State | 1973 | 1975 | |
1 | Mississippi | 0.2 | 0.6 |
2 | Arkansas | 2.9 | 6.3 |
3 | Montana | 3.1 | 9.9 |
4 | Maine | 3.5 | 9.5 |
5 | South California | 3.8 | 10.3 |
6 | Tennessee | 4.2 | 19.2 |
7 | Texas | 6.8 | 19.1 |
8 | Arizona | 6.9 | 15.8 |
9 | Ohio | 7.3 | 17.9 |
10 | Nebraska | 7.3 | 14.3 |
11 | Virginia | 7.8 | 18.0 |
12 | Iowa | 8.8 | 14.7 |
13 | Massachusetts | 10.0 | 25.7 |
14 | Pennsylvania | 12.1 | 18.5 |
15 | Colorado | 14.4 | 24.6 |
16 | Florida | 15.8 | 30.5 |
71 | Michigan | 18.7 | 20.3 |
18 | Hawaii | 26.3 | 31.6 |
19 | California | 30.8 | 33.6 |
20 | New York | 53.5 | 40.7 |
Source: U.S. Bureau of the Census. 1977. Statistical Abstract of the United States: 1977. Washington, DC: Government Printing Office, 1977.
To find:
The mean, median, range, interquartile range and standard deviation for the given years.
Given:
The following table shows the rates of abortion per 100, 000 women for 20 states in 1973 and 1975.
State | 1973 | 1975 |
Mississippi | 0.2 | 0.6 |
Arkansas | 2.9 | 6.3 |
Montana | 3.1 | 9.9 |
Maine | 3.5 | 9.5 |
South California | 3.8 | 10.3 |
Tennessee | 4.2 | 19.2 |
Texas | 6.8 | 19.1 |
Arizona | 6.9 | 15.8 |
Ohio | 7.3 | 17.9 |
Nebraska | 7.3 | 14.3 |
Virginia | 7.8 | 18.0 |
Iowa | 8.8 | 14.7 |
Massachusetts | 10.0 | 25.7 |
Pennsylvania | 12.1 | 18.5 |
Colorado | 14.4 | 24.6 |
Florida | 15.8 | 30.5 |
Michigan | 18.7 | 20.3 |
Hawaii | 26.3 | 31.6 |
California | 30.8 | 33.6 |
New York | 53.5 | 40.7 |
Formula used:
Let the data values be
The formula to calculate median for even number of terms is given by,
The formula to calculate interquartile range is given by,
Where,
And,
The formula to calculate range is given by,
The formula to calculate mean is given by,
The formula to calculate standard deviation is given by,
Where,
Calculation:
For the year 1973,
Arrange the data in the increasing order.
The data in increasing order is given by,
S. No | Rate |
1 | 0.2 |
2 | 2.9 |
3 | 3.1 |
4 | 3.5 |
5 | 3.8 |
6 | 4.2 |
7 | 6.8 |
8 | 6.9 |
9 | 7.3 |
10 | 7.3 |
11 | 7.8 |
12 | 8.8 |
13 | 10 |
14 | 12.1 |
15 | 14.4 |
16 | 15.8 |
17 | 18.7 |
18 | 26.3 |
19 | 30.8 |
20 | 53.5 |
The number of terms is 20, which is even.
The formula to calculate median for even number of terms is given by,
Substitute 20 for
The value corresponding to
The required median is,
The highest rate is 53.5 and the lowest cost is 0.2.
The range is given by,
Substitute 53.5 for highest rate and 0.2 for lowest rate in the above mentioned formula,
The size of the population is 20.
The value at
And,
The value at
The formula to calculate interquartile range is given by,
Substitute 3.8 for
The mean is given by,
Substitute 20 for
Consider the following table of sum of squares,
0.2 | 144.2401 | |
2.9 | 86.6761 | |
3.1 | 82.9921 | |
3.5 | 75.8641 | |
3.8 | 70.7281 | |
4.2 | 64.1601 | |
6.8 | 29.2681 | |
6.9 | 28.1961 | |
7.3 | 24.1081 | |
7.3 | 24.1081 | |
7.8 | -4.41 | 19.4481 |
8.8 | 11.6281 | |
10 | 4.8841 | |
12.1 | 0.0121 | |
14.4 | 2.19 | 4.7961 |
15.8 | 3.59 | 12.8881 |
18.7 | 6.49 | 42.1201 |
26.3 | 14.09 | 198.5281 |
30.8 | 18.59 | 345.5881 |
53.5 | 41.29 | 1704.864 |
From equation
Square the both sides of the equation.
Proceed in the same manner to calculate
The standard deviation is given by,
From equation
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