Exploring and Describing Data

Question 1

Mean

Answer 1

Average

Question 2

Median

Answer 2

The median is the middle score. To find the median, list all the scores in increasing order and select the middle one.

Question 3

Mode

Answer 3

The mode is the score that occurs the most. It is the score with the highest frequency.

Question 4

Range

Answer 4

Range = Highest score – Lowest score

Question 5

Interquartile range

Answer 5

IQR = Third quartile – First quartile = Q 3 − Q 1

Question 6

Standard deviation

Answer 6

Standard deviation is the spread of data about the mean. Population standard deviation – σ n or σ x.
Sample standard deviation – σ n −1 or S x .

Question 7

Outlier

Answer 7

An outlier is a score that is separated from the majority of the data.
Use Q1 −1.5× IQR and Q3 +1.5× IQR as criteria to determine an outlier.

Question 8

Describing datasets

Answer 8

• Shape of the graph is described in terms of smoothness, symmetry and the number of modes.
• Positively skewed data has a long tail on the right-hand side. * Negatively skewed data has a long tail on the left-hand side.

Question 9

Comparing datasets

Answer 9

The selection and the use of the appropriate measure of location (mean or median) and measure of spread (range, interquartile range or standard deviation) depends on the nature of the data and the relative merits of each measure.

Question 10

Parallel box-and-whisker plots

Answer 10

Two box-and-whisker plots on the same scale. They are used to compare two sets of data.