Frequency tables and grouped frequency distributions

. Grouped Frequency Distributions:

Age Group 1:

Interval (ms)

Tally

Frequency

Relative Frequency

Cumulative Frequency

Cumulative Relative Frequency

-16 to -11

-

0.2

2

0.2

-10 to -6

---

-

0

0

-5 to -1

-------

0.1

1

0.2

0 to 4

-------------

0.2

2

0.2

5 to 9

-------

0.2

2

0.2

10 to 14

---

0.33

3

0.33

Age Group 2:

Interval (ms)

Tally

Frequency

Relative Frequency

Cumulative Frequency

Cumulative Relative Frequency

-3 to 1

-------

0.2

2

0.2

2 to 6

---

0.4

4

0.4

7 to 11

-------

0.33

3

0.33

12 to 16

-------------

0.1

1

0.1

2. Answers:

A) The percentage of over-50-year-olds who made errors of 5 milliseconds or less can be found by adding the relative frequencies of the intervals with positive errors that are 5 ms or less:

0.2 + 0 + 0.2 = 0.4 or 40%

Therefore, 40% of the over-50-year-olds made errors of 5 milliseconds or less.

B) To determine how many participants in age group 1 made underestimations of the time interval, we need to add up the frequencies of the intervals with negative errors:

1 + 1 + 1 + 1 = 4

Therefore, 4 participants in age group 1 made underestimations of the time interval.

C) To determine how many over-50-year-olds made underestimations, we need to add up the frequencies of the intervals with negative errors:

0 + 0 + 1 + 0 + 0 + 0 + 0 = 1

Therefore, 1 over-50-year-old participant made an underestimation of the time interval.

D) To determine how many participants made overestimations, we need to add up the frequencies of the intervals with positive errors:

0 + 0 + 1 + 3 + 2 + 2 + 0 + 2 + 2 + 1 = 13

Therefore, 13 participants made overestimations of the time interval.

3. Data Types:

A) Age group is nominal data, as it represents categorical groups without any inherent order or ranking.

B) Errors (in milliseconds) are interval data, as they represent numerical data with equal intervals between values, but there is no true zero

c) Coffee serving size (short, tall, grande, venti, trenta) represents nominal data because the categories (sizes) have no inherent order or numerical meaning. Each size is simply a label that distinguishes it from the other sizes.