Distributions And Probability

Question 1

What defines a normal distribution?

1) A distribution where the mean is greater than the median
2) A symmetrical distribution where the mean, median, and mode are equal
3) A distribution with a higher frequency of extreme values
4) A skewed distribution where outliers dominate

Answer 1

A symmetrical distribution where the mean, median, and mode are equal

Question 2

Which of the following is an example of data that typically follows a normal distribution?

1) Shoe sizes
2) Number of siblings in a family
3) Hair colours in a population
4) Favourite ice cream flavours

Answer 2

Shoe sizes

Question 3

What does a negatively skewed distribution look like?

1) The tail is longer on the right side of the distribution
2) The tail is longer on the left side of the distribution
3) It has no clear central tendency
4) It is perfectly symmetrical

Answer 3

The tail is longer on the left side of the distribution

Question 4

How can Pearson’s coefficient of skew be interpreted?

1) Values greater than 0 indicate positive skew; values less than 0 indicate negative skew
2) Values greater than 0 indicate negative skew; values less than 0 indicate positive skew
3) Values equal to 0 indicate a perfectly skewed distribution
4) It is only used for nominal data

Answer 4

Values greater than 0 indicate positive skew; values less than 0 indicate negative skew

Question 5

What is a z-score?

1) The difference between the highest and lowest data points
2) The number of standard deviations a score is from the mean
3) A measure of the central tendency in skewed data
4) The square of the standard deviation

Answer 5

The number of standard deviations a score is from the mean

Question 6

What percentage of data falls within ±1 standard deviation in a normal distribution?

1) 68%
2) 95%
3) 99.7%
4) 50%

Answer 6

68%

Question 7

Why are z-scores useful in data analysis?

1) They convert data into a categorical format
2) They transform data onto a standardised scale for comparison
3) They eliminate outliers from the dataset
4) They only apply to non-parametric tests

Answer 7

They transform data onto a standardised scale for comparison

Question 8

What is the standard error of the mean (SE)?

1) The variability of the population standard deviation
2) An estimate of how much a sample mean deviates from the population mean
3) The total range of the sample data
4) A measure of correlation between variables

Answer 8

An estimate of how much a sample mean deviates from the population mean

Question 9

How does increasing the sample size affect the standard error?

1) It increases the standard error
2) It decreases the standard error
3) It has no effect on the standard error
4) It reduces the population variance

Answer 9

It decreases the standard error

Question 10

What does a confidence interval represent?

1) The variability of data within a dataset
2) The likelihood that a sample value is a true population mean
3) The range of values within which a population parameter is likely to fall
4) The probability of rejecting the null hypothesis

Answer 10

The range of values within which a population parameter is likely to fall

Question 11

What range does a 95% confidence interval typically cover in a normal distribution?

1) ±1 standard deviation
2) ±1.96 standard deviations
3) ±2.96 standard deviations
4) ±3 standard deviations

Answer 11

±1.96 standard deviations

Question 12

What does it mean if two confidence intervals do not overlap?

1) The means of the groups are likely significantly different
2) The null hypothesis cannot be rejected
3) The sample size is insufficient
4) The groups are not comparable

Answer 12

The means of the groups are likely significantly different

Question 13

What is the purpose of transforming data into z-scores?

1) To remove all variance from the data
2) To reduce the impact of skew and standardise
comparisons
3) To identify the mean of the population
4) To simplify calculations of median and mode

Answer 13

To reduce the impact of skew and standardise
comparisons

Question 14

What is the relationship between standard deviation and standard error?

1) Standard deviation measures data spread; standard error measures sample variability from the population mean
2) Standard deviation and standard error are interchangeable
3) Standard error measures data spread, while standard deviation estimates population means
4) Standard deviation applies only to samples, while standard error applies only to populations

Answer 14

Standard deviation measures data spread; standard error measures sample variability from the population mean

Question 15

What does a z-score of -2 indicate?

1) The score is 2 standard deviations above the mean
2) The score is 2 standard deviations below the mean
3) The score is exactly at the mean
4) The score is within 2% of the population mean

Answer 15

The score is 2 standard deviations below the mean

Question 16

What assumption underlies parametric tests like the t-test?

1) Data must follow a normal distribution
2) Data can only include ordinal variables
3) Data must have no outliers
4) Data must be bimodal

Answer 16

Data must follow a normal distribution

Question 17

What is the shape of a Gaussian curve?

1) Symmetrical and bell-shaped
2) Skewed with a long tail
3) Uniform with equal frequencies
4) U-shaped with a central dip

Answer 17

Symmetrical and bell-shaped

Question 18

What percentage of data lies beyond ±3 standard deviations in a normal distribution?

1) 1%
2) 0.3%
3) 5%
4) 10%

Answer 18

0.3%

Question 19

What is the formula for calculating a z-score?

1) Z = Score - Mean / Standard Deviation
2) Z = Mean - Score / Standard Deviation
3) Z = Standard Deviation / Score
4) Z = Score x Standard Deviation

Answer 19

Z = Score - Mean / Standard Deviation

Question 20

How is a confidence interval visually represented in a graph?

1) As a single point
2) As error bars around the mean
3) As a box-and-whisker plot
4) As a histogram

Answer 20

As error bars around the mean