data summary

Question 1

what is quantitative data

Answer 1

Quantitative data measure some quantity resulting in a numerical value, e.g. weight, salary.

Question 2

what is qualitative data

Answer 2

Qualitative data measure the quality of something resulting in a value that does not have a numerical meaning, e.g. colour, religion, season.

Question 3

what is discrete quantitative data

Answer 3

Discrete: data with distinct values and possible values take only a distinct series of numbers (e.g. number of traffic accidents, number of children born to a women)

Question 4

what is continuous quantitative data

Answer 4

Continuous: a value that can be measured evermore precisely and hence become essentially continuous (e.g. height, speed).

Question 5

what is ordinal qualitative data

Answer 5

Ordinal: non-numeric value but the values have some natural ordering; e.g. poor, fair, good, excellent.

Question 6

what is nominal qualitative data

Answer 6

Nominal: unordered, distinct by name only; e.g. retail, construction, manufacturing.

Question 7

what are frequency distribution

Answer 7

A frequency distribution summarizes discrete variables or qualitative data by counting how often each value occurs.

Question 8

what is the mode

Answer 8

The mode is the most frequently occurring value in a dataset

Question 9

What is a bimodal distribution?

Answer 9

A bimodal distribution has two distinct peaks in the frequency of values.

Question 10

What are the 3 measures of centre in statistics?

Answer 10

mode
mean
median

Question 11

4 measures of spread

Answer 11

range
interquartile range (IQR)
sample variance
standard deviation.

Question 12

Why is it important to know both the centre and spread of a dataset?

Answer 12

Knowing both provides a better understanding of the data’s behavior. The center gives us a “typical” value, while the spread tells us how much variability or dispersion exists in the data.

Question 13

what is the population mean and sample mean

Answer 13

The population mean is a parameter (𝜇) which is typically unknown

we take a sample and obtain an estimate (𝜇̂), the sample mean

Question 14

how to find the position of an even and odd sample median

Answer 14

even: (𝑛 + 2)/2
odd: (𝑛 + 1)/2
𝑛 - sample size

Question 15

what is the range

Answer 15

The range is the difference between the maximum and minimum value.

Question 16

one disadvantage of range

Answer 16

can be misleading if one number is different to the rest. (outlier)

Question 17

what is an outlier

Answer 17

An outlier is a value that is very different to the other values recorded.

Question 18

What are percentiles and how are they used?

Answer 18

Percentiles: Values that divide the dataset into 100 equal parts.

25th percentile (lower quartile or 1st quartile): 25% of data lies below it.

75th percentile (upper quartile or 3rd quartile): 75% of data lies below it.

Question 19

what is the interquartile range

Answer 19

The difference between the 75th percentile and 25th percentile, representing the spread of the middle 50% of data.

Question 20

population variance formula

Answer 20

𝜎² = ∑(𝑦𝑖 - 𝜇)² / 𝑁

𝑁: population size
𝑦𝑖: each value.

Question 21

what does variance measure

Answer 21

Measures the spread of data from the population mean (𝜇).

Question 22

What is sample variance and how is it different from population variance?

Answer 22

Measures the spread of data from the sample mean (𝜇̂).
Sample variance divides by (𝑛 - 1) instead of 𝑁 to correct for bias in estimating population variance

Question 23

sample variance formula

Answer 23

𝑠² = ∑(𝑦𝑖 - 𝜇̂)² / (𝑛 - 1)

where n-1 is the degrees of freedom

Question 24

why do we use standard deviation

Answer 24

unit of variance give a squared answer so we want to root them

Question 25

standard deviation formula

Answer 25

𝑠 = √(𝑠²)

Question 26

What is a bar plot and when is it used?

Answer 26

A bar plot represents frequency information across discrete categories or groups. The height of each bar corresponds to the count or proportion of observations

Question 27

why are pie charts useful

Answer 27

Pie charts are useful for displaying frequency distributions across different groups.

Question 28

What is a histogram and what does it show?

Answer 28

A histogram is used to display continuous data by grouping values into bins. The x-axis represents data bins, and the y-axis represents frequency. It helps visualize the center, spread, and skewness of the data.

Question 29

how to find the median in a histogram

Answer 29

the median is the point where 50% of the area of a histogram is to the left and 50% to the right

Question 30

what is skewness

Answer 30

skewness is a measure of asymmetry about the mean.

Question 31

How can you tell if data is skewed using a histogram?

Answer 31

Right (positive) skewed: Long right tail, mean > median. Left (negative) skewed: Long left tail, mean < median. Symmetric distribution: Mean = median.

Question 32

How do you convert frequency to density in a histogram?

Answer 32

Density in interval 𝑖 = Frequency in interval / (Bin interval × Total number of observations) This standardizes the histogram so that the total area sums to 1, making it easier to compare different distributions.

Question 33

What information does a box plot convey?

Answer 33

the lower limit of the box is the 25th percentile, the upper limit is the 75th percentile the box spans the IQR Median is a line inside the box. Whiskers extend to extreme values (or 1.5×IQR beyond the box). Outliers are plotted beyond the whiskers.

Question 34

what do notched box plots include

Answer 34

Notched box plots show a confidence interval for the median.

Question 35

what are violin plots

Answer 35

A violin plot combines a box plot with a smoothed, sideways histogram: Displays the median (red dot) and quartiles (box). Shows the distribution shape to understand data spread.

Question 36

When should you use a cross-tabulation?

Answer 36

Used when both variables are qualitative or discrete with a small number of values. Helps summarize relationships between categorical variables.

Question 37

How can histograms or box plots compare two variables?

Answer 37

If one variable is continuous and the other is discrete, use side-by-side histograms or box plots to compare groups.

Question 38

What is a scatter plot used for?

Answer 38

A scatter plot is used to visualize the relationship between two continuous variables by plotting: Response variable on the y-axis Explanatory variable on the x-axis This helps identify trends, correlations, and patterns in data.

Question 39

What is a quilt plot?

Answer 39

A quilt plot is used for summarizing relationships between three continuous variables The x and y axes form a grid of sections. Each grid square is colored based on the average value of a third variable (e.g., water depth). Useful for spatial analysis and heat maps.

Question 40

what can be seen from a random component

Answer 40

values might follow a recognisable distribution (e.g. Normal) used to decide if the chosen fixed component is useful

Question 41

What are the two components of data partitioning in linear models?

Answer 41

Fixed Component Represents the systematic part of the data Can be complex (e.g., includes multiple predictors) Random Component Represents random variation or error Often follows a recognizable distribution (e.g., Normal) Helps assess whether the fixed component is useful Measurement = Fitted Value ± Residual

Question 42

What are key visual summaries in data analysis?

Answer 42

Histograms (distribution) Box plots (spread and outliers) Scatter plots (relationships)