1. Which numbers describe the Center of the Data? (5 points) a. 1006.891 and 110

Question

1. Which numbers describe the Center of the Data? (5 points) a. 1006.891 and 1102 b. 968 and 298.7546 c. 1006.891 and 968 d. 298.7546 and 1102 e. None of these 2. How many subjects participated in this study? (5 points) a. 1532 b. 1102 c. 46317 d. 46 3. What is the approximate variation of the murders in Florida data? (5 points) a. 1102 b. 298.75 c. 44.049 d. 968 e. None of these 4. What was the lowest number of murders recorded? (5 points) a. 46 b. 430 c. 1532 d. 934 e. None of these 5. Which of the following quantities is NOT sensitive toward outliers? (5 points) a. Standard Deviation b. Median c. Mean d. Minimum e. Maximum Florida Violent Crime Murder and nonnegligent Manslaughter 1960 537 Florida Violent Crime Murder and nonnegligent Manslaughter 1961 487 Florida Violent Crime Murder and nonnegligent Manslaughter 1962 430 Florida Violent Crime Murder and nonnegligent Manslaughter 1963 473 Florida Violent Crime Murder and nonnegligent Manslaughter 1964 499 Florida Violent Crime Murder and nonnegligent Manslaughter 1965 528 Florida Violent Crime Murder and nonnegligent Manslaughter 1966 622 Florida Violent Crime Murder and nonnegligent Manslaughter 1967 640 Florida Violent Crime Murder and nonnegligent Manslaughter 1968 741 Florida Violent Crime Murder and nonnegligent Manslaughter 1969 730 Florida Violent Crime Murder and nonnegligent Manslaughter 1970 870 Florida Violent Crime Murder and nonnegligent Manslaughter 1971 943 Florida Violent Crime Murder and nonnegligent Manslaughter 1972 934 Florida Violent Crime Murder and nonnegligent Manslaughter 1973 1190 Florida Violent Crime Murder and nonnegligent Manslaughter 1974 1201 Florida Violent Crime Murder and nonnegligent Manslaughter 1975 1140 Florida Violent Crime Murder and nonnegligent Manslaughter 1976 913 Florida Violent Crime Murder and nonnegligent Manslaughter 1977 869 Florida Violent Crime Murder and nonnegligent Manslaughter 1978 959 Florida Violent Crime Murder and nonnegligent Manslaughter 1979 1094 Florida Violent Crime Murder and nonnegligent Manslaughter 1980 1397 Florida Violent Crime Murder and nonnegligent Manslaughter 1981 1532 Florida Violent Crime Murder and nonnegligent Manslaughter 1982 1419 Florida Violent Crime Murder and nonnegligent Manslaughter 1983 1209 Florida Violent Crime Murder and nonnegligent Manslaughter 1984 1274 Florida Violent Crime Murder and nonnegligent Manslaughter 1985 1306 Florida Violent Crime Murder and nonnegligent Manslaughter 1986 1381 Florida Violent Crime Murder and nonnegligent Manslaughter 1987 1381 Florida Violent Crime Murder and nonnegligent Manslaughter 1988 1426 Florida Violent Crime Murder and nonnegligent Manslaughter 1989 1415 Florida Violent Crime Murder and nonnegligent Manslaughter 1990 1389 Florida Violent Crime Murder and nonnegligent Manslaughter 1991 1258 Florida Violent Crime Murder and nonnegligent Manslaughter 1992 1218 Florida Violent Crime Murder and nonnegligent Manslaughter 1993 1234 Florida Violent Crime Murder and nonnegligent Manslaughter 1994 1175 Florida Violent Crime Murder and nonnegligent Manslaughter 1995 1047 Florida Violent Crime Murder and nonnegligent Manslaughter 1996 1087 Florida Violent Crime Murder and nonnegligent Manslaughter 1997 1022 Florida Violent Crime Murder and nonnegligent Manslaughter 1998 977 Florida Violent Crime Murder and nonnegligent Manslaughter 1999 869 Florida Violent Crime Murder and nonnegligent Manslaughter 2000 913 Florida Violent Crime Murder and nonnegligent Manslaughter 2001 884 Florida Violent Crime Murder and nonnegligent Manslaughter 2002 921 Florida Violent Crime Murder and nonnegligent Manslaughter 2003 934 Florida Violent Crime Murder and nonnegligent Manslaughter 2004 956 Florida Violent Crime Murder and nonnegligent Manslaughter 2005 893

Explanation / Answer

We are given the following the data

Florida Violent Crime Murder and nonnegligent Manslaughter

Year(column A) no. of murders(column B)

1960 537

1961 487

1962 430

1963 473

1964 499

1965 528

1966 622

1967 640

1968 741

1969 730

1970 870

1971 943

1972 934

1973 1190

1974 1201

1975 1140

1976 913

1977 869

1978 959

1979 1094

1980 1397

1981 1532

1982 1419

1983 1209

1984 1274

1985 1306

1986 1381

1987 1381

1988 1426

1989 1415

1990 1389

1991 1258

1992 1218

1993 1234

1994 1175

1995 1047

1996 1087

1997 1022

1998 977

1999 869

2000 913

2001 884

2002 921

2003 934

2004 956

2005 893

From the above data we find centers of the data namely, mean, median and mode

If we represents the no. of murders in any year by the variable x

The total murders from the year 1960 to 2005 = x = 46317

The total no. of years from which the data has been taken represented by N= (2005-1960)+1 = 46

Therefore the mean is,

   Mean= x/N= 46317/46 = 1006.891

To find median first we arrange all the data in column B (no. of murders) in increasing order

After arrangement the data looks like this

               430          473         487         499         528         537         622         640         730         741         869 869         870         884         893 913         913         921         934         934         943         956         959         977         1022       1047       1087       1094       1140       1175 1190       1201       1209       1218       1234       1258       1274       1306       1381       1381       1389       1397       1415       1426       1532

Total no. of data, N = 46   an even number

Therefore the median = [(N/2)th term + (N/2 +2)th term]/2 = [23th term +24th term]/2

NOTE: these terms are taken from the rearranged data and not the original data

From the rearranged data

               430          473         487         499         528         537         622         640         730         741         869         869         870         884         893 913         913         921         934         934         943         956         959         977         1022       1047       1087       1094       1140       11 1190       1201       1209       1218       1234       1258       1274       1306       1381       1381       1389       1397       1415       1426       1532

23rd term = 959

And 24rth term = 977

Therefore, median = (959 + 977)/2 = 968

Since mode is the data that appears most often in a given data set

Therefore form the rearranged data set we find that the values 869, 913, 934 and 1381 all appear twice

Recall that mode may not be unique for a set of data hence , the modes for the given data set are 869, 913, 934 and 1381

ANSWER TO PART 1

Since the centers of data are mean , median and mode which we calculated above for the given data set which are

Mean = 1006.891 and median = 968

hence the answer is

       c. 1006.891 and 968

ANSWER TO PART 2

The total number of murders in all the years in the data provided is the total number of subjects which participated in the study

We calculated, total no. of murders, x = 46317

Hence the correct option is

c. 46317

ANSWER TO PART 3

The approximate variation of the murders in Florida data is expressed by the standard deviation of the given data set, as s.d measures the dispersion from the mean value of the data.

Calculating the standard deviation by formula

s.d = (1/(N-1))[(x1-)2+(x2-)2+………..+(xN-)2]

s.d = 298.75

hence the correct option is

b. 298.75

ANSWER TO PART 4

From the rearranged table(which is in increasing order) of data we find the the first term i.e., lowest value is 430

Hence the correct option is

       b. 430

ANSWER TO PART 5

Recall that an outlier is an observation that is distant from other observations in the distribution.

The minimum and maximum values in the data set can be too small or too large(repectively) compared to others values of the data set. One or two such values can have considerable effect on the mean making it sensitive to the outliers. Hence, the minimum value, maximum value and mean all are sensitive to outliers. Since standard deviation is the measure of dispersion in the data set, a single outlier can affect its value by raising the standard deviation, therefore standard deviation too, is sensitive to outliers.

Median is the middle value of the distribution, therefore, it is least affected by the outliers

Hence, the correct option is

b. Median

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