VARIANCE AND STANDARD DEVIATION Statistics

Statistics

1. MEASURES OF VARIABILITY/DISPERSION VARIANCE & STANDARD DEVIATION

2. STANDARD DEVIATION Standard deviation is also a measure of how spread out a set of data from their mean or average value. It is calculated by finding the square root of the variance. VARIANCE Variance is a measure of how spread out a set of data from their mean or average value. Also known as squared deviation. It is calculated by finding the average of the squared differences between each data point and the mean. DEFIN ITION

3. GROUPED DATA Grouped data is a set of data that has been organized into intervals or classes. To calculate variance and standard deviation for grouped data, we use formulas that involve finding the midpoint of each interval and the frequency of data points within each interval. This process is more efficient than for ungrouped data. UNGROUPED DATA Ungrouped data is a set of raw data without any organization. To calculate variance and standard deviation for ungrouped data, we use formulas that involve finding the mean and the difference between each data point and the mean. This process can be time- consuming for large datasets. DEFIN ITION

4. UNGROUPED DATA

5. VARIANCE FORM ULA STANDARD DEVIATION N N N N

6. = (22 + 24 + 21 + 21 + 25 + 26 + 22)/7 A dataset of temperature in degree Celsius (°C) was recorded for a period of seven days: Monday - 22°C, Tuesday - 24°C, Wednesday - 21°C, Thursday - 21°C, Friday - 25°C, Saturday - 26°C, Sunday - 22°C. Find the average temperature, variance, and standard deviation. EXAMPLE: Variance Standard Deviation = 7 = 23°C

7. A dataset of temperature in degree Celsius (°C) was recorded for a period of seven days: Monday - 22°C, Tuesday - 24°C, Wednesday - 21°C, Thursday - 21°C, Friday - 25°C, Saturday - 26°C, Sunday - 22°C EXAMPLE: TEMPERATURE (°C) 22 23 -1 1 24 23 1 1 21 23 -2 4 21 23 -2 4 25 23 2 4 26 23 3 9 22 23 -1 1 24

8. A dataset of temperature in degree Celsius (°C) was recorded for a period of seven days: Monday - 22°C, Tuesday - 24°C, Wednesday - 21°C, Thursday - 21°C, Friday - 25°C, Saturday - 26°C, Sunday - 22°C EXAMPLE: = 24 / (7-1) = 4   = 4   = 2 °C Variance Standard Deviation

9. GROUPED DATA

10. STANDARD DEVIATION VARIANCE FORM ULA N N N N

11. A dataset of temperature in degree Celsius (°C) was recorded for a period of a month. Find the average temperature, variance, and standard deviation. EXAMPLE: CLASS (°C) FREQUENCY ( f) 20-21 3 22-23 6 24-25 8 26-27 9 28-29 4

12. A dataset of temperature in degree Celsius (°C) was recorded for a period of a month. Find the average temperature in a year, variance, and standard deviation. EXAMPLE: CLASS (°C) FREQUENCY ( f) MIDPOINT (m) f (m) 20-21 3 20.5 61.5 22-23 6 22.5 135 24-25 8 24.5 196 26-27 9 26.5 238.5 28-29 4 28.5 114 ∑ f 30 ∑ f m 745 = ∑ f m / ∑ f = 745 / 30 = 24.83

13. A dataset of temperature in degree Celsius (°C) was recorded for a period of a month. Find the average temperature in a year, variance, and standard deviation. EXAMPLE: CLASS (°C) FREQUENCY ( f) MIDPOINT (m) 20-21 3 20.5 24.83 -4.33 18.7489 56.2467 22-23 6 22.5 24.83 -2.33 5.4289 32.5734 24-25 8 24.5 24.83 -0.33 0.1089 0.8712 26-27 9 26.5 24.83 1.67 2.7889 25.1001 28-29 4 28.5 24.83 3.67 13.4689 53.8756 ∑ f 30 168.667 n = ∑ f = 30

14. A dataset of temperature in degree Celsius (°C) was recorded for a period of a month. Find the average temperature in a year, variance, and standard deviation. EXAMPLE: Variance Standard Deviation = 168.667 / (30-1) = 5.82   = 5.82   = 2.41 °C