Statistical Variables and Data Analysis Exercises

Posted on Jan 16, 2025 in Statistics

Exercise 1: Identifying Qualitative and Quantitative Variables

Indicate which variables are qualitative and which are quantitative:

1. Favorite Food (Qualitative)
2. Profession you like (Qualitative)
3. Number of goals scored by your favorite team last season (Quantitative)
4. Number of students in your Institute (Quantitative)
5. The eye color of your classmates (Qualitative)
6. IQ of your classmates (Quantitative)

Exercise 2: Identifying Discrete and Continuous Variables

Indicate which variables are discrete and which are continuous:

1. Number of shares sold each day in the stock market (Discrete)
2. Temperatures recorded each hour by an observatory (Continuous)
3. Term of a car loan (Continuous)
4. The diameter of the wheels of several cars (Continuous)
5. Number of children of 50 families (Discrete)
6. Annual census of the Spanish population (Discrete)

Exercise 3: Classifying Variables

Sort the following qualitative and quantitative variables into discrete or continuous:

1. The nationality of a person (Qualitative)
2. Number of gallons of water contained in a tank (Continuous)
3. Number of books on a library shelf (Discrete)
4. Sum of points obtained from the roll of a pair of dice (Discrete)
5. The occupation of a person (Qualitative)
6. The area of the different tiles of a building (Continuous)

Exercise 4: Frequency Distribution and Polygon

The scores obtained by a test group were: 15, 20, 15, 18, 22, 13, 13, 16, 15, 19, 18, 15, 16, 20, 16, 15, 18, 16, 14, 13.

Construct the frequency distribution table and draw the frequency polygon.

Exercise 5: Frequency Distribution and Diagram

The number of stars of hotels in a city is given by the following series: 3, 3, 4, 3, 4, 3, 1, 3, 4, 3, 3, 3, 2, 1, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1, 2, 2, 4, 1.

Construct the frequency distribution table and draw the diagram.

Exercise 6: Frequency Distribution and Diagram

The scores of 50 students in mathematics were as follows: 5, 2, 4, 9, 7, 4, 5, 6, 5, 7, 7, 5, 5, 2, 10, 5, 6, 5, 4, 5, 8, 8, 4, 0, 8, 4, 8, 6, 6, 3, 6, 7, 6, 6, 7, 6, 7, 3, 5, 6, 9, 6, 1, 4, 6, 3, 5, 5, 6, 7.

Construct the frequency distribution table and draw the diagram.

Exercise 7: Frequency Table, Histogram, and Polygon

The weights of the 65 employees of a factory are given by the following table:

1. Construct the frequency table.
2. Show the histogram and frequency polygon.

Exercise 8: Frequency Table, Histogram, and Polygon

The 40 students in a class have achieved the following scores out of 50 on a physical examination: 3, 15, 24, 28, 33, 35, 38, 42, 23, 38, 36, 34, 29, 25, 17, 7, 34, 36, 39, 44, 31, 26, 20, 11, 13, 22, 27, 47, 39, 37, 34, 32, 35, 28, 38, 41, 48, 15, 32, 13.

1. Construct the frequency table.
2. Draw the histogram and frequency polygon.

Exercise 9: Statistical Measures

A statistical distribution is given by the following table:

Calculate:

1. The mode, median, and mean.
2. The range, standard deviation, variance, and coefficient of variation.

Exercise 10: Mean, Median, and Mode

Calculate the mean, median, and mode for the following set of numbers: 5, 3, 6, 5, 4, 5, 2, 8, 6, 5, 4, 8, 3, 4, 5, 4, 8, 2, 5, 4.

Exercise 11: Variance and Standard Deviation

Find the variance and standard deviation of the following data series: 12, 6, 7, 3, 15, 10, 18, 5.

Exercise 12: Mean, Median, and Mode

Find the mean, median, and mode of the following set of numbers: 3, 5, 2, 6, 5, 9, 5, 2, 8, 6.

Exercise 13: Mean Deviation, Variance, and Standard Deviation

Find the mean deviation, variance, and standard deviation of the series of numbers: 2, 3, 6, 8, 11 and 12, 6, 7, 3, 15, 10, 18, 5.

Exercise 14: Histogram and Cumulative Frequency Polygon

A test has been applied to factory workers, resulting in the following table:

Draw the histogram and cumulative frequency polygon.

Exercise 15: Statistical Measures

Given the statistical series: 3, 5, 2, 7, 6, 4, 9 and 3, 5, 2, 7, 6, 4, 9, 1.

Calculate:

• The mode, median, and mean.
• The mean deviation, variance, and standard deviation.
• Quartiles 1 and 3.
• The deciles 2 and 7.
• 32nd and 85th percentiles.

Exercise 16: Statistical Measures

A statistical distribution is given by the following table:

Find:

• The mode, median, and mean.
• The range, standard deviation, and variance.
• Quartiles 1 and 3.
• The deciles 3 and 6.
• 30th and 70th percentiles.

Exercise 17: Statistical Measures

Given the statistical distribution:

Calculate:

• The median and mode.
• Quartile 2 and 3.
• Mean.