S1.2 Summary Statistics

Question 1

Statistics

Statistics is the science of collecting, classifying and analyzing information.

Answer 1

Question 2

Statistic

A statistic is a numerical value (such as the mean or range) calculated from a set of data.

Answer 2

Question 3

Measures of Location

Answer 3

The mean, median and mode are three summary statistics that represesent the centre or the average of a set of data. They are called the measures of central tendency ( or measures of location).

Question 4

Mean

(Measure of Location)

Answer 4

The mean is the average score in a set of data.

Question 5

Median

(Measure of Location)

Answer 5

The median is the score which is located in the middle of an ordered set of data. The median divides the data into two equal groups.

Question 6

Mode

(Measure of Location)

Answer 6

The mode is the most occuring score in a set of data. The mode is more useful for categorical data.

Question 7

Quantiles

Answer 7

Quantiles are points in a set of ordered data which divide the data into equal groups. Commonly used quantiles are quartiles, deciles and percentiles.

Question 8

Quartiles

Quartiles (Q₁, Q₂, Q₃) divide a data set into 4 equal groups.

Answer 8

Q3 separates the lower 75% of scores from the uper 25% of scores.

Question 9

Deciles

Deciles (D₁, D₂, … D_{<span>9</span>}) divide a set of data into 10 equal groups.

Answer 9

D₂ cuts of the lower 20% of scores from the upper 80% of scores

Question 10

Percentiles

Percentiles (P₁, P₂, P₃, … P₁₀₀) seperate a large set of data into 100 equal groups.

Answer 10

Question 11

Measures of Spread

A second important feature of a set of data is how spread out its scores are.

Answer 11

Three statistics which measure the spread of the scores in a set of data are the range, interquartile range (IQR) and standard deviation.

Question 12

Range

(Measure of Spread)

Answer 12

The range is a measure of spread.

Question 13

Interquartile Range

(Measure of Spread)

Answer 13

Question 14

Standard Deviation

(Measure of Spread)

Answer 14

Standard deviation measures how different each score in a data set is from the mean.

Question 15

Outlier

Answer 15

An outlier is a very high or a very low score in a set of data which is clearly apart from the other scores.

Question 16

Effect of Outliers

Outliers can affect the reliability of some measures of spread and location.

Answer 16

Question 17

Detecting Outliers

Answer 17

Question 18

Five Number Summary

Answer 18

Question 19

Boxplot

A boxplot (or box-and-whisker plot) is a plot of a five-number summary.

Answer 19

Question 20

Cumulative Frequency Graph & Polygon

Answer 20

The CF polygon (ogive) starts from the beginning of the histogram and joins the top right-hand corner of each column.

Question 21

Estimating Quartiles

Q₁, Q₂, and Q₃ can be estimated using the Cumulative Frequency Polygon (Ogive).

Answer 21

Question 22

Shape of a Distribution

Answer 22

The shape of a distribution (a set of data) shows how the data is spread. The distribution of a set of data can often be classified as being either symmetric, positively skewed or negatively skewed.

Question 23

Symmetric Distribution

A symmetric distribution is evenly spread either side of its centre.

Answer 23

Question 24

Positively Skewed

Positively skewed data has a higher propotion of low scores.

Answer 24

Question 25

Negatively Skewed
Negatively skewed data has a higher proportion of high scores.

Answer 25

Question 26

Samples & Populations

Answer 26

The population mean and standard deviation are called parameters, The sample mean and standard deviation are statistics used to estimate the values of the population parameters.