Assignment 6
Name:Grace Lin
Class:碩專二甲
Number:Na2c0023
1-1a Answer
The table is given below
Statistics
N
Valid
TOEFL 1: LISTENING
TOEFL 2: STRUCT & WRITING
TOEFL 3: VOCAB & READING
STANDARD SCORE
STANDARD SCORE
STANDARD SCORE
1448
1448
1448
40
40
40
49.62
51.12
51.49
49.73a
51.12a
52.00a
51
54
54
6.665
6.900
6.696
44.428
47.604
44.839
-.074
-.241
-.503
.064
.064
.064
-.293
-.041
.080
.129
.129
.129
Range
39
43
38
Minimum
29
25
28
Maximum
68
68
66
71848
74019
74556
Missing
Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of
Skewness
Kurtosis
Std. Error of Kurtosis
Sum
a. Calculated from grouped data.
1-1b: Answer
Aaccording to negatively skewed distribution, the scores conditions would be: Skewness < 0, and
probably Midpoint< Mean< Median< Mode. It means that the scores are bunched up toward the right side of
the graph, so that the tail goes to the left and toward smaller and negative.
Otherwise, the scores conditions of positively skewed distribution would be: Skewness > 0, and
probably Midpoint> Mean> Median> Mode. It means that the scores are bunched up toward the left side of
the graph, so that the tail goes to the right and toward larger numbers.
When Kurtosis < 0, it is Platykurtic. The distribution is too flat at the peak of the normal curve.
When Kurtosis > 0, it is Leptokurtic. The curve has too many scores collected in the center of the
distribution. When Kurtosis =0, it is Mesokurtic. The curve shows a normal distributed situation.
Skewness=-.074 Kurtosis=-.293 Midpoint=48.5
Mean=49.62
Median=49.73
Mode=51
*Skewness=-.074
-.074<0
*Midpoint< Mean< Median< Mode
*48.5<49.62<49.73<51
From the stitistical data of Tlcstd, we can
reconignize that Tlcstd is negatively skewed. The
scores are bunched up a little bit toward the right
side of the graph, the tail goes to the left.
*Kurtosis=-.293
-293<0
The Kurtosis is Platykurtic. The curve is lower
and flat at the peak of the normal curve.
Skewness=-.241 Kurtosis=-.041 Midpoint=46.5
Mean=51.12
Median=51.12
Mode=54
*Skewness=-.241
-.241<0
*Midpoint< Mean= Median< Mode
*46.5<51.12=51.12 <54.
From the stitistical data of Tswsyd, we can
reconignize that Tswsyd is negatively skewed. The
scores are bunched up a toward the right side of the
graph , the tail goes to the left.
*Kurtosis=-.041
-.041<0
The Kurtosis is Platykurtic. The curve is a little
bit lower than normal, but is higher than the other
two distribution.
Skewness=-.503 Kurtosis=.080
Mean=51.49
Median=52.00
Midpoint=47
Mode=54
*Skewness=-.503
-.503<0
*Midpoint< Mean < Median< Mode
* 47<51.49<52.00 <54.
From the stitistical data of Tvrstd, we can
reconignize that that Tvrstd is negatively skewed.
*Kurtosis=.080 -.080<0
The Kurtosis is Platykurtic. It means that the
curve is lower and flat at the peak of the normal
curve.
2-1a Answer
The table is given below
Statistics
TOEFL STANDARD SCORE
TOTAL
N
Valid
SPEAK:
GRAMMAR
SPEAK:
RATING
PRONUNCIATION
RATING
1448
1304
1314
40
507.43
184
1.93
174
2.13
510.26a
1.93a
2.18a
497b, 523
2
2
58.863
.454
.380
3464.867
.206
.145
-.280
.010
-.919
.064
.068
.067
-.233
-.115
1.731
Std. Error of Kurtosis
.129
.135
.135
Range
337
3
3
Minimum
310
0
0
Maximum
647
3
3
734755
2521
2804
Missing
Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtosis
Sum
a. Calculated from grouped data.
b. Multiple modes exist. The smallest value is shown =497b
Aaccording to negatively skewed distribution, the scores conditions would be: Skewness < 0, and
probably Midpoint< Mean< Median< Mode. It means that the scores are bunched up toward the right side of
the graph, so that the tail goes to the left and toward smaller and negative.
Otherwise, the scores conditions of positively skewed distribution would be: Skewness > 0, and
probably Midpoint> Mean> Median> Mode. It means that the scores are bunched up toward the left side of
the graph, so that the tail goes to the right and toward larger numbers.
When Kurtosis < 0, it is Platykurtic. The distribution is too flat at the peak of the normal curve.
When Kurtosis > 0, it is Leptokurtic. The curve has too many scores collected in the center of the
distribution. When Kurtosis =0, it is Mesokurtic. The curve shows a normal distributed situation.
2-2a Answer
Skewness=-.280
Midpoint=478.5
Median=510.26
Kurtosis=-.233
Mean=507.43
Mode=497 & 523
*Skewness=-.280
-.280<0
*Midpoint< Mean< Median< Mode
*478.5<507.43<510.26 <523
From the stitistical data of Tstdtot, we can
reconignize that Tstdtot is negatively skewed. The
scores are bunched up a little bit toward the right
side of the graph, the tail goes to the left.
*Kurtosis=-.233 -.233<0
The Kurtosis is Platykurtic. The curve is lower
and flat at the peak of the normal curve.
Skewness=.010
Kurtosis=-.115
Midpoint=1.5
Mean=1.93
Median=1.93
Mode=2
*Skewness=.010
0<.010
*Midpoint< Mean= Median< Mode
*1.5<1.93=1.93 <2
From the stitistical data of Spgram, the scores
have met negatively skewed conditions; however,
the Skewness is .010. The curve looks like a little
bit positively skewed. Thus, we can reconignize that
Spgram has a central tendency as a normal
distribution.
*Kurtosis=-.115
-.115<0
The Kurtosis is Platykurtic. The curve is lower
than normal, and flat at the peak of the normal
curve.
Skewness=-.919
Kurtosis=1.731
Midpoint=1.5
Mean=2.13
Median= 2.18a
Mode=2
*Skewness=-.919
* Mode< Mean < Median
* 2<2.13<2.18 .
From the stitistical data: Mode< Mean < Median, it
seems that Sppront is likely to be positively skewed.
However, from the the data of Skewness: -.919, it
shows a negatively skewed situation.
*Kurtosis=1.731 0<1.731
The Kurtosis is Leptokurtic. The curve has many
scores collected in the center of the distribution. It
shows a high narrow peak off the center.
3-1.Answer
Frequencies
Statistics
FCE PAPER 1:
N
CAMB. SCALED SCORE TOTAL
Valid
1359
Missing
129
Mean
25.94
Std. Error of Mean
.133
Median
26.90
27a
Mode
Std. Deviation
4.896
Variance
23.976
Skewness
-.474
Std. Error of Skewness
.066
Kurtosis
.030
Std. Error of Kurtosis
.133
Range
31
Minimum
10
Maximum
40
Sum
a. Multiple modes exist. The smallest value is shown
*Skewness=-.474
-.474<0
Midpoint< Mean< Median< Mode=25< 25.94<26.90<27
FCE PAPER 1 is negatively skewed.
*Kurtosis=.030
0<.030
The Kurtosis is Leptokurtic.
35259
27 28
Frequencies
Statistics
FCE PAPER 2:
N
CAMB. SCALED SCORE TOTAL
Valid
Missing
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Variance
Skewness
1357
131
24.30
.164
24.40
23
6.043
36.518
-.495
Std. Error of Skewness
.066
Kurtosis
.998
Std. Error of Kurtosis
.133
Range
40
Minimum
0
Maximum
40
Sum
*Skewness=-.495 -.495<0
Mode< Mean<Median
23<24.30<24.40
FCE PAPER 2 is negatively skewed.
*Kurtosis=.998 0<.998
The Kurtosis is Leptokurtic.
32979
Frequencies
Statistics
FCE PAPER 4:
N
GRADE
Valid
1344
Missing
144
Mean
1.96
Std. Error of Mean
.027
Median
2.00
Mode
1
Std. Deviation
.996
Variance
.992
Skewness
.561
Std. Error of Skewness
.067
Kurtosis
Std. Error of Kurtosis
-.935
.133
Range
3
Minimum
1
Maximum
4
Sum
2640
Skewness=.561
Mode< Mean < Median =1<1.96<2.00
FCE PAPER 4 is positively skewed. The shape of distribution is not bell-shaped at all.
Kurtosis=-.935
-.935<0
The Kurtosis is Platykurtic.
Frequencies
Statistics
FCE PAPER 5:
N
FLUENCY RATING
Valid
Missing
1379
109
Mean
3.57
Std. Error of Mean
.025
Median
4.00
Mode
4
Std. Deviation
.927
Variance
.860
Skewness
-.399
Std. Error of Skewness
.066
Kurtosis
.106
Std. Error of Kurtosis
.132
Range
5
Minimum
0
Maximum
5
Sum
*Skewness=-.399
-.399<0
Midpoint< Mean< Median= Mode
2.5<3.57<4.00=4
FCE PAPER 5 is negatively skewed.
*Kurtosis=.106 0<.106
The Kurtosis is Leptokurtic.
4927