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 STATISTICS - SEMINAR 3

GROUPING STATISTICAL DATA

1. A real estate agency, located in the central area of a town, intends to open a new office in a

 peripheral area. In order to study the geographical distribution of the apartments sold by the agency,

a researcher randomly selects 30 apartments sold last month. Each apartment is located in one of the

following areas: North!est "N!#, NorthEast "NE#, $outh!est "$!# and $outhEast "$E#. %hedata are presented in the following table:

Apartment Location area Apartment Location area

1   NW   16   NE

2   SE   17   NE

3   SE   18   NW

4   NW   19   NW

5   SW   20   SW

6   NW   21   NE

7   NE   22   NW

8   SW   23   SW

9   NW   24   SE10   SE   25   SW

11   NW   26   NW

12   SE   27   NW

13   SW   28   SE

14   NW   29   NE

15   SW   30   SW

a. Identify the population, the sample, the statistical unit and the &ariable. 'escribe the &ariable and

identify its measurement scale.

 b. (roup the a&ailable data and graph the results.

c. 'etermine the percentage of apartments located in each area and plot the results.

). %he number of orders recei&ed by )* companies last wee+ is presented in the following table:

Company Number of orders Company Number of orders

1   3   14   4

2   5   15   2

3   1   16   3

4   4   17   0

5   4   18   2

6   4   19   0

7   2   20   5

8   5   21   4

9   3   22   2

10   6   23   3

11   4   24   3

12   5   25   1

13   1

a. Identify the population, the sample, the statistical unit and the &ariable. 'escribe the &ariable and

identify its measurement scale.

 b. (roup the a&ailable data and graph the results.

c. 'etermine the relati&e freuencies and the cumulati&e freuencies and construct the relati&e

freuency distribution and the cumulati&e freuency distributions. Interpret the &alues corresponding

to the -th class.

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3. %he annual turno&er "thousand Euros# for *0 companies has the following &alues:

Company Annual turnover (thousand Eur) Company Annual turnover (thousand Eur)

1 )   26 /)

2 )   27 10-

3 /   28 13-

4 /   29 -

5 11-   30

6 3   31 /37 3   32 10*

8 11/   33 1-*

9 -   34

10 -   35

11 /0   36 /-

12 //   37 10

13 1)3   38 1-

14 *   39

15 -   40

16 /1   41 /*

17 101   42 110

18 13)   43 1-

19 /   44 /

20 *   45 /

21 /1   46 /

22 10)   47 113

23 133   48 1-

24 )   49 /

25   50 10)

a. (roup the a&ailable data into eual classinter&als2 graph the results.

 b. 'etermine and plot the relati&e freuencies. Interpret the &alue for the second class.

c. 'etermine and plot the cumulati&e freuencies "ascending and descending#. Interpret the &alues forthe *th class.

d. ompute midpoints for the determined classinter&als.

Observation: use Excel tools for grouping the data.

-. %he length of time it ta+es to assemble a particular electronic component &aries from an employee to

another. 4anagement has collected the time "in minutes# it too+ )0 different employees to assemble

the component. %he information is summari5ed in the following freuency distributions generated by

E6cel:

Bin Frequency % Cumulatie %

10 1 7 *

1* / 7 *0

)0 1 7 **)* 7 7

4ore 7 7 100

a. 8ind the missing &alues.

 b. !hich of the following statements is true:

1. It too+ *09 of all wor+ers e6actly 1* minutes to assemble the component.

). It too+ 1009 of all wor+ers longer than )* minutes to assemble the component.

3. 11 wor+ers assembled the component in )0 minutes or less.

4. It too+ wor+ers )* minutes or longer to assemble the component.

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