10 Questions
What is the primary advantage of using the median as a measure of central tendency?
It is not affected by outliers, making it a more robust measure.
A dataset has two modes, what is it called?
Bimodal
What is the formula to calculate the mean of a dataset?
Sum of values divided by the number of values
What is the purpose of using a weighted average?
To assign different importance or weights to each value
What is the formula to calculate the average speed?
Total distance divided by total time
What is the unit of average speed?
Distance per unit time
What is the median of the dataset 2, 4, 6, 8, 10?
7
What is the mode of the dataset 1, 2, 2, 3, 4, 4, 4, 5?
4
What is the weighted average of 80 (30% of total), 70 (20% of total), 90 (50% of total)?
84.5
What is the average speed of a car that traveled 360 km in 6 hours?
60 km/h
Study Notes
Averages
Median
- The middle value in a dataset when arranged in order
- If the dataset has an even number of values, the median is the average of the two middle values
- Not affected by outliers, making it a more robust measure than the mean
- Example: Find the median of 1, 3, 5, 7, 9 → Arrange in order: 1, 3, 5, 7, 9 → Median = 5
Mode
- The value that appears most frequently in a dataset
- A dataset can have multiple modes (bimodal, multimodal) or no mode at all
- Example: Find the mode of 1, 2, 2, 3, 4, 4, 4 → Mode = 4 (since it appears most frequently)
Mean
- The sum of all values divided by the number of values
- Also known as the arithmetic mean
- Sensitive to outliers, which can greatly affect the result
- Example: Find the mean of 2, 4, 6, 8, 10 → Sum = 30, Count = 5 → Mean = 30/5 = 6
Weighted Average
- A type of average that assigns different importance or weights to each value
- Used when the values have different significance or frequencies
- Formula: Weighted Average = (Value 1 × Weight 1) + (Value 2 × Weight 2) + ... + (Value n × Weight n) / Total Weight
- Example: Find the weighted average of 80 (30% of total), 70 (20% of total), 90 (50% of total) → Weighted Average = (80 × 0.3) + (70 × 0.2) + (90 × 0.5) / 1 = 84.5
Average Speed
- The total distance traveled divided by the total time taken
- Units: distance per unit time (e.g., km/h, mph, m/s)
- Formula: Average Speed = Total Distance / Total Time
- Example: Find the average speed of a car that traveled 240 km in 4 hours → Average Speed = 240 km / 4 h = 60 km/h
Averages
Median
- Middle value in a dataset when arranged in order, resistant to outliers
- For even-numbered datasets, median is the average of the two middle values
- Median of 1, 3, 5, 7, 9 is 5, since it's the middle value when arranged in order
Mode
- Value that appears most frequently in a dataset
- Can have multiple modes (bimodal, multimodal) or no mode at all
- Mode of 1, 2, 2, 3, 4, 4, 4 is 4, since it appears most frequently
Mean
- Sum of all values divided by the number of values
- Also known as the arithmetic mean
- Sensitive to outliers, which can greatly affect the result
- Mean of 2, 4, 6, 8, 10 is 6, since sum is 30 and count is 5
Weighted Average
- Assigns different importance or weights to each value
- Used when values have different significance or frequencies
- Formula: Weighted Average = (Value 1 × Weight 1) + (Value 2 × Weight 2) +...+ (Value n × Weight n) / Total Weight
- Weighted average of 80 (30% of total), 70 (20% of total), 90 (50% of total) is 84.5
Average Speed
- Total distance traveled divided by the total time taken
- Units: distance per unit time (e.g., km/h, mph, m/s)
- Formula: Average Speed = Total Distance / Total Time
- Average speed of a car that traveled 240 km in 4 hours is 60 km/h
Learn about median, mode, and other measures of central tendency in statistics. Understand how to calculate and interpret these values in datasets.
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