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NURS/HSCI 597Frequency Distribution

Heibatollah Baghi, and

Mastee Badii

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• Nominal-Level data is merely descriptive (e.g. religion, country name, region). Any assigned numerical value is merely for convenience (e.g. Christian = 1, Jewish = 2, Buddhist = 3)

• Ordinal-Level data has rank order, though intervals between data points cannot be considered equal (e.g. high/medium/low income, GDP/capita rank, HDI rank)

• Interval-Level data has equal intervals between data points

• Ratio-Level data has equal intervals between data points and a true zero

Levels of Measurement

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Table 1: Grades from 50 Students75 89 57 88 6190 79 91 69 9983 85 82 79 7278 73 86 86 8680 87 72 92 8198 77 68 82 7882 84 51 77 9070 70 88 68 8178 86 62 70 7689 67 87 85 80

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1. Sort the data

2. Tally the data (mutually exclusive and collectively exhaustive)

3. Sum the tally (Sum of frequencies = sample size)

Ungrouped Frequency Distribution of Heart Rates

60 65 63 57 64 65

70 72 68 64 62 66

56 69 67 73 68 63

60 66 61 60 65 67

65 72 66 58 62 60

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Ungrouped Frequency Distribution of Heart Rate Scores

Score Frequency Score Frequency

56 1 65 4

57 1 66 3

58 1 67 2

59 0 68 2

60 4 69 1

61 1 70 1

62 2 71 0

63 2 72 2

64 2 73 1

Sum 30

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Frequency Percentages & Cumulative Percentages

• % = (f / N) * 100

• Percentage = First divide frequency by sample size and then multiply by 100

• Cumulative percentage shows the percentage of scores that are equal to or lesser than a specified score.

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SPSS Steps for Frequency Distribution

1. Read data into SPSS

2. Select from Analyze

3. Select variable & press OK3. Get results

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Heart Rate Frequency Distribution

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Choose the Type of Chart that Best Describes a Variable Characteristic

• Bar chart is used for Nominal or Ordinal data– Pie chart is an alternative to the bar chart

• Histogram is appropriate for interval ratio– Polygon is equivalent to histogram but appear

smoother

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Bar Graph

• Works for Nominal or Ordinal data

• Consists of a horizontal (X-axis) and vertical dimension (Y-axis)

• Categories are along the X-axis

• Frequencies or percentages are displayed on Y-axis

• SPSS can draw a bar graph for you

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SPSS Steps: Recode for Bar Chart

2. Select variable

3. Rename

4. Indicatechanges

5.Show range

6. Shownew

values & add

1. Selectto

recode

7. Heart raterecoded into3 categories

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SPSS Steps: Bar Chart1. Follow steps for

Frequency Distribution

2. Selectchart

3. Select bar chart

4. Seeresults

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Bar Chart for Heart Rate Categories

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Histograms(Grouped Frequency Distribution)

• Used for interval or ratio level data

• X-axis shows the categories, next to each other

• Y-axis shows the frequency or relative frequency

• Histograms are grouped-data frequency distributions

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Histogram for Student Grades

1. Find the lowest and highest score2. Find the range of scores3. Decide on the number of intervals

(e.g., 5)4. Divide the range by number of

intervals5. Determine the lowest class interval6. List all class intervals.7. Tally the number of scores that fall

in each class interval.8. Convert each tally to a frequency.

75 89 57 88 6190 79 91 69 9983 85 82 79 7278 73 86 86 8680 87 72 92 8198 77 68 82 7882 84 51 77 9070 70 88 68 8178 86 62 70 7689 67 87 85 80

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Histogram of Student Grades

• The lowest score and highest score (51,99)

• The range of scores (99 – 51 = 48)• Number of intervals (5)• Range (48 / 5 ~ 10)• Lowest class interval (51-60)• All class intervals 51-60,61-70,71-

80,81-90,91-100• Tally the number of cases that fall

within each interval• Frequency counts: 2,9,14,21,4

75 89 57 88 6190 79 91 69 9983 85 82 79 7278 73 86 86 8680 87 72 92 8198 77 68 82 7882 84 51 77 9070 70 88 68 8178 86 62 70 7689 67 87 85 80

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SPSS Steps: Histogram1. Follow steps for

Frequency Distribution

2. Selectchart

3. Select histogram

4. Seeresults

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Histogram of Student Grades

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Characteristics of Frequency Distributions

• Central Tendency– Mean – Median

• Variability– Range– Standard deviation

• Shape (Normal, Bimodal, Skewed, J-Shaped, Kurtosis)

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Normal

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Bi-modal

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Negatively skewed

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Positively skewed

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J-shaped

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Rectangular

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Platykurtic

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Take Home Lesson

Data can be described by the central tendency, variability and shape of

the frequency distribution