LECTURE 4 Flashcards
What is central tendency?
A single value representing a group of data, summarizing the dataset.
What are the two types of averages?
- Simple Averages: Mean, Median, Mode 2. Special Averages: Geometric Mean, Harmonic Mean.
What is the arithmetic mean (mean)?
The sum of all observations divided by the number of observations.
What is the formula for mean for raw data?
Mean = Sum of observations ÷ Number of observations.
What is the formula for mean for grouped data?
Mean = (Σ(f × x)) ÷ n.
What is the shortcut formula for mean?
Mean = A + (Σ(f × d)) ÷ n.
What are the merits of arithmetic mean?
- Simple to calculate 2. Rigidly defined 3. Reliable for large datasets 4. Basis for comparison.
What are the demerits of arithmetic mean?
- Sensitive to extreme values 2. Not suitable for qualitative data 3. Cannot handle open-end classes.
What is the median?
The middle value in an ordered dataset.
How is the median calculated for raw data?
- If n is odd: Median = Middle value. 2. If n is even: Median = Mean of two middle values.
How is the median calculated for grouped data?
- Find cumulative frequency. 2. Identify the median class. 3. Use the formula: Median = l + [(n/2 - m)/f] × c.
What are the merits of median?
- Not influenced by extreme values 2. Handles open-end intervals 3. Useful for incomplete data.
What are the demerits of median?
- Affected by small changes in data 2. Not suitable for advanced calculations 3. Ignores other observations.
What is the mode?
The value that occurs most frequently in a dataset.
How is mode calculated for grouped data?
- Identify the modal class. 2. Use the formula: Mode = l + [(fm - fp) / (2fm - fp - fs)] × c.
What are the merits of mode?
- Represents the most typical value 2. Useful for qualitative data 3. Simple to understand.
What are the demerits of mode?
- May not exist 2. May have multiple values 3. Not suitable for mathematical analysis.
What is the geometric mean (GM)?
The n-th root of the product of all observations.
What is the formula for GM for grouped data?
GM = Antilog(Σ(f × log x) ÷ n).
What are the uses of GM?
- Growth rates 2. Bacterial growth 3. Economic studies.
What is the harmonic mean (HM)?
The reciprocal of the arithmetic mean of reciprocals of observations.
What is the formula for HM?
HM = n ÷ Σ(1/x).
What are the merits of HM?
- Ideal for rates and speeds 2. Weighted toward smaller values 3. Defined for all observations.
What are the demerits of HM?
- Difficult to compute 2. Rarely used for grouped data 3. Not easily understood.
What are percentiles?
Values dividing a dataset into 100 equal parts, each containing 1% of observations.
What are quartiles?
Values dividing a dataset into 4 equal parts (Q1, Q2, Q3).
How is the 25th percentile (Q1) calculated for grouped data?
Q1 = l + [(n/4 - m)/f] × c.
How is the 75th percentile (Q3) calculated for grouped data?
Q3 = l + [(3n/4 - m)/f] × c.
What are the steps to calculate quartiles for grouped data?
- Find cumulative frequency. 2. Identify Q1 and Q3 classes. 3. Use respective formulas.
What is the difference between mean, median, and mode?
Mean: Arithmetic average. Median: Middle value. Mode: Most frequent value.
Define central tendency with examples.
A central value summarizing data, e.g., mean, median, mode.
The middle value of an ordered series is called what?
2nd quartile, 5th decile, or 50th percentile.
For a set of values, the mode can be what?
Unimodal, bimodal, or trimodal.
Is mode suitable for qualitative data?
Yes, it is suitable.
What does deciles divide the group into?
Ten equal parts.
Is the mean affected by extreme values?
Yes, it is affected.
Can geometric mean be calculated for negative values?
No, it cannot.
What type of data is mode used for?
Both qualitative and quantitative data.
How do you calculate arithmetic mean for raw data?
Sum all values and divide by the number of observations.
How do you calculate the median for grouped data?
Find cumulative frequencies and use the median formula.
How do you calculate the mode for grouped data?
Use the modal class and the mode formula.
