Grafik, Persentil 3i6k54
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- Pages: 22
POLIGON and HISTOGRAM
1
POLIGON 2
SCORE
f
Xc
Lower Exact Limit Upper Exact Limit
64 -67
1
65.5
63.5
67.5
60 - 63
0
61.5
59.5
63.5
56 - 59
2
57.5
55.5
59.5
52 - 55
4
53.5
51.5
55.5
48 - 51
11 49.5
47.5
51.5
44 - 47
8
45.5
43.5
47.5
40 - 43
5
41.5
39.5
43.5
36 - 39
3
37.5
35.5
39.5
32 - 35
3
33.5
31.5
35.5
28 - 31
2
29.5
27.5
31.5
24 - 27
1
25.5
23.5
27.5 3
f 12 10
8 6
Class Interval’s MIDPOINT
4 2
0 4
X 21.5
29.5 37.5 45.5 53.5 61.5 25.5 33.5 41.5 49.5 57.5 65.5
69.5
f 12 10
8 6
4 2
0 5
X 21.5
29.5 37.5 45.5 53.5 61.5 25.5 33.5 41.5 49.5 57.5 65.5
69.5
HISTOGRAM 6
SCORE
f
Xc
Lower Exact Limit Upper Exact Limit
64 -67
1
65.5
63.5
67.5
60 - 63
0
61.5
59.5
63.5
56 - 59
2
57.5
55.5
59.5
52 - 55
4
53.5
51.5
55.5
48 - 51
11 49.5
47.5
51.5
44 - 47
8
45.5
43.5
47.5
40 - 43
5
41.5
39.5
43.5
36 - 39
3
37.5
35.5
39.5
32 - 35
3
33.5
31.5
35.5
28 - 31
2
29.5
27.5
31.5
24 - 27
1
25.5
23.5
27.5 7
f 12 10
8
Class Interval’s EXACT LIMIT
6
4 2
0 8
X 27.5 35.5 43.5 51.5 59.5 67.5 23.5 31.5 39.5 47.5 55.5 63.5
f 12 10
8 6
4 2
0 9
X 27.5 35.5 43.5 51.5 59.5 67.5 23.5 31.5 39.5 47.5 55.5 63.5
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
Symmetrical
positive
Skewed
negative
The scores tend to pile up toward one end of the scale and taper off gradually at the other end 10
Describe the shape of distribution for the data in the following table X 5 4 3 2 1 11
f 4 6 3 1 1
The distribution is negatively skewed
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
12
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
X
f 5 4 3 2 1
cf 1 5 8 4 2
20 19 14 6 2
c% 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%
14
15
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
Using the following distribution of scores we will find the percentile rank corresponding to X=7
X
f
10 9 8 7 6 5 16
2 8 4 6 4 1
cf
c%
25 23 15 11 5 1
100 92 60 44 20 4
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
Scores (X) – percentage 7.5 7.0
6.5
44% …….. ??
20%
STEP 1 For the scores, the width of the interval is 1 point. For the percentage, the width is 24 points
STEP 2
STEP 3
Our particular score is located 0.5 point from the top of the interval. This is exactly halfway down the interval
Halfway down on the percentage scale would be
STEP 4 17
½ (24 points) = 12 points
For the percentage, the top of the interval is 44%, so 12 points down would be 32%
Using the following distribution of scores we will use interpolation to find the 50th percentile X 20 - 24 15 - 19 10 - 14 5-9 0-4
18
f 2 3 3 10 2
cf 20 18 15 12 2
c% 100 90 75 60 10
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
Scores (X) – percentage 9.5 ?? 4.5
60% …….. 50% 10%
STEP 2
19
For the scores, the width of the interval is 5 point. For the percentage, the width is 50 points
STEP 3
The 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 4
STEP 1
Using this fraction, we obtain 1/5 (5 points) = 1 point The location we want is 1 point down fom the top of the score interval Because the top of the interval is 9.5, the position we want is 9.5 – 1 = 8.5 the 50th percentile = 8.5
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,
X
f
40 - 49 30 - 39 20 - 29 10 - 19 0-9 20
cf 4 6 10 3 2
c% 25 21 15 5 2
100 84 60 20 8
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
SCORE
Frequency
57 -59 54 – 56
1 3
51 48 45 42 39 36 33 30 27 24
4 8 9 7 6 5 3 2 1 1
– – – – – – – – – –
53 50 47 44 41 38 35 32 29 26
HOMEWORK a. 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 21
SCORE
Frequency Xc
Exact Limit Lower
Upper
57 - 59
1
58
56.5
59.5
54 – 56
3
55
53.5
56.5
51 – 53
4
52
50.5
53.5
48 – 50
8
49
47.5
50.5
45 – 47
9
46
44.5
47.5
42 – 44
7
43
41.5
44.5
39 – 41
6
40
38.5
41.5
36 – 38
5
37
35.5
38.5
33 – 35
3
34
32.5
35.5
30 – 32
2
31
29.5
32.5
27 – 29
1
28
26.5
29.5
24 – 26
1
25
23.5
26.5
e. Make a polygon or histogram graph for the distribution Polygon Xc
Histogram E.L. 22
1
POLIGON 2
SCORE
f
Xc
Lower Exact Limit Upper Exact Limit
64 -67
1
65.5
63.5
67.5
60 - 63
0
61.5
59.5
63.5
56 - 59
2
57.5
55.5
59.5
52 - 55
4
53.5
51.5
55.5
48 - 51
11 49.5
47.5
51.5
44 - 47
8
45.5
43.5
47.5
40 - 43
5
41.5
39.5
43.5
36 - 39
3
37.5
35.5
39.5
32 - 35
3
33.5
31.5
35.5
28 - 31
2
29.5
27.5
31.5
24 - 27
1
25.5
23.5
27.5 3
f 12 10
8 6
Class Interval’s MIDPOINT
4 2
0 4
X 21.5
29.5 37.5 45.5 53.5 61.5 25.5 33.5 41.5 49.5 57.5 65.5
69.5
f 12 10
8 6
4 2
0 5
X 21.5
29.5 37.5 45.5 53.5 61.5 25.5 33.5 41.5 49.5 57.5 65.5
69.5
HISTOGRAM 6
SCORE
f
Xc
Lower Exact Limit Upper Exact Limit
64 -67
1
65.5
63.5
67.5
60 - 63
0
61.5
59.5
63.5
56 - 59
2
57.5
55.5
59.5
52 - 55
4
53.5
51.5
55.5
48 - 51
11 49.5
47.5
51.5
44 - 47
8
45.5
43.5
47.5
40 - 43
5
41.5
39.5
43.5
36 - 39
3
37.5
35.5
39.5
32 - 35
3
33.5
31.5
35.5
28 - 31
2
29.5
27.5
31.5
24 - 27
1
25.5
23.5
27.5 7
f 12 10
8
Class Interval’s EXACT LIMIT
6
4 2
0 8
X 27.5 35.5 43.5 51.5 59.5 67.5 23.5 31.5 39.5 47.5 55.5 63.5
f 12 10
8 6
4 2
0 9
X 27.5 35.5 43.5 51.5 59.5 67.5 23.5 31.5 39.5 47.5 55.5 63.5
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
Symmetrical
positive
Skewed
negative
The scores tend to pile up toward one end of the scale and taper off gradually at the other end 10
Describe the shape of distribution for the data in the following table X 5 4 3 2 1 11
f 4 6 3 1 1
The distribution is negatively skewed
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
12
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
X
f 5 4 3 2 1
cf 1 5 8 4 2
20 19 14 6 2
c% 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%
14
15
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
Using the following distribution of scores we will find the percentile rank corresponding to X=7
X
f
10 9 8 7 6 5 16
2 8 4 6 4 1
cf
c%
25 23 15 11 5 1
100 92 60 44 20 4
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
Scores (X) – percentage 7.5 7.0
6.5
44% …….. ??
20%
STEP 1 For the scores, the width of the interval is 1 point. For the percentage, the width is 24 points
STEP 2
STEP 3
Our particular score is located 0.5 point from the top of the interval. This is exactly halfway down the interval
Halfway down on the percentage scale would be
STEP 4 17
½ (24 points) = 12 points
For the percentage, the top of the interval is 44%, so 12 points down would be 32%
Using the following distribution of scores we will use interpolation to find the 50th percentile X 20 - 24 15 - 19 10 - 14 5-9 0-4
18
f 2 3 3 10 2
cf 20 18 15 12 2
c% 100 90 75 60 10
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
Scores (X) – percentage 9.5 ?? 4.5
60% …….. 50% 10%
STEP 2
19
For the scores, the width of the interval is 5 point. For the percentage, the width is 50 points
STEP 3
The 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 4
STEP 1
Using this fraction, we obtain 1/5 (5 points) = 1 point The location we want is 1 point down fom the top of the score interval Because the top of the interval is 9.5, the position we want is 9.5 – 1 = 8.5 the 50th percentile = 8.5
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,
X
f
40 - 49 30 - 39 20 - 29 10 - 19 0-9 20
cf 4 6 10 3 2
c% 25 21 15 5 2
100 84 60 20 8
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
SCORE
Frequency
57 -59 54 – 56
1 3
51 48 45 42 39 36 33 30 27 24
4 8 9 7 6 5 3 2 1 1
– – – – – – – – – –
53 50 47 44 41 38 35 32 29 26
HOMEWORK a. 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 21
SCORE
Frequency Xc
Exact Limit Lower
Upper
57 - 59
1
58
56.5
59.5
54 – 56
3
55
53.5
56.5
51 – 53
4
52
50.5
53.5
48 – 50
8
49
47.5
50.5
45 – 47
9
46
44.5
47.5
42 – 44
7
43
41.5
44.5
39 – 41
6
40
38.5
41.5
36 – 38
5
37
35.5
38.5
33 – 35
3
34
32.5
35.5
30 – 32
2
31
29.5
32.5
27 – 29
1
28
26.5
29.5
24 – 26
1
25
23.5
26.5
e. Make a polygon or histogram graph for the distribution Polygon Xc
Histogram E.L. 22
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