CompTIA Data+ Exam DAO-001 - Lesson 9: Applying Descriptive Statistical Methods

Use Measures of Central Tendency

• Mean: The average of a set of numbers.
• Median: The middle number in a sorted set of numbers.
• Mode: The number that appears most frequently in a data set.

Mean Calculation

• The mean is calculated by adding all values together, counting the number of values, and dividing the sum by that number.

Median Determination

• The median is the middle value in an ordered set of numbers.

Mode Identification

• The mode is the value that shows up most frequently in a set of numbers.
• If two or more values appear an equal number of times, you have multiple modes.

Measures of Dispersion

• Min: The smallest number in the data set.
• Max: The largest number in the data set.
• Range: The difference between the highest and lowest values.
• Variance: The average squared distance from the mean of the data for a single data point.
• Standard Deviation: Shows how dispersed the data is in relation to the mean of all the data.
  • Formula for Standard Deviation Calculation: $\sqrt{\frac{\Sigma(x-\bar{x})^2}{n-1}}$, where $\bar{x}$ is the mean.
• Z-scores: Show how many standard deviations a data point is from the mean.

Standard Deviation - Step-by-Step Calculation

1. Calculate the mean of the data set.
2. For each value, subtract the mean (Score - 81).
3. Square the result of each subtraction $((\text{Score} - \text{Mean})^2)$.
4. Sum up all the squared differences $\Sigma(x-\bar{x})^2$.
5. Divide by $n-1$ (where n is the number of values) to get the variance: $\frac{\Sigma(x-\bar{x})^2}{n-1}$.
6. Take the square root of the variance to find the standard deviation.

Z-Scores

• Z-scores indicate how many standard deviations away a value lies from the mean.
• The STANDARDIZE function in Excel can be used to calculate Z-scores.

Distribution of a Data Set

• Center: Mean, median, and mode.
• Outermost Values: Range.
• Deviation: Standard deviation.
• Position: Z-score.

Normal Distribution (Bell Curve)

• 68.26% of data falls within one standard deviation of the mean.
• 95.44% of data falls within two standard deviations of the mean.
• 99.74% of data falls within three standard deviations of the mean.

Skewed Distribution

• Skewed Left: The mean is less than the median and mode.
• Skewed Right: The mean is greater than the median and mode.

Frequencies and Percentages

• Frequency: The count of how often each value occurs.
• Pivot tables and histograms are used to display frequency data.

Percentage Difference

• Expresses the difference between two data sets.

Percentage Change

• Calculated as: $\frac{{\text{New Value} - \text{Last Value}}}{{\text{Last Value}}} \times 100\%$.

Exam Review

• Outliers are values in the data set that don’t seem to be within the norm of all the other data.
• Calculation that involves finding the highest (maximum) value and the lowest (minimum) value is the range.
• x-\bar is the x-bar representative of in the calculation for standard deviation.
• The empirical rule is following a bell shape curve, with the mean being the middle and all other data following three points to the left or three points to the right of the mean.