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Answers:
(a) The enrollment data is a population
(b) <span><span>Mean: 22,150.62
</span><span>(c) Median: 18,670
</span><span>(d) Range: 57,776
(e) Standard Deviation: </span></span><span>14,258.49
Explanations:
(a) As we noticed in the problem, the enrollment data is used for the study of the number of enrollments in all of the public universities in Ohio. Since the given enrollment data contains the number of enrollments in all of the public univeristies in Ohio, the enrollment data is a population.
(b) To compute the mean, we get the sum of all the data points and divide it by the number of data points.
Since,
Sum of all data points = </span><span> 1725 + 4344 + 14655 + 15693 + 17338 + 18641 18670 + 20251 + 20839 + 25612 + 34187 + 36502 </span> +<span> <span>59,501
</span></span>Sum of all data points = <span> <span> 287,958
and the number of data points = 13,
mean = </span></span>287,958 ÷ 13 = <span> <span> 22,150.62
(c) The median is computed when the data points are arranged from least to greatest and it is equal to either:
>> the middle number - if the number of data points is an odd number, or</span></span>
>> the average of 2 middle numbers - if the number of data points is an even number
In the enrollment data, when the data points are arranged from lowest to highest, the following is the result:
1725, 4344, 14655, 15693, 17338, 18641, 18670, 20251, 20839, 25612, 34187, 36502, 59,501
Since the number of data points is 13 and 13 is an odd number, we find the middle number, which is the 7th lowest number = 18670.
Hence, the median is 18670.
(d) The range of the data is the difference between the highest data point and the lowest data point.
Since the highest data point is 59,501, the lowest data point is 1725 and their difference is 59,501 - 1725 =<span> 57,776. The range of the enrollment data is </span><span> <span> 57,776.
(e) To compute for standard deviation,
>> First, we compute the squares of all the data points and find their sum:
Sum of the squares of data points </span></span>= 1725² + 4344² + 14655² + 15693² + 17338² + 18641² + 18670² + 20251² + 20839² + 25612² + 34187² + 36502² + 59,501²
Sum of the squares of data points = <span> <span> 9,021,404,700
</span></span>
>> Then, we compute the average of the squares of all data points by dividing the sum of the squares of all data points by the number of data points:
Average of the squares
= Sum of the squares of data points ÷ number of data points
= 9,021,404,700 ÷ 13
Average of the squares = <span><span>693,954,207.69231
</span> </span>
>> Finally, the standard deviation is the square root of the difference of the average of squares and the square of the average of the data points:
where:
So, the standard deviation is given by
Therefore, the standard deviation is <span><span><span>14,258.49.</span></span></span>
(a) The enrollment data is a population
(b) <span><span>Mean: 22,150.62
</span><span>(c) Median: 18,670
</span><span>(d) Range: 57,776
(e) Standard Deviation: </span></span><span>14,258.49
Explanations:
(a) As we noticed in the problem, the enrollment data is used for the study of the number of enrollments in all of the public universities in Ohio. Since the given enrollment data contains the number of enrollments in all of the public univeristies in Ohio, the enrollment data is a population.
(b) To compute the mean, we get the sum of all the data points and divide it by the number of data points.
Since,
Sum of all data points = </span><span> 1725 + 4344 + 14655 + 15693 + 17338 + 18641 18670 + 20251 + 20839 + 25612 + 34187 + 36502 </span> +<span> <span>59,501
</span></span>Sum of all data points = <span> <span> 287,958
and the number of data points = 13,
mean = </span></span>287,958 ÷ 13 = <span> <span> 22,150.62
(c) The median is computed when the data points are arranged from least to greatest and it is equal to either:
>> the middle number - if the number of data points is an odd number, or</span></span>
>> the average of 2 middle numbers - if the number of data points is an even number
In the enrollment data, when the data points are arranged from lowest to highest, the following is the result:
1725, 4344, 14655, 15693, 17338, 18641, 18670, 20251, 20839, 25612, 34187, 36502, 59,501
Since the number of data points is 13 and 13 is an odd number, we find the middle number, which is the 7th lowest number = 18670.
Hence, the median is 18670.
(d) The range of the data is the difference between the highest data point and the lowest data point.
Since the highest data point is 59,501, the lowest data point is 1725 and their difference is 59,501 - 1725 =<span> 57,776. The range of the enrollment data is </span><span> <span> 57,776.
(e) To compute for standard deviation,
>> First, we compute the squares of all the data points and find their sum:
Sum of the squares of data points </span></span>= 1725² + 4344² + 14655² + 15693² + 17338² + 18641² + 18670² + 20251² + 20839² + 25612² + 34187² + 36502² + 59,501²
Sum of the squares of data points = <span> <span> 9,021,404,700
</span></span>
>> Then, we compute the average of the squares of all data points by dividing the sum of the squares of all data points by the number of data points:
Average of the squares
= Sum of the squares of data points ÷ number of data points
= 9,021,404,700 ÷ 13
Average of the squares = <span><span>693,954,207.69231
</span> </span>
>> Finally, the standard deviation is the square root of the difference of the average of squares and the square of the average of the data points:
where:
So, the standard deviation is given by
Therefore, the standard deviation is <span><span><span>14,258.49.</span></span></span>