MODULE 2: DESCRIPTIVE STATISTICS AND DATA VISUALIZATION

Descriptive Statistics and Data Visualization

By: Engr. Franz Johann B. De Vera,EngrD

2.1 Measures of Central Tendency

These are values that represent the center or typical value of a dataset:

Mean: The average of a dataset, calculated by summing all values and dividing by the total count.

Example: For the numbers [2, 4, 6, 8], the mean is (2+4+6+8)/4 = 5.

The middle value when the data is ordered. If there's an even number of observations, it's the average of the two middle numbers.

Example: [ 1,2,3,4,6,6,6,7]
MEDIAN: 5

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Median

​The most frequently occurring value(s) in a dataset.

Ex: [ 1,2,3,3,4,4,5]
Mode: 3,4

Mode

2.2 MEASURE OF DISPERSION

The average of the squared differences from the mean. It indicates how much the data varies.

Example: If data points are close to the mean, variance is small.

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VARIANCE

The square root of the variance; it measures the average distance from the mean.

Practice Exercise: Find the standard deviation for [3, 4, 5, 6, 7].

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STANDARD DEVIATION

The difference between the highest and lowest values in a dataset.

Practice Exercise: Determine the range for the dataset [22, 35, 18, 40, 27].

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RANGE

2.3 DATA VISUALIZATION TECHNIQUE

SHOW THE DISTRIBUTION OF DATA OVER INTERVALS

Practice Exercise: Create a histogram for the dataset [5, 7, 8, 9, 10, 10, 12, 14, 15, 15, 15].

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HISTOGRAM

Display the distribution through quartiles and identify outliers.

Practice Exercise: Draw a box plot for the dataset [5, 7, 8, 10, 12, 13, 14, 18, 21, 25, 30].

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BOX PLOT

SHOW RELATIONSHIP BETWEEN TWO VARIABLES

Practice Exercise: Plot a scatter plot using the following data points: X = [1, 2, 3, 4, 5], Y = [2, 4, 6, 8, 10].

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SCATTER PLOT

2.4 IDENTIFYING PATTERN, TREND AND OUTLIERS

Recurring characteristics or trends in the data (e.g., seasonal sales patterns).

Practice Exercise: Identify any patterns in this dataset representing monthly sales over a year: [120, 150, 130, 140, 160, 170, 200, 190, 180, 160, 150, 140]

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PATTERN

Long-term movements or shifts (e.g., increasing revenue over years).

Practice Exercise: Analyze the following revenue data to identify any trends: [1000, 1200, 1500, 1700, 1800, 2100, 2300].

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TRENDS

Open Ended

Short Activity: Descriptive Statistics and Data Visualization

Instructions:

Complete the following tasks using the concepts learned from Module 2. Show your calculations or provide graphs where needed.

Part 1: Central Tendency

1. Calculate the Mean, Median, and Mode of the following dataset:

   • [8, 12, 15, 20, 20, 25, 30, 35, 40, 45]

2. Reflection Question:

   • Which measure best represents the center of this dataset? Why?

Part 2: Measures of Dispersion

1. Calculate the Range, Variance, and Standard Deviation for this dataset:

   • [4, 6, 8, 10, 12, 14, 16, 18, 20, 22]

2. Short Answer:

   • What does the standard deviation tell you about the spread of the data?

Part 3: Data Visualization

1. Create a Histogram for the following scores:

   • [55, 60, 65, 70, 75, 80, 85, 90, 90, 95, 100]

2. Draw a Box Plot to identify any outliers:

   • [5, 7, 8, 10, 12, 13, 14, 18, 21, 25, 50]

3. Plot a Scatter Plot using:

   • X = [1, 2, 3, 4, 5, 6, 7]

   • Y = [2, 4, 6, 8, 10, 12, 14]

Part 4: Identifying Patterns, Trends, and Outliers

1. Identify the trend from the following monthly revenue:

   • [2000, 2200, 2500, 2700, 3000, 3200, 3500]

2. Spot the outlier in this dataset:

   • [15, 16, 17, 18, 19, 100, 20, 21, 22]

Submission:

• Submit your calculations, graphs, and short reflections for evaluation.

• Be ready to discuss your findings in the next class.

Data points significantly different from others; they can indicate errors or rare events

Practice Exercise: Find outliers in the dataset: [10, 12, 13, 14, 50, 15, 16, 17, 18].

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OUTLIER