Unit 2

Question 1

What is univariate descriptive statistics?

Answer 1

Univariate descriptive statistics provides a summarized description and analysis of a single variable. It aims to answer questions like:
●What are the scores in the variable?
●Are there significant differences among its values?
●What is the proportion of subjects exceeding a certain value?

Question 2

What is absolute frequency (fi)?

Answer 2

Absolute frequency (fi) represents the number of times a specific value of a variable is repeated within a dataset

Question 3

What is relative frequency (f’i)?

Answer 3

Relative frequency (f’i) is the proportion of a particular value’s frequency compared to the total sample size. It is calculated as: f’i = (frequency of a value) / (total sample size)

Question 4

What is percentage (pi)

Answer 4

Percentage (pi) expresses the proportion of a value within the sample as a percentage out of 100. It is calculated by multiplying the relative frequency (f’i) by 100: pi = f’i * 100

Question 5

What is cumulative relative frequency (F’i)?

Answer 5

Cumulative relative frequency (F’i) represents the cumulative proportion of values up to a certain point in the distribution. It is calculated as: F’i = (cumulative frequency of a value) / (total sample size)

Question 6

What is cumulative percentage (Pi)?

Answer 6

Cumulative percentage (Pi) expresses the cumulative relative frequency (F’i) as a percentage. It is calculated as: Pi = F’i * 100.

Question 7

What is a cyclogram/pie chart? When is it used?

Answer 7

A cyclogram, also known as a pie chart, is a circular graph divided into slices, with each slice’s size representing the frequency of a corresponding value. It can be used to display absolute frequency, relative frequency, or percentages. Cyclograms are suitable for nominal, ordinal, and discrete quantitative variables with relatively few distinct values

Question 8

What is a bar chart? When is it used?

Answer 8

A bar chart uses bars of varying heights to represent the frequencies of different values. The height of each bar corresponds to the frequency of the value it represents. Bar charts can display absolute, relative, or percentage frequencies. They are suitable for nominal, ordinal, and discrete quantitative variables with a limited number of values.

Question 9

What is a polygon of frequencies? When is it used?

Answer 9

A polygon of frequencies, also known as a frequency polygon, is a line graph that connects points representing the frequencies of different values. Points on the graph represent the frequency of each value and are connected by lines. It is particularly useful for comparing groups or illustrating data profiles, typically for quantitative variables, especially discrete ones.

Question 10

What is a histogram? When is it used?

Answer 10

A histogram resembles a bar chart but uses connected bars to represent the frequencies of continuous data grouped into intervals. This connected bar format highlights the continuous nature of the variable. Histograms are suitable for displaying continuous quantitative variables, and data is grouped into class intervals when dealing with a large number of values.

Question 11

What is a stem-and-leaf diagram? When is it used?

Answer 11

A stem-and-leaf diagram is a way to visualize data by separating each data point into a ‘stem’ and a ‘leaf,’ revealing the distribution’s shape. It is helpful in identifying potential outliers or unusual patterns in the variable’s distribution.

Question 12

What is a box plot? When is it used?

Answer 12

A box plot, also known as a box-and-whisker plot, provides a visual summary of a dataset’s distribution based on quartiles, effectively showing the data’s form, including its symmetry and potential outliers.

Question 13

What are the four properties of a frequency distribution?

Answer 13

●Central tendency: The point around which the data tends to cluster.
●Variability: The degree to which data points are spread out from the center.
●Skewness: The extent to which data is distributed symmetrically or asymmetrically around the central tendency.
●Kurtosis: The peakedness or flatness of the distribution, indicating data concentration around the center.

Question 14

What are the types of kurtosis?

Answer 14

●Mesokurtic: A normal distribution with a balanced shape.
●Leptokurtic: Positive kurtosis, characterized by a tall and narrow peak, indicating data concentration at the center.
●Platykurtic: Negative kurtosis, characterized by a flatter distribution with more data in the tails.

Question 15

How can you determine skewness from a SPSS output?

Answer 15

●Statistic < (Error x 2) = Symmetrical distribution
●Statistic > (Error x 2) = Asymmetrical distribution
●- = Negative skewness
●+ = Positive skewness

Question 16

How can you determine kurtosis from a SPSS output

Answer 16

●-0.5 – 0.5 = Mesokurtic
●<-0.5 = Platykurtic

Question 17

What are measures of position? When are they used?

Answer 17

Measures of position, also known as quantiles, pinpoint a value’s location within a distribution relative to other values. They divide datasets into equal parts, helping to understand a value’s relative standing. These measures are commonly used in psychological test scales and require variables to be at least on an ordinal scale

Question 18

What are the types of quantiles?

Answer 18

●Centiles/Percentiles (Ck or Pk): Values that divide the data into 100 equal parts, with a specific centile representing the value below which a certain percentage of the sample falls.
●Deciles (Dk): Values that divide the data into 10 equal parts, each representing 10% of the sample.
●Quartiles (Qk): Values that divide the data into 4 equal parts, each representing 25% of the sample

Question 19

What is the formula to calculate the position of a percentile?

Answer 19

The formula to calculate the position of a percentile is: Pk = (k / 100) * (n + 1) Where:
●k = The desired percentile
●n = The sample size

Question 20

What is the formula to calculate the position of a decile?

Answer 20

The formula to calculate the position of a decile is: Dk = (k / 10) * (n + 1) Where:
●k = The desired decile
●n = The sample size

Question 21

What is the formula to calculate the position of a quartile?

Answer 21

The formula to calculate the position of a quartile is: Qk = (k * (n + 1)) / 4 Where:
●k = The desired quartile
●n = The sample size

Question 22

What is interpolation and when is it used with quantiles?

Answer 22

When the calculated position of a quantile (percentile, decile, or quartile) falls between two data points (resulting in a decimal), interpolation is used to determine the precise quantile value.

Question 23

What is the formula for interpolation when calculating quantiles?

Answer 23

The interpolation formula is: Quantile (P, D, or Qk) = E1 + ((E2 - E1) * e) Where:
●E1 = Value at the position of the quantile
●E2 = The following value in the dataset
●e = The decimal portion of the calculated position

Question 24

What are measures of central tendency? What are some examples

Answer 24

Measures of central tendency represent the average or typical value of a dataset, providing insights into the data’s central tendency. The most common measures of central tendency are:
●Mode (Mo): The value that occurs most frequently in the distribution.
●Median (Mdn): The middle value when the data is arranged in order.
●Mean (M): The sum of all values divided by the number of values (the average)

Question 25

What is the median?

Answer 25

The median is the middle value in a dataset when it is sorted from smallest to largest. The median splits the data in half, with 50% of the values above it and 50% below it. In a normal distribution, it is equivalent to the 50th percentile (P50), the 5th decile (D5), and the 2nd quartile (Q2).

Question 26

What is the mean?

Answer 26

The mean is the arithmetic average of a dataset, calculated by summing all values and dividing by the number of values. It is often represented by the symbol x̄. The mean is sensitive to extreme values (outliers), which can distort its representation of the typical value.

Question 27

What are measures of variability?

Answer 27

Measures of variability describe the spread or dispersion of data points in a dataset. They tell us how much individual values differ from each other and from the central tendency. They provide information about the data’s homogeneity or heterogeneity

Question 28

What are some common measures of variability?

Answer 28

Common measures of variability include:
●Range: The difference between the highest and lowest values in the data.
●Amplitude: Similar to range, it represents the difference between the maximum and minimum values.
●Interquartile Range (IQR): The range of the middle 50% of the data, calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
●Variance: The average squared deviation of each data point from the mean.
●Standard Deviation: The square root of the variance, representing the average distance of data points from the mean.