Ask Question
18 October, 00:33

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

+1
Answers (1)
  1. 18 October, 00:36
    0
    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

    6
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers