Chapter Objectives
- Recognize and differentiate between key terms.
- Apply various types of sampling methods to data collection.
- Create and interpret frequency tables.
Assignment
Answers and Rounding Off
- Don’t sweat reducing fractions
- Avoid rounding decimal values until the very end
- For final answers, round to one more decimal place than was in the original data
- E.g., Original data had three decimal place, round final answers to four decimal places
Levels of Measurement
Nominal
- Pure categorical data
- Calculations not possible, only grouping
Ordinal
- Looks like qualitative data, but can be ordered
- Calculations still not possible
- E.g., excellent, good, satisfactory, and unsatisfactory
Interval
- Quantitative data with no real starting point
- Zero doesn’t mean zero
- E.g., Fahrenheit/Celsius, SAT scores
- Calculations are possible except for ratio-related ones
- 60° is not twice as hot as 30°
Ratio
- Quantitative data where zero mean zero
- Most measurements fall in this category
- All calculations are possible
- 4 meters is twice the distance as 2 meters
Comparison of Levels of Measurement
| Level of Measurement |
Put data in categories |
Arrange data in order |
Subtract data values |
Determine whether one data value is a multiple of another |
| Nominal |
Yes |
No |
No |
No |
| Ordinal |
Yes |
Yes |
No |
No |
| Interval |
Yes |
Yes |
Yes |
No |
| Ratio |
Yes |
Yes |
Yes |
Yes |
Frequency
| DATA VALUE |
FREQ. |
RELATIVE |
CUMUL. |
| 2 |
3 |
0.15 |
0.15 |
| 3 |
5 |
0.25 |
0.40 |
| 4 |
3 |
0.15 |
0.55 |
| 5 |
6 |
0.30 |
0.85 |
| 6 |
2 |
0.10 |
0.95 |
| 7 |
1 |
0.05 |
1.00 |
- Number of times a data value occurs
- Relative frequency is ratio to the total
- Cumulative relative frequency is the accumulation of previous ones
| HEIGHTS (INCHES)* |
FREQUENCY |
RELATIVE FREQUENCY |
CUMULATIVE RELATIVE FREQUENCY |
| 59.95–61.95 |
5 |
5/100 = 0.05 |
0.05 |
| 61.95–63.95 |
3 |
3/100 = 0.03 |
.05 + .03 = 0.08 |
| 63.95–65.95 |
15 |
15/100 = 0.15 |
.08 + .15 = 0.23 |
| 65.95–67.95 |
40 |
40/100 = 0.40 |
.23 + .40 = 0.63 |
| 67.95–69.95 |
17 |
17/100 = 0.17 |
.63 + .17 = 0.80 |
| 69.95–71.95 |
12 |
12/100 = 0.12 |
.80 + .12 = 0.92 |
| 71.95–73.95 |
7 |
7/100 = 0.07 |
.92 + .07 = 0.99 |
| 73.95–75.95 |
1 |
1/100 = 0.01 |
.99 + .01 = 1.00 |
| |
Total = 100 |
Total = 1.00 |
|
* Data had one decimal place, so ranges have two to prevent overlap