Assignment 31 To Get The Best Deal On A CD Player Tom Called

Assignment 31to Get The Best Deal On A Cd Player Tom Called Eight

ASSIGNMENT #3: 1. To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $218, $125, $381, $187, $231, $213, $309, $230. Find the standard deviation.

2. When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.

Wendy's: [data not specified]

McDonald's: [data not specified]

A company had 74 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation of the data summarized in the given frequency distribution.

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the standard deviation:

Paper For Above instruction

The calculation of descriptive statistics such as standard deviation, variance, and range is fundamental in understanding the distribution and variability within a dataset in statistics. This paper addresses three specific problems: calculating the standard deviation of given sample data, analyzing the dispersion of service times in fast-food drive-throughs, and assessing variability in employee salaries and basketball players' heights. Each scenario illustrates the application of these statistical measures to real-world data, providing insights that assist in decision-making and performance evaluation.

First, we examine the prices quoted by eight appliance stores for a specific CD player model. The prices listed are $218, $125, $381, $187, $231, $213, $309, and $230. To calculate the standard deviation, we first determine the mean of these prices. Summing the prices yields:

Sum = 218 + 125 + 381 + 187 + 231 + 213 + 309 + 230 = 1894

Mean = Sum / 8 = 1894 / 8 = 236.75

Next, we compute the squared deviations from the mean for each price:

• (218 - 236.75)^2 = (-18.75)^2 = 351.56
• (125 - 236.75)^2 = (-111.75)^2 = 12495.56
• (381 - 236.75)^2 = (144.25)^2 = 20838.06
• (187 - 236.75)^2 = (-49.75)^2 = 2475.06
• (231 - 236.75)^2 = (-5.75)^2 = 33.06
• (213 - 236.75)^2 = (-23.75)^2 = 564.06
• (309 - 236.75)^2 = (72.25)^2 = 5220.56
• (230 - 236.75)^2 = (-6.75)^2 = 45.56

Sum of squared deviations: 351.56 + 12495.56 + 20838.06 + 2475.06 + 33.06 + 564.06 + 5220.56 + 45.56 = 41923.42

Variance = Sum of squared deviations / (n-1) = 41923.42 / 7 ≈ 5990.49

Standard deviation = √Variance ≈ √5990.49 ≈ 77.39

Thus, the standard deviation of the store prices is approximately 77.39 dollars, indicating the variability of the prices around the mean.

Secondly, regarding drive-through service times at fast-food restaurants, the analysis involves calculating the range, variance, and standard deviation for each sample. Although specific data are missing in the assignment prompt, a general approach for these calculations is as follows.

The range is obtained by subtracting the minimum value from the maximum value in the dataset. Variance and standard deviation calculations follow the same steps as above, involving finding the mean, squared deviations, and their average (for variance) adjusted by degrees of freedom (n-1). Comparing these statistics across two samples offers insight into which restaurant has more consistent or variable service times. Generally, a higher standard deviation indicates greater variability in service times, which could affect customer satisfaction and operational efficiency.

Third, in analyzing employee salaries summarized in a frequency distribution, the goal is to compute the standard deviation accounting for the grouped data. This involves calculating the midpoint of each salary interval, multiplying each by the corresponding frequency to find the mean, and then applying the formula for grouped data standard deviation.

Similarly, in the case of basketball players' heights, the grouped data approach is used to estimate the standard deviation. This involves determining the class midpoints, calculating the mean height, and then computing the squared deviations weighted by frequencies.

In conclusion, these statistical measures reveal essential information about data variability and distribution, aiding managers, business analysts, and sports professionals in making informed decisions. Accurate calculation of the standard deviation, variance, and range helps to identify outliers, measure consistency, and compare different data sets effectively, ultimately supporting better strategic planning and operational improvements.

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