LECTURE 4

Question 1

What is central tendency?

Answer 1

A single value representing a group of data, summarizing the dataset.

Question 2

What are the two types of averages?

Answer 2

1. Simple Averages: Mean, Median, Mode 2. Special Averages: Geometric Mean, Harmonic Mean.

Question 3

What is the arithmetic mean (mean)?

Answer 3

The sum of all observations divided by the number of observations.

Question 4

What is the formula for mean for raw data?

Answer 4

Mean = Sum of observations ÷ Number of observations.

Question 5

What is the formula for mean for grouped data?

Answer 5

Mean = (Σ(f × x)) ÷ n.

Question 6

What is the shortcut formula for mean?

Answer 6

Mean = A + (Σ(f × d)) ÷ n.

Question 7

What are the merits of arithmetic mean?

Answer 7

1. Simple to calculate 2. Rigidly defined 3. Reliable for large datasets 4. Basis for comparison.

Question 8

What are the demerits of arithmetic mean?

Answer 8

1. Sensitive to extreme values 2. Not suitable for qualitative data 3. Cannot handle open-end classes.

Question 9

What is the median?

Answer 9

The middle value in an ordered dataset.

Question 10

How is the median calculated for raw data?

Answer 10

1. If n is odd: Median = Middle value. 2. If n is even: Median = Mean of two middle values.

Question 11

How is the median calculated for grouped data?

Answer 11

1. Find cumulative frequency. 2. Identify the median class. 3. Use the formula: Median = l + [(n/2 - m)/f] × c.

Question 12

What are the merits of median?

Answer 12

1. Not influenced by extreme values 2. Handles open-end intervals 3. Useful for incomplete data.

Question 13

What are the demerits of median?

Answer 13

1. Affected by small changes in data 2. Not suitable for advanced calculations 3. Ignores other observations.

Question 14

What is the mode?

Answer 14

The value that occurs most frequently in a dataset.

Question 15

How is mode calculated for grouped data?

Answer 15

1. Identify the modal class. 2. Use the formula: Mode = l + [(fm - fp) / (2fm - fp - fs)] × c.

Question 16

What are the merits of mode?

Answer 16

1. Represents the most typical value 2. Useful for qualitative data 3. Simple to understand.

Question 17

What are the demerits of mode?

Answer 17

1. May not exist 2. May have multiple values 3. Not suitable for mathematical analysis.

Question 18

What is the geometric mean (GM)?

Answer 18

The n-th root of the product of all observations.

Question 19

What is the formula for GM for grouped data?

Answer 19

GM = Antilog(Σ(f × log x) ÷ n).

Question 20

What are the uses of GM?

Answer 20

1. Growth rates 2. Bacterial growth 3. Economic studies.

Question 21

What is the harmonic mean (HM)?

Answer 21

The reciprocal of the arithmetic mean of reciprocals of observations.

Question 22

What is the formula for HM?

Answer 22

HM = n ÷ Σ(1/x).

Question 23

What are the merits of HM?

Answer 23

1. Ideal for rates and speeds 2. Weighted toward smaller values 3. Defined for all observations.

Question 24

What are the demerits of HM?

Answer 24

1. Difficult to compute 2. Rarely used for grouped data 3. Not easily understood.

Question 25

What are percentiles?

Answer 25

Values dividing a dataset into 100 equal parts, each containing 1% of observations.

Question 26

What are quartiles?

Answer 26

Values dividing a dataset into 4 equal parts (Q1, Q2, Q3).

Question 27

How is the 25th percentile (Q1) calculated for grouped data?

Answer 27

Q1 = l + [(n/4 - m)/f] × c.

Question 28

How is the 75th percentile (Q3) calculated for grouped data?

Answer 28

Q3 = l + [(3n/4 - m)/f] × c.

Question 29

What are the steps to calculate quartiles for grouped data?

Answer 29

1. Find cumulative frequency. 2. Identify Q1 and Q3 classes. 3. Use respective formulas.

Question 30

What is the difference between mean, median, and mode?

Answer 30

Mean: Arithmetic average. Median: Middle value. Mode: Most frequent value.

Question 31

Define central tendency with examples.

Answer 31

A central value summarizing data, e.g., mean, median, mode.

Question 32

The middle value of an ordered series is called what?

Answer 32

2nd quartile, 5th decile, or 50th percentile.

Question 33

For a set of values, the mode can be what?

Answer 33

Unimodal, bimodal, or trimodal.

Question 34

Is mode suitable for qualitative data?

Answer 34

Yes, it is suitable.

Question 35

What does deciles divide the group into?

Answer 35

Ten equal parts.

Question 36

Is the mean affected by extreme values?

Answer 36

Yes, it is affected.

Question 37

Can geometric mean be calculated for negative values?

Answer 37

No, it cannot.

Question 38

What type of data is mode used for?

Answer 38

Both qualitative and quantitative data.

Question 39

How do you calculate arithmetic mean for raw data?

Answer 39

Sum all values and divide by the number of observations.

Question 40

How do you calculate the median for grouped data?

Answer 40

Find cumulative frequencies and use the median formula.

Question 41

How do you calculate the mode for grouped data?

Answer 41

Use the modal class and the mode formula.