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The data sets show the years of the coins in two collections.

Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910

Paul's collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920

Find the indicated measures of center and the measures of variation for each data set. Round your answer to the nearest hundredth, if necessary.

Derek's

collection

Paul's

collection
find the
mean
median
range
IQR
MAD
for Derek's collection and Paul's collection

Respuesta :

tangito
Firstly, put Derek and Paul's collection together:
1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910, 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920

1950+1952+1908+1902+1955+1954+ 1901+1910+1929+1935+1928+1930+ 1925+ 1932+1933+1920
=30864
=30864÷16
=1929
∴the mean is 1929.

Median:
1901, 1902, 1908, 1910, 1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935,
1950, 1952, 1954, 1955
1930÷1929
=1.0005184
= Median

Range:
1955-1901
=54
∴the range is 54.





Answer:

for Derek's collection :

Mean= 1929

Median= 1930

Range= 54

IQR = 48

MAD= 23.75

for Paul's collection:

Mean= 1929

Median= 1929.5

Range= 15

IQR = 6

MAD= 3.5

Step-by-step explanation:

Derek's collection:

1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910

Mean is given by:

[tex]Mean=\dfrac{1950+1952+1908+1902+1955+1954+1901+1910}{8}\\\\\\Mean=\dfrac{15432}{8}\\\\\\Mean=1929[/tex]

Now absolute deviation from mean is:

|1950-1929|= 21

|1952-1929|= 23

|1908-1929|= 21

|1902-1929|= 27

|1955-1929|= 26

|1954-1929|= 25

|1901-1929|= 28

|1910-1929|= 19

and the mean of these absolute deviation gives the MAD of the data i.e.

  [tex]MAD=\dfrac{21+23+21+27+26+25+28+19}{8}\\\\\\MAD=23.75[/tex]

Now, on arranging the data in increasing order we get:

    1901   1902    1908   1910    1950  1952    1954   1955

The least value is: 1901

Maximum value is: 1955

Range is: Maximum value-Least value

          Range=1955-1901

          Range= 54

Also, the median lie between 1910 and 1950 and is calculated as:

       [tex]Median=\dfrac{1910+1950}{2}\\\\\\Median=\dfrac{3860}{2}\\\\\\Median=1930[/tex]

Also, the lower set of data is:

   1901   1902    1908   1910

and the median of lower set of data also known as first quartile or lower quartile is:

[tex]Q_1=\dfrac{1902+1908}{2}\\\\\\Q_1=\dfrac{3810}{2}\\\\\\Q_1=1905[/tex]

and upper set of data is:

1950  1952    1954   1955

and the median of upper set of data i.e. upper quartile or third quartile is:

[tex]Q_3=\dfrac{1952+1954}{2}\\\\\\Q_3=\dfrac{3906}{2}\\\\\\Q_3=1953[/tex]

Hence, IQR is calculated as:

  [tex]IQR=Q_3-Q_1\\\\\\i.e.\\\\\\IQR=1953-1905\\\\\\IQR=48[/tex]

Paul's collection:

1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920

Mean is given by:

[tex]Mean=\dfrac{1929+1935+1928+1930+1925+1932+1933+1920}{8}\\\\\\Mean=1929[/tex]

Now absolute deviation from mean is:

|1929-1929|=0

|1935-1929|= 6

|1928-1929|= 1

|1930-1929|= 1

|1925-1929|= 4

|1932-1929|= 3

|1933-1929|= 4

|1920-1929|= 9

Hence, we get:

[tex]MAD=\dfrac{6+1+1+4+3+4+9}{8}\\\\\\MAD=\dfrac{28}{8}\\\\\\MAD=3.5[/tex]

Now, on arranging the data in increasing order we get:

1920   1925   1928   1929   1930   1932   1933   1935  

Least value= 1920

Maximum value= 1935

Range=  15 ( Since, 1935-1920=15 )

The median lie between 1929 and 1930

Hence, Median= 1929.5

Also, lower set of data is:

1920   1925   1928   1929  

and median of lower set of data is the first quartile or upper quartile and is calculated as:

[tex]Q_1=\dfrac{1925+1928}{2}\\\\\\Q_1=1926.5[/tex]

and the upper set of data is:

1930   1932   1933   1935  

Hence, we get:

[tex]Q_3=\dfrac{1932+1933}{2}\\\\\\Q_3=1932.5[/tex]

Hence, IQR is calculated as:

[tex]IQR=Q_3-Q_1\\\\\\IQR=1932.5-1926.5\\\\\\IQR=6[/tex]

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