This preview shows pages 1–5. Sign up to view the full content.
10
20
30
40
50
Count
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
Monthly Returns
Monthly Returns
Monthly Returns
Cengiz Rahmioglu
37479511
STAT 101 HW
1.
(a)
Histograms of Dell, IBM and Microsoft
Dell
Quantiles
100.0%
maximum
0.4982
99.5%
0.4982
97.5%
0.3983
90.0%
0.2570
75.0%
quartile
0.1726
50.0%
median
0.0487
25.0%
quartile
0.0505
10.0%
0.1641
2.5%
0.2851
0.5%
0.3475
0.0%
minimum
0.3475
Moments
Mean
0.0517943
Std Dev
0.1645617
Std Err Mean
0.0126962
upper 95% Mean
0.0768601
lower 95% Mean
0.0267285
N
168
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 10
20
30
40
50
Count
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
Cengiz Rahmioglu
37479511
IBM
Quantiles
100.0
%
maximum
0.3538
99.5%
0.3538
97.5%
0.1949
90.0%
0.1348
75.0%
quartile
0.0707
50.0%
median
0.0132
25.0%
quartile
0.0494
10.0%
0.0911
2.5%
0.1844
0.5%
0.2619
0.0%
minimum
0.2619
Moments
Mean
0.01414
Std Dev
0.0947959
Std Err Mean
0.0073137
upper 95% Mean
0.0285791
lower 95% Mean
0.000299
N
168
10
20
30
40
50
Count
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
Cengiz Rahmioglu
37479511
Microsoft
Quantiles
100.0
%
maximum
0.4078
99.5%
0.4078
97.5%
0.2815
90.0%
0.1525
75.0%
quartile
0.0872
50.0%
median
0.0242
25.0%
quartile
0.0383
10.0%
0.1042
2.5%
0.1611
0.5%
0.3435
0.0%
minimum
0.3435
Moments
Mean
0.0288831
Std Dev
0.1102868
Std Err Mean
0.0085088
upper 95% Mean
0.0456818
lower 95% Mean
0.0120844
N
168
All three histograms are unimodal, normally distributed and symmetrical which means that we could use
the empirical rule to estimate the standard deviation of monthly returns. The histogram of Microsoft has
many outliers and the median return is around 2%. The histogram of IBM has fewer outliers and the
median monthly return is slightly lower. The data in the histogram of Dell doesn’t have that many outliers
but the data is more widespread therefore the standard derivation is larger.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Cengiz Rahmioglu
37479511
Dell
IBM
Microsoft
Mean
0.05179
0.01414
0.02888
Standard Deviation
0.16456
0.09479
0.11028
(b)
For simple data, a histogram summarizes the variation of data and shows where the values concentrate.
These three stock returns data look simple so the mean and the SD are good summaries of the variation of
the returns for the values in the center. However, the mean and the SD fail in predicting extreme events at
the tails of the normal distribution(e.g. market crashes). The bell shaped distribution of the percentage
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 06/22/2008 for the course STAT 101 taught by Professor Heller during the Fall '08 term at UPenn.
 Fall '08
 Heller
 Histograms

Click to edit the document details