Density Functional Theory

In: Science

Submitted By ugochukwu
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CENTRAL TENDENCY: Mean, Median, Mode

New Statistical Notation

Σ : sigma
– The symbol Σ means to sum (add) the scores

Central Tendency

What Is Central Tendency?
• A score that indicates where the center of the distribution tends to be located. • Tells us about the shape and nature of the distribution. d b

Measures of Central Tendency
• Mode • Median • Mean

The Mode
• The most frequently occurring score. • Typically useful in describing central tendency when the scores reflect a nominal scale of measurement. l f

The Mode
• It does not make sense to take the average in nominal data.
– Gender: 67 males --- 1 50 females ---- 2

14 13 14

14 10 15

13 12 17

15 13 14

11 14 14

15 13 15

Score S
17 16 15 14 13 12 11 10

1 0 4 6 4 1 1 1

What is the mode?


Unimodal Distributions
When Wh a polygon h l has one hump (such as on the normal curve) the distribution is called


14 15 15

14 10 15

13 12 17

15 13 12

11 12 15

12 13 12

Score S
17 16 15 14 13 12 11 10

1 0 5 2 3 5 1 1

What is the mode?


Bimodal Distributions
When distribution Wh a di ib i has two scores that are most frequently occurring, it is called d bimodal.

Score S
7 6 5 4 3 2 1

1 4 5 4 6 7 9 N=36

What is the mode?

Uses of The Mode
• In nominal data
– Since we cannot use mean or median

• Also in ordinal, interval or ratio data, along with mean and median ih d di

Problems with The Mode
• Gives us limited information about a distribution
– Might be misleading g g – EXP: 7 7 7 20 20 21 22 22 23 24
• What is the mode here?

The Median (Mdn)
• The score at the 50th percentile, (in the middle) • Used to summarize ordinal or highly skewed interval or ratio scores scores.

Determining the Median
• When data are normally distributed, the median is the…...

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