Examples of Descriptive Statistics

Roger Ebert Movie Ratings

• Rating Scale (Ordinal): 0*, 0.5*,…,3.5*,4*• 5501 Films (rogerebert.com, circa 3/2006)

Rating Frequency Relative Freq Cumulative Freq

0.0 56 1.02% 1.02%

0.5 76 1.39% 2.41%

1.0 284 5.18% 7.58%

1.5 309 5.63% 13.22%

2.0 907 16.53% 29.75%

2.5 568 10.35% 40.10%

3.0 1684 30.70% 70.80%

3.5 840 15.31% 86.11%

4.0 762 13.89% 100.00%

Ebert Movie Ratings

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Rating

Pe

rce

nt

Note: Median (and Modal) Category is 3.0, LQ is 2.0, UQ is 3.5

Profit Margins of Businesses• Net Profits/Losses (%) for department Stores• 351 Firms (1925): Source: Harvard BBR

Retail Earnings

0

10

20

30

40

50

60

70

80

90

-11 -9 -7 -5 -3 -1 1 3 5 7 9 11

Profits/Loss (%)

Fre

qu

ency

Mean 0.277407

SD 3.846284

IQR 5.065

Percentile  

10 -4.69

25 -2.125

50 0.36

75 2.94

90 5

   

%<mean-2s 2.849003

% in (m-2s,m-s) 13.10541

% in (m-s,m) 31.90883

% in (m,m+s) 37.32194

% in (m+s,m+2s) 13.39031

%>mean+2s 1.424501

Total % 100

Philadelphia Monthly Rainfall 1825-1869 (1/100")

0

20

40

60

80

100

120

140

rain100

Fre

qu

ency

100

200

300

400

500

600

700

800

900

1000

1100

1200

More

Example - Philadelphia Rainfall

340341339 :Amounts Ordered

68.367540

198547198547

)Population as (Treating Months 540

)271()270(

540

1

Myy

y

N

ii

Note: The mean is higher than median as a few very large amounts were observed.

Example - Philadelphia Rainfall (Population)

)9.750,0(2.3837.3672

)3.559,1.176(6.1917.367

6.1918.36708

8.36708540

19822752

19822752)(

25.23575.232468 :Range Quartile-Inter

468 :Percentile75

232.75 :Percentile25

*

2

540

1

2

th

th

i

iy

IQR

Note: 383 (71%) Months lie within 1 of and 518 (96%) within 2