Descriptive Statistics for Quantitative Data

Descriptive Statistics for Quantitative Data

• Descriptive statistics is a way to summarize and describe a data set using brief descriptive coefficients.
• It is used to provide a visual summary of data.
• Prior to gathering data, it is essential to identify the level of measurement of the quantitative data and determine the kind of descriptive statistics to be performed.

Measures of Central Tendency

• Measures of central tendency describe the center position of a distribution for a data set.
• The three types of measures of central tendency are:
  • Mean: the average of the numbers, used if the level of measurement is interval or ratio.
  • Median: the middle value of the data, used if the level of measurement is ordinal.
  • Mode: the data that appears most often, used if the level of measurement is nominal.

Measures of Variability

• Measures of variability describe the spread of scores in a set of data.
• The three types of measures of variability are:
  • Standard deviation: represents the measure of how spread out the scores are, and can be obtained using the formula: σ = √(Σ(X-μ)^2 / N)
  • Sample variance: shows how varied a sample is, and is the square of the standard deviation.
  • Range: the difference between the highest and lowest score of the data.

Distribution of the Data

• Skewness refers to the distortion or asymmetry in a symmetrical bell curve.
• Kurtosis refers to the sharpness of the peak of a distribution.
• A distribution can be:
  • Positively skewed: most of the data are clustered to the left side of the distribution.
  • Negatively skewed: most of the data are clustered to the right side of the distribution.
  • Moderately skewed: skewness is between -1 and -0.5 or between 0.5 and 1.
  • Approximately symmetric: skewness is between -0.5 and 0.5.
  • Perfectly symmetrical: skewness is 0.
  • Mesokurtic: kurtosis is between -1 and 1.
  • Leptokurtic: kurtosis is greater than 1.
  • Platykurtic: kurtosis is less than -1.

Other Descriptive Statistics

• Minimum value: the smallest value in a set of data.
• Maximum value: the largest value in a set of data.
• Sum: the value when all the values of the data are added.
• Count: the number of data.
• Kth largest value: the highest kth number of the data.
• Kth smallest value: the lowest kth number of the data.
• Confidence level: the suitable interval above and below the mean to estimate the population mean with a specified confidence level.

Using Microsoft Excel for Descriptive Statistics

• To perform descriptive statistics in Microsoft Excel, follow these steps:
  1. Enter the data on the spreadsheet.
  2. Under the Data ribbon, click "Data Analysis."
  3. Click "Descriptive Statistics" and press "OK."
  4. Under the input range, highlight the cells that contain the data.
  5. Tick the checkbox under "Summary statistics" and set it to 95%.
  6. Tick the checkboxes under Confidence Level of the Mean, Kth Largest, and Kth Smallest.
  7. Press "OK."