Statistics Problems
1. Indicate whether the following variables are categorical or quantitative:
1 Favorite food.
2 Favorite profession.
3 Number of goals scored by your favorite team last season.
4 Number of students at your school.
5 The eye color of your classmates.
6 IQ of your classmates
2. Indicate whether the following variables are discrete or continuous:
1 Number stocks sold every day in the stock exchange.
2Hourly temperatures recorded at an observatory.
3 Lifetime of a car.
4 The diameter of the wheels of several cars.
5 Number of children from 50 families.
6 Annual Census of Americans.
3. Classify the following variables as categorical, quantitative discrete or continuous.
1 The nationality of a person.
2 Number of liters of water contained in a tank.
3 Number of books on a library shelf.
4 Sum of points tallied from a set of dice.
5 The profession of a person.
6 The area of the different tiles on a building.
4. The marks obtained by a group of students in a test are:
15, 20, 15, 18, 22, 13, 13, 16, 15, 19, 18, 15, 16, 20, 16, 15, 18, 16, 14, 13.
Construct a frequency distribution table for the data and draw the corresponding frequency polygon.
5. Given 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 a frequency distribution table for the data and draw the corresponding bar chart.
6. Given the following series:
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 a frequency distribution table for the data and draw the corresponding bar chart.
7. The weights of 65 children are represented by the following table:
Weight | [50, 60) | [60, 70) | [70, 80) | [80,90) | [90, 100) | [100, 110) | [110, 120) |
f_{i} | 8 | 10 | 16 | 14 | 10 | 5 | 2 |
1 Construct the frequency table.
2 Plot the histogram and frequency polygon.
8. 40 students in a class have obtained the following test scores out of 50.
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.
9. Given the statistical distribution of the table.
x_{i } | 61 | 64 | 67 | 70 | 73 |
f_{i} | 5 | 18 | 42 | 27 | 8 |
Calculate:
2 The range, average deviation, variance and standard deviation.
10.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.
11 Find the variance and standard deviation for the following data series:
12, 6, 7, 3, 15, 10, 18, 5.
12 Find the mean, median and mode for the following set of numbers:
3, 5, 2, 6, 5, 9, 5, 2, 8, 6.
13. Find the average deviation, variance and standard deviation for the following series of numbers:
2, 3, 6, 8, 11.
12, 6, 7, 3, 15, 10, 18, 5.
14 The test results from a group of employees from a factory are represented in the following table:
f_{i} | |
[38, 44) | 7 |
[44, 50) | 8 |
[50, 56) | 15 |
[56, 62) | 25 |
[62, 68) | 18 |
[68, 74) | 9 |
[74, 80) | 6 |
Draw the histogram and the cumulative frequency polygon.
15. Given the series:
3, 5, 2, 7, 6, 4, 9.
3, 5, 2, 7, 6, 4, 9, 1.
Calculate:
The mode, median and mean.
The average deviation, variance and standard deviation.
The quartiles 1 and 3.
The deciles 2 and 7.
The percentiles 32 and 85.
16. A statistical distribution is given by the following table:
[10, 15) | [15, 20) | [20, 25) | [25, 30) | [30, 35) | |
f_{i} | 3 | 5 | 7 | 4 | 2 |
Calculate:
The mode, median and mean.
The range, average deviation and variance.
The quartiles 1 and 3.
The deciles 3 and 6.
The percentiles 30 and 70.
17. Given the statistical distribution:
[0, 5) | [5, 10) | [10, 15) | [15, 20) | [20, 25) | [25, ∞) | |
f_{i} | 3 | 5 | 7 | 8 | 2 | 6 |
Calculate the mode.