# STAT 3010 Lecture Notes - Lecture 12: Confidence Interval, Data Set, Standard Deviation

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Table 12. 1 Descriptive Statistics for the Random Data set of 30 cell phone customers

MNTHREV

INCOME

PRCNTMNTHINC

Mean

$ 52.00

Mean

$ 2,603.11

Mean

2.00%

Mode

$ 40.00

Mode

N/A

Mode

N/A

Standard

Deviation

$ 18.44

Standard Deviation

$ 932.40

Standard Deviation

0.14%

Skewness

-0.13

Skewness

-0.05

Skewness

-0.24

Range

$ 74.00

Range

$ 3,775.36

Range

0.89%

Minimum

$ 14.00

Minimum

$ 781.11

Minimum

1.54%

Q1

$ 40.00

Q1

$ 2,108.07

Q1

1.91%

Median

$ 54.00

Median

$ 2,599.90

Median

2.00%

Q3

$ 64.00

Q3

$ 3,273.47

Q3

2.10%

Maximum

$ 88.00

Maximum

$ 4,556.47

Maximum

2.43%

IQR

$ 24.00

IQR

$ 1,165.39

IQR

0.19%

Count

30

Count

30

Count

30

The random sample of 30 customers in Table 12.1, shows that the average monthly revenue that

the cell phone companies receive is $52.00 while the true monthly revenue is $50.71. The

monthly income of the cell phone customers on average is truly $2,529.02, whereas the random

sample of 30 customers shows that the average income for the customers is $2,603.11. The

average percent of monthly income is truly 2.01%, while the random sample of 30 customers

shows that the average percent of monthly income is 2.00%.

In the random sample of 30 customers the data shows that the most often monthly revenue that

the companies receive is $40. The actual most often occurring monthly revenue that the

companies receive from the 75 customers is $48. In both the random sample of 30 cell phone

customers and the true 75 cell phone customers neither had a most often occurring income or

percent of monthly income.

The random sample of 30 customers shows that the average monthly revenue that the cell phone

companies receive is $18.44 away from the overall average of $52.00. The random sample of

income of the 30 cell phone customers will be $932.40 off from the overall average of

$2,603.11. The true sample of the income of all 75 cell phone customers will be off $802.29

from the overall average of $2,529.02. Percent of income for the random sample of 30 cell phone

customers will be 0.14% off from the overall average of 2.00%.

The random sample of 30 customers in Table 12.1, shows that the middle 50% of the monthly

revenue occurs between $64.00 and $40.00 for a spread of $24.00. The actual data of all 75

customers in Table 3.1, shows that the middle 50% of the monthly revenue occurs between

$62.00 and $40.00 for a spread of $22.00. The random sample of 30 customers in Table 12.1,

shows that the middle 50% of the customers income falls between $3,273.47 and $42,108.07 for

a spread of $1,165.39. The actual data of all 75 customers in Table 3.1, shows that the middle

50% of the customers income falls between $3,101.19 and $1,993.93 for a spread of $1,107.26.

The random sample of 30 customers in Table 12.1, shows that the middle 50% of the percent of

monthly income occurs between 2.10% and 1.91% for a spread of 0.19%. The actual data of all