Descriptive Statistics

Question 1

What is a population in the context of descriptive statistics?

1) A subset of individuals selected from a larger group
2) The entire group of individuals being studied
3) A sample chosen randomly from a population
4) A fixed set of continuous variables

Answer 1

The entire group of individuals being studied

Question 2

What is the main difference between a sample and a population?

1) A population includes all possible observations, while a sample is a subset
2) A sample includes only nominal data, while a population includes all data types
3) A population requires statistical analysis, while a sample does not
4) A sample consists of independent variables, while a population consists of dependent variables

Answer 2

A population includes all possible observations, while a sample is a subset

Question 3

What type of data is measured on a continuous scale?

1) Hair colour
2) Shoe size
3) Reaction times
4) Test scores ranked from highest to lowest

Answer 3

Reaction times

Question 4

Which measure of central tendency can be used with nominal data?

1) Mean
2) Median
3) Mode
4) Range

Answer 4

Mode

Question 5

What is the formula for calculating the mean?

1) Sum of the data points divided by the total number of data points
2) The difference between the highest and lowest values
3) The middle value in an ordered dataset
4) The frequency of the most common data point

Answer 5

Sum of the data points divided by the total number of data points

Question 6

Which measure of central tendency is least affected by outliers?

1) Mean
2) Median
3) Mode
4) Variance

Answer 6

Median

Question 7

What does the interquartile range (IQR) measure?

1) The spread of scores in the entire dataset
2) The range of scores within the middle 50% of the data
3) The difference between the highest and lowest values in the dataset
4) The average of squared deviations from the mean

Answer 7

The range of scores within the middle 50% of the data

Question 8

What is the main disadvantage of using the range as a measure of spread?

1) It is difficult to calculate without software
2) It does not account for extreme values in the dataset
3) It is highly sensitive to outliers
4) It ignores the middle 50% of the data

Answer 8

It is highly sensitive to outliers

Question 9

What does the variance measure in a dataset?

1) The difference between the highest and lowest scores
2) The average squared deviation of each score from the mean
3) The number of unique values in the dataset
4) The central point of the dataset

Answer 9

The average squared deviation of each score from the mean

Question 10

Why is the standard deviation preferred over variance?

1) It is easier to calculate without a computer
2) It uses the same unit of measurement as the data
3) It eliminates the need for squared values
4) It is unaffected by the sample size

Answer 10

It uses the same unit of measurement as the data

Question 11

What does a standard deviation of 0 indicate?

1) The data is normally distributed
2) There is no variability; all data points are identical
3) The data has a high degree of variability
4) The mean and median are equal

Answer 11

There is no variability; all data points are identical

Question 12

What is the difference between discrete and continuous data?

1) Discrete data can take any fractional value, while continuous data has fixed values
2) Discrete data has fixed, ordered values, while continuous data can take any fractional value
3) Continuous data includes nominal variables, while discrete data does not
4) Discrete data measures only dependent variables, while continuous data measures independent variables

Answer 12

Discrete data has fixed, ordered values, while continuous data can take any fractional value

Question 13

What is the primary use of cumulative frequency distributions?

1) To show the variability within a dataset
2) To display the total count or percentage up to a certain value
3) To rank data points from highest to lowest
4) To summarize nominal data

Answer 13

To display the total count or percentage up to a certain value

Question 14

What is the primary drawback of using the mean for skewed data?

1) It ignores extreme values in the dataset
2) It is not a meaningful measure for ordinal data
3) It is highly sensitive to outliers
4) It does not consider the entire dataset

Answer 14

It is highly sensitive to outliers

Question 15

Which measure of spread should be used with the median?

1) Standard deviation
2) Variance
3) Range
4) Interquartile range

Answer 15

Interquartile range

Question 16

What does the sum of squared errors (SS) represent?

1) The total deviation of scores from the mean
2) The squared difference between the highest and lowest scores
3) The cumulative frequency of all data points
4) The total variance in a dataset

Answer 16

The total deviation of scores from the mean

Question 17

What is the relationship between variance and standard deviation?

1) Standard deviation is the square root of variance
2) Variance is the square root of standard deviation
3) They measure completely different aspects of a dataset
4) Variance and standard deviation are always equal

Answer 17

Standard deviation is the square root of variance

Question 18

Which type of data cannot be summarized using the mean?

1) Ratio
2) Ordinal
3) Interval
4) Nominal

Answer 18

Nominal

Question 19

Why is the median often preferred over the mean for income data?

1) The median uses all data points, unlike the mean
2) Income data is often nominal and unsuitable for mean calculations
3) The median is less affected by extreme values or outliers
4) The mean cannot accurately summarize large datasets

Answer 19

The median is less affected by extreme values or outliers

Question 20

What type of frequency distribution is most useful for datasets with numerous unique values?

1) Cumulative frequency distribution
2) Raw frequency distribution
3) Grouped frequency distribution
4) Percentage frequency distribution

Answer 20

Grouped frequency distribution