Representation and summary of data

Question 1

Describe a stem and leaf diagram

Answer 1

Each number is split into a stem and leaf. The stems form a column, and the leaves go in the row belonging to the appropriate stem, in ascending order. A key shows what each stem and leaf combination represents

Question 2

What is an outlier?

Answer 2

A value that is either greater than Q₃+1.5(Q₃-Q₁) or less than Q₁-1.5(Q₃-Q₁)

Question 3

Describe a box plot

Answer 3

Outliers are represented by crosses. The lowest and highest values (excluding outliers), the lower and upper quartiles and the median are represented by vertical lines, with a box representing the interquartile range

Question 4

How is the frequency density calculated?

Answer 4

frequency/class width

Question 5

Describe a histogram

Answer 5

There are no gaps between the bars. The area of the bar is proportional to the frequency

Question 6

If Q₂-Q₁=Q₃-Q₂, what can be said about the distribution?

Answer 6

It is symmetrical

Question 7

If Q₂-Q₁<Q₃-Q₂, what can be said about the distribution?

Answer 7

It is positively skewed

Question 8

If Q₂-Q₁>Q₃-Q₂, what can be said about the distribution?

Answer 8

It is negatively skewed

Question 9

If the mode=median=mean, what can be said about the distribution?

Answer 9

It is symmetrical

Question 10

If the mode<median<mean, what can be said about the distribution?

Answer 10

It is positively skewed

Question 11

If the mode>median>mean, what can be said about the distribution?

Answer 11

It is negatively skewed

Question 12

How can the skewness of data be calculated?

Answer 12

3(mean-median)/standard deviation

Question 13

How can the skewness of data as calculated by 3(mean-median)/standard deviation be interpreted?

Answer 13

The closer to 0 it is, the more symmetrical the data. A positive number means a positive skew, and vice versa