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 mean median range IQR MAD

Question

Mathematics

Nyasia Frank

18 June, 00:56

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 mean median range IQR MAD

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Answers (1)

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Macy Klein · Answer 1

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

Step-by-step 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

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