Data Analysis and Z-Scores Quiz

What is the calculation for the mean given that the total is 139.9 and the number of values is 17?

Which of the following represents the mode in the provided dataset?

What is the standard deviation based on the variance of 0.581?

What is the value of P25 given the data provided and using the formula P25 = 75 + 0.75 * (85 - 75)?

What is the z-score for a value of 214 mg/dL, given a mean of 182 and a standard deviation of 44.2?

Data Analysis and Statistics

Mean: 8.23 for a data set of 17 values
Median: 9 for the same data set
Mode: 8.9 for the same data set
Range: 2.1 (calculated as 9.1 - 7.0)
Variance: 0.581
Standard Deviation: 0.76 (calculated from the variance)
Mean: 6630, 112 for different data sets

Calculating Z-Scores

Formula: z = (X - μ) / σ (where X is the value, μ is the mean, and σ is the standard deviation)
Example Calculation (for Z-score for 214mg/dL):
- z = (214 - 182) / 32 = 102/32 = 0.72 (rounded)
Calculation Showing Negative Z-Score: z= (102) / (-1.58)= -1.58
Another calculation: 214mg/dL, with mean 182mg/dL and standard deviation= 32 = (214-182)/32 =102/32 = 3.10

Weighted Average

Three weights and the associated scores determine Alan's final course grade -Tests: weighted 4x15% -Alan's scores: 80, 78, 92, 84 -Term paper: weighted 20% - score: 84 -Final exam: weighted 20% -score: 88
Formula: (Tests total x 0.15) + (Term paper x 0.20) + (Final exam x 0.20)
Weighted average: 84.5
Alan's final course grade was calculated based on the above weights and scores.

Percentiles and Quartiles

P25 (25th percentile) calculation: 75 + 0.75 * (85 - 75) = 82.5
D5 (Median): 75
D9 (90th percentile) calculation:116 + 0.9 * (132 - 116) = 129.8

Test your understanding of data analysis concepts including mean, median, mode, range, variance, standard deviation, and the calculation of Z-scores. This quiz also covers the application of weighted averages in determining final grades. Prepare to apply statistical methods to various data sets and interpret the results accurately.