Question

Plez help I need this for homework now

Answer 1

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 2

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:

$Mean=\dfrac{1950+1952+1908+1902+1955+1954+1901+1910}{8}\\\\\\Mean=\dfrac{15432}{8}\\\\\\Mean=1929$

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.

  $MAD=\dfrac{21+23+21+27+26+25+28+19}{8}\\\\\\MAD=23.75$

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:

       $Median=\dfrac{1910+1950}{2}\\\\\\Median=\dfrac{3860}{2}\\\\\\Median=1930$

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:

$Q_1=\dfrac{1902+1908}{2}\\\\\\Q_1=\dfrac{3810}{2}\\\\\\Q_1=1905$

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:

$Q_3=\dfrac{1952+1954}{2}\\\\\\Q_3=\dfrac{3906}{2}\\\\\\Q_3=1953$

Hence, IQR is calculated as:

  $IQR=Q_3-Q_1\\\\\\i.e.\\\\\\IQR=1953-1905\\\\\\IQR=48$

Paul's collection:

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

Mean is given by:

$Mean=\dfrac{1929+1935+1928+1930+1925+1932+1933+1920}{8}\\\\\\Mean=1929$

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:

$MAD=\dfrac{6+1+1+4+3+4+9}{8}\\\\\\MAD=\dfrac{28}{8}\\\\\\MAD=3.5$

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:

$Q_1=\dfrac{1925+1928}{2}\\\\\\Q_1=1926.5$

and the upper set of data is:

1930   1932   1933   1935  

Hence, we get:

$Q_3=\dfrac{1932+1933}{2}\\\\\\Q_3=1932.5$

Hence, IQR is calculated as:

$IQR=Q_3-Q_1\\\\\\IQR=1932.5-1926.5\\\\\\IQR=6$