Descriptive Statistics: An Overview of Central Tendency and Variation, Slide di Lingua Inglese

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Sorting and Displaying

the Data

“I disliked numbers, and they

didn't think much of me either.”

― R.J. Anderson, Ultraviolet

Statistics:

1. Descriptive Statistics

Descriptive statistics are used by researchers to summarize the data gathered from sample

Summary descriptions of measurements (variables) taken about a group of people/things (sample)

By summarizing information, descriptive statistics speed up and simplify comprehension of a sample’s characteristics

Sample vs. Population Population

Sample

Descriptive Statistics Class A--IQs of 13 Students 102 115 128 109 131 89 98 106 140 119 93 97 110 Class B--IQs of 13 Students 127 162 131 103 96 111 80 109 93 87 120 105 109 An Illustration: Which Group is Smarter?

Each individual may be different. If you try to understand a group by remembering

the qualities of each member, you become overwhelmed and fail to understand the

group.

Descriptive Statistics

Which group is smarter now? Class A--Average IQ Class B--Average IQ 110.54 110. They’re roughly the same! With a summary descriptive statistic, it is much easier to answer our question.

Descriptive Statistics Types of descriptive statistics:  Organize Data  Tables  Graphs  Summarize Data  Central Tendency  Variation

Frequency Frequency (f): the number of sth/response/ Relative Frequency (f): f/n= PROPORTION Cumulative Frequency: how many scores fall below that particular point/score/case in the distribution (F)

Ratio In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). The ratio of two quantities a and b in the same units, is the fraction and we write it as a : b.

Percentile Rank The percentile rank of a score is the percentage of scores in its frequency distribution that are equal to or lower than it. For example, a test score that is greater than or equal to 75% of the scores of people taking the test is said to be at the 75th percentile rank. Percentile= (100) F/N

Percentile Rank Example 1 The math test scores were: 50, 65, 70, 72, 72, 78, 80, 82, 84, 84, 85, 86, 88, 88, 90, 94, 96, 98, 98, 99. Find the percentile rank for a score of 84 on this test. Be sure the scores are ordered from smallest to largest. Locate the 84.

Normal Distribution

Normal Distribution

Skewness

SPSS Output for

Frequency Distribution Total Valid Frequency Percent Valid Percent Cumulative

 - 1 4.2 4.2 4. IQ - 1 4.2 4.2 8. - 1 4.2 4.2 12. - 2 8.3 8.3 20. - 1 4.2 4.2 25. - 1 4.2 4.2 29. - 1 4.2 4.2 33. - 1 4.2 4.2 37. - 1 4.2 4.2 41. - 1 4.2 4.2 45. - 1 4.2 4.2 50. - 1 4.2 4.2 54. - 1 4.2 4.2 58. - 1 4.2 4.2 62. - 1 4.2 4.2 66. - 1 4.2 4.2 70. - 1 4.2 4.2 75. - 1 4.2 4.2 79. - 1 4.2 4.2 83. - 2 8.3 8.3 91. - 1 4.2 4.2 95. - 1 4.2 4.2 100. 

• 24 100.0 100.