and a standard deviation (o) of 5, a z-score of 1.14 corresponds to a voter age estimate of 71 when rounded to the nearest whole number.

Missing Data Value Calculation

A z-score of -2.1, given a mean of 43 and standard deviation of 2, indicates a missing data value of 39 when calculated and rounded.

Comparing Test Scores

Mrs. Rodrigues should utilize standard deviation as the statistic to compare the spread of test scores across her two biology classes, as it provides an insight into variability.

Standard Deviation Formula for Sample Data

The first formula outlined is the standard formula for calculating standard deviation in sample data sets, critical for accurately measuring dispersion.

Variance Calculation for Test Scores

For the geometry class test scores (90, 75, 72, 88, 85), the numerator of the variance calculation yields a total of 258, quantifying the sum of squared deviations from the mean.

Description

This quiz explores the concepts of mean and standard deviation as applied to the age distributions of four different swim teams. Participants will analyze which team's ages are most dispersed based on provided data. Test your understanding of statistical measures in a real-world context.