1

MAKING GRAPHPOLIGON and HISTOGRAM

2

MAKING GRAPH

POLIGON

3

PERCEPTUAL

SPEED

SCORE

f XcLower Exact

LimitUpper Exact

Limit

64 -67 165.

563.5 67.5

60 - 63 061.

559.5 63.5

56 - 59 257.

555.5 59.5

52 - 55 453.

551.5 55.5

48 - 5111

49.5

47.5 51.5

44 - 47 845.

543.5 47.5

40 - 43 541.

539.5 43.5

36 - 39 337.

535.5 39.5

32 - 35 333.

531.5 35.5

28 - 31 229.

527.5 31.5

24 - 27 125.

523.5 27.5

4

POLIGON

X

f

0 29.5 37.5 45.5 53.5 61.525.5 33.5 41.5 49.5 57.5

65.5

12

10

8

6

4

2

21.5 69.5

Class Interval’s MIDPOINT

5

PERCEPTUAL SPEED

X

f

0 29.5 37.5 45.5 53.5 61.525.5 33.5 41.5 49.5 57.5

65.5

12

10

8

6

4

2

21.5 69.5

6

MAKING GRAPH

HISTOGRAM

7

PERCEPTUAL

SPEED

SCORE

f XcLower Exact

LimitUpper Exact

Limit

64 -67 165.

563.5 67.5

60 - 63 061.

559.5 63.5

56 - 59 257.

555.5 59.5

52 - 55 453.

551.5 55.5

48 - 5111

49.5

47.5 51.5

44 - 47 845.

543.5 47.5

40 - 43 541.

539.5 43.5

36 - 39 337.

535.5 39.5

32 - 35 333.

531.5 35.5

28 - 31 229.

527.5 31.5

24 - 27 125.

523.5 27.5

8

HISTOGRAM

X

f

0 27.5 35.5 43.5 51.5 59.5 67.523.5 31.5 39.5 47.5 55.5

63.5

12

10

8

6

4

2

Class Interval’s EXACT LIMIT

9

POLIGON and HISTOGRAM

X

f

0 27.5 35.5 43.5 51.5 59.5 67.523.5 31.5 39.5 47.5 55.5

63.5

12

10

8

6

4

2

10

THE SHAPE OF A FREQUENCY DISTRIBUTION

Symmetrical

It is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other

Skewed

The scores tend to pile up toward one end of the scale and taper off gradually at the other end

positive negative

11

Describe the shape of distribution for the data in the following table

X f

54321

46311

LEARNING CHECK

The distribution is negatively skewed

12

PERCENTILES and PERCENTILE RANKS

A percentile is a point on the measurement scale below which specified percentage of the cases in the distribution falls

The rank or percentile rank of a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value

When a score is identified by its percentile rank, the score called percentile

13

Suppose, for example that A have a score of X=78 on an exam and we know exactly 60% of the class had score of 78 or lower….…

Then A score X=78 has a percentile of 60%, and A score would be called the 60th percentile

Percentile Rank refers to a percentagePercentile refers to a score

14

X f cf c%

54321

15842

CUMMULATIVE FREQUENCY and CUMULATIVE PERCENTAGE

20191462

100%95%70%30%10%

1.What is the 95th percentile?

Answer: X = 4.5

2.What is the percentile rank for X = 3.5

Answer: 70%

15

INTERPOLATION

It is possible to determine some percentiles and percentile ranks directly from a frequency distribution table

However, there are many values that do not appear directly in the table, and it is impossible to determine these values precisely

16

INTERPOLATIONUsing the following distribution of scores we will find the percentile rank corresponding to X=7X f cf c%

1098765

284641

2523151151

100926044204

Notice that X=7 is located in the interval bounded by the real limits of 6.5 and 7.5

The cumulative percentage corresponding to these real limits are 20% and 44% respectively

17

Scores (X) – percentage7.5

44%7.0 …….. ??

6.520%

STEP 1

For the scores, the width of the interval is 1 point.

For the percentage, the width is 24 points

STEP 2

Our particular score is located 0.5 point from the top of the interval. This is exactly halfway down the interval

STEP 3

Halfway down on the percentage scale would be

½ (24 points) = 12 points

STEP 4For the percentage, the top of the interval is 44%, so 12 points down would be 32%

18

Using the following distribution of scores we will use interpolation to find the 50th percentile

X f cf c%

20 - 2415 - 1910 - 145 - 90 - 4

233102

201815122

10090756010

A percentage value of 50% is not given in the table; however, it is located between 10% and 60%, which are given.

These two percentage values are associated with the upper real limits of 4.5 and 9.5

19

Scores (X) – percentage9.5

60%?? …….. 50%4.510%

STEP 1

For the scores, the width of the interval is 5 point.For the percentage, the width is 50 points

STEP 2The value of 50% is located 10 points from the top of the percentage interval. As a fraction of the whole interval this is 1/5 of the total interval

STEP 3

Using this fraction, we obtain 1/5 (5 points) = 1 pointThe location we want is 1 point down fom the top of the score interval

STEP 4Because the top of the interval is 9.5, the position we want is 9.5 – 1 = 8.5 the 50th percentile = 8.5

20

On a statistics exam, would you rather score at the 80th percentile or at the 40th percentile?

For the distribution of scores presented in the following table,

LEARNING CHECK

X f cf c%40 - 4930 - 3920 - 2910 - 190 - 9

461032

25211552

1008460208

a.Find the 60th percentile

b.Find the percentile rank for X=39.5

c.Find the 40th percentile

d.Find the percentile rank for X=32

21

SCOREFrequen

cy

57 -59 1

54 – 56 3

51 – 53 4

48 – 50 8

45 – 47 9

42 – 44 7

39 – 41 6

36 – 38 5

33 – 35 3

30 – 32 2

27 – 29 1

24 – 26 1

H O M E W O R Ka.Make a polygon or

histogram graph for the distribution of scores presented in the following table

b.Describe the shape of distribution

c.Find the 25th, 50th, and 75th percentile

d.Find the percentile rank for X=25, X=50, and X=75

22

SCORE

Frequency

Xc

Exact Limit

Lower Upper

57 - 59 1 5

8 56.5 59.5

54 – 56 3 5

5 53.5 56.5

51 – 53 4 5

2 50.5 53.5

48 – 50 8 4

9 47.5 50.5

45 – 47 9 4

6 44.5 47.5

42 – 44 7 4

3 41.5 44.5

39 – 41 6 4

0 38.5 41.5

36 – 38 5 3

7 35.5 38.5

33 – 35 3 3

4 32.5 35.5

30 – 32 2 3

1 29.5 32.5

27 – 29 1 2

8 26.5 29.5

24 – 26 1 2

5 23.5 26.5

e.Make a polygon or histogram graph for the distribution

Histogram

PolygonXc

E.L.