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Mode: Are there two students who have the same number of children (could be zero)? If yes that’s the mode If not there is no mode Median: Put all five numbers in a row from lowest to greatest The one in the middle is the median Range: Take the difference of the greatest minus the lowest and that is the range

Mean Median Mode and Range - Paulding County School District

Notes 8/16/16 10 August 16 2016 Dec 2­3:05 PM How do I find the mode? Step 1: Arrange the data in order from least to greatest Step 2: The mode is the number that occurs the most often There may be one mode more than one mode or no mode Mode Money Spent on Gifts Name Tony Kara Lisa Ray Jay Money $5 $9 $4 $6 $5

Use Your Shoe

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Note that the number of scores on either side of the mode does not have to be equal It might be equal but it doesn’t have to be In this example there are three scores below the mode and five scores above the mode Nor does the numerical distance of the scores from the mode on either side of the mode have to balance

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CENTRALCENTRAL

TENDENCY:TENDENCY:Mean, Median, Mode

New Statistical Notation

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

Central Tendency

What Is Central Tendency?

• A score that indicates where the centerof the distribution tendsto be located. • Tells us about the shape and nature of the dbd istri b ution.

Measures of Central Tendency

•Mode•

Median

Median

• Mean

The Mode

• The most frequently occurring score.•

Typically useful in describing central

Typically

useful in describing central tendency when the scores reflect a nominal l f sca le o f measurement.

The Mode

• It does not make sense to take the average in nominal data.

Gender: 67 males --- 1

50 females ---- 2

14 14 13 15 11 1513 10 12 13 14 13

14 15 17 14 14 15

S f 17

What is the mode?

1 S core f

171615

What is the mode? 104

151413

464

131211

411
1110
11 N=18

Unimodal Distributions

Wh l hWh

en a po l ygon h as one hump (such as on the normal curve) the distribution is called unimodal.

14 14 13 15 11 1215 10 12 13 12 13

15 15 17 12 15 12

S f 17

What is the mode?

1 S core f

171615

What is the mode? 105

151413

523

131211

351
1110
11 N=18

Bimodal Distributions

Wh di ib iWh

en a di str ib ut i on has two scores that are most frequently d occurring, it is calle d bimoda l

Example

S f 7 1 S core f

What is the mode?

765
145
543
546
321
679
1 9 N=36

Uses of The Mode

• In nominal data - Since we cannot use mean or median • Also in ordinal, interval or ratio data, along ih d di w i t h mean an d me di an

Problems with The Mode

• Gives us limited information about a distribution Mi g ht be misleadin g gg - EXP: 7 7 7 20 20 21 22 22 23 24

What is the mode here?

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 scoresinterval or ratio scores

Determining the Median

• When data are normally distributed, the median is hhd t h e same score as t h e mo d e. W hen data are not normall y distributed follow the

Wy,following procedure:

Arrange the scores from highest to the lowest.Arrange the scores from highest to the lowest. - If there are an odd number of scores, the median is the score in the middle p osition. p - If there are an even number of scores, the median is the average of the two scores in the middle.

The Median (Mdn)

• A better measure of central tendency than mode - Only one score can be the median- It will always be around where the most scores are.

EXP: 12334791011

EXP: 1 2 3 3 4 7 9 10 11 EXP: 1 2 3 3 4 6 7 9 1 0 11 EXP: 3 3 4 6 7 9 0

14 14 13 15 11 1513 10 12 13 14 13

14 15 17 14 14 15

S f 17

What is the median?

1 S core f

171615

What is the median? 104

151413

464

131211

411
1110
11 N=18

The Mean

• The score located at the mathematical center of a distributionUdt i it l tidti U se d t o summar i ze i n t erva l or ra ti o d a t a i n situations when the distribution is symmetrical and unimodal

Determining the Mean

• The formula for the sample mean is X N X X N

14 14 13 15 11 1513 10 12 13 14 13

14 15 17 14 14 15

S f 17

What is the mean?

1 S core f

171615

What is the mean? 104

151413

464

131211

411
1110
11 N=18

Central Tendency

and

NlDiibiN

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