Descriptive Statistics

Question 1

What is the mean?

Answer 1

The average of a set of numbers.

Question 2

How do you calculate the median?

Answer 2

Divide the ordered dataset into two halves; if the number of observations is odd, the middle number is the median, if even, it is the average of the two middle numbers.

Question 3

What does the mode represent in a dataset?

Answer 3

The most frequently occurring value in a dataset.

Question 4

Define the range in statistics.

Answer 4

The difference between the highest and lowest values.

Question 5

How is variance calculated in a dataset?

Answer 5

The average of the squared differences from the Mean.

Question 6

Explain how standard deviation is used in data analysis.

Answer 6

It measures the amount of variation or dispersion of a set of values.

Question 7

What does a high variance indicate about a dataset?

Answer 7

It suggests a wider spread of data points in the dataset.

Question 8

How do you find the interquartile range?

Answer 8

The difference between the 75th and 25th percentiles.

Question 9

What is a boxplot and what does it show?

Answer 9

A graphical representation of the distribution of data points.

Question 10

Why is it important to know the shape of the distribution?

Answer 10

It provides insights into the symmetry and spread of data.

Question 11

What is skewness in statistical terms?

Answer 11

A measure of how much data deviates from being symmetrical.

Question 12

Explain kurtosis in a dataset.

Answer 12

A measure of the “tailedness” of the probability distribution.

Question 13

How does one identify outliers in data?

Answer 13

By identifying data points that significantly differ from other observations.

Question 14

What is a frequency distribution?

Answer 14

The organization of data by the frequency of their values.

Question 15

How can a histogram help in understanding data?

Answer 15

It visually shows the distribution of data.

Question 16

What is a scatter plot used for?

Answer 16

To display values involving two variables.

Question 17

How do quartiles divide a dataset?

Answer 17

They divide the dataset into four equal parts.

Question 18

What is the difference between absolute deviation and mean deviation?

Answer 18

Absolute deviation is the absolute differences, mean deviation is the average of these absolute differences.

Question 19

How do you calculate a percentile rank?

Answer 19

The position of a value in a dataset as a percentage of the total number of data points.

Question 20

What is a cumulative frequency distribution?

Answer 20

The sum of relative frequencies up to a certain point in a dataset.

Question 21

Explain the concept of a relative frequency distribution.

Answer 21

It shows the proportion of each class relative to the total number of cases.

Question 22

What role does the mean play in symmetrical distributions?

Answer 22

It represents the balance point of the distribution.

Question 23

What is the best measure of central tendency for skewed data?

Answer 23

Median.

Question 24

Why might one use the median instead of the mean?

Answer 24

It is less affected by outliers and skewed data.

Question 25

How is the mode different from the mean and median?

Answer 25

The mode is categorical unlike mean and median which are numerical.

Question 26

When is the range not a good measure of dispersion?

Answer 26

When the dataset contains outliers.

Question 27

What is the significance of a high standard deviation?

Answer 27

More data points are far from the mean.

Question 28

How do variance and standard deviation relate?

Answer 28

Standard deviation is the square root of variance.

Question 29

What are the limitations of using the range in data analysis?

Answer 29

It doesn't account for the distribution between the highest and lowest values.

Question 30

What statistical measure can help compare data sets with different units?

Answer 30

Coefficient of variation.

Question 31

How does one interpret the standard error of the mean?

Answer 31

It represents the distribution of sampling means.

Question 32

What does a low interquartile range indicate?

Answer 32

The values are closely packed around the median.

Question 33

Why is the mean sensitive to outliers?

Answer 33

It can be distorted by extreme values.

Question 34

What type of data is best summarized by the mode?

Answer 34

Categorical data where numbers repeat often.

Question 35

How does one decide between using standard deviation and variance?

Answer 35

Depends on the analysis requirement—standard deviation is more intuitive.

Question 36

What is the benefit of using the median in real-world data?

Answer 36

It provides a more accurate measure for skewed data.

Question 37

How do you handle outliers before calculating statistical measures?

Answer 37

By either removing them or adjusting them based on the context.

Question 38

What insights can the coefficient of variation provide?

Answer 38

It shows the ratio of the standard deviation to the mean.

Question 39

Why might a bimodal distribution be significant?

Answer 39

It indicates two dominant groups within the dataset.

Question 40

How can measures of central tendency mislead if not used properly?

Answer 40

How measures can be misleading when not considering the nature of the data.