Answer:
Derek's collection :
Mean= 1929
Median= 1930
Range= 54
IQR = 48
MAD= 23.75
Paul's collection:
Mean= 1929
Median= 1929.5
Range= 15
IQR = 6
MAD= 3.5
Explanation:
1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Mean is given by:
(1950+1952+ 1908+1902+1955+1954+1901+1910)/8
=1929
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
from the mean of absolute deviation gives the MAD of the data i.e.
(21+23+21+27+26+25+28+`9)/8
23.75
:arrange the given data to get the range and median
1901 1902 1908 1910 1950 1952 1954 1955
The minimum value is: 1901
Maximum value is: 1955
Range is: Maximum value-minimum value
Range=1955-1901
Range= 54
median is (1910+1950)/2
1930
the lower set of data=
1901 1902 1908 1910
first quartile becomes
1902+1908)/2
Q1=1905
and upper set of data is:
1950 1952 1954 1955
we find the median of the upper quartile or third quartile is:
1952+1954)/2=1953
Q3-Q1=1953-1905=
IQR=48
Paul's collection:
1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Mean is given by:
1929+1935+ 1928+ 1930+ 1925+ 1932+1933+1920)/8
1929
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=0+6+1+1+4+3+4+9/8
28/8
3.5
arrange the data in ascending order we get:
1920 1925 1928 1929 1930 1932 1933 1935
Minimum value= 1920
Maximum value= 1935
Range= 15 ( 1935-1920=15 )
The median is between 1929 and 1930
Hence, Median= 1929.5
Also, lower set of data is:
1920 1925 1928 1929
the first quartile or upper quartile is
1925+1928/2
1926.5
and the upper set of data is:
1930 1932 1933 1935
We have
1932+1933)/2
1932.5
IQR is calculated as:
Q3-Q1
6