grafik, persentil
TRANSCRIPT
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.