Question

Age of entry Percent of DACA beneficiaries 0 4.5% 1 7.6 2 8.3 3 9.7 4 8 5 8.7 6 7.4 7 7.4 8 6.5 9 6.2 10 5.6 11 5 12 3.9 13 3.5 14 4.1 15 3.7 Please find the Mean, Median, Mode, Range, Standard Deviation, any unusual values and outliers.

Answer 1

To analyze the given data on the age of entry for DACA beneficiaries, we can calculate various statistical measures. Let's start with the Mean, Median, Mode, Range, and Standard Deviation:

1. Mean (Average):

To find the mean, sum up all the values and divide by the total number of values (in this case, 16 values).

Mean = (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15) / 16

Mean = 120 / 16

Mean = 7.5

So, the mean age of entry for DACA beneficiaries is 7.5.

2. Median (Middle Value):

To find the median, first, arrange the data in ascending order, and then find the middle value. Since there are 16 values, the median will be the average of the 8th and 9th values.

Median = (7 + 7) / 2

Median = 7

The median age of entry is 7.

3. Mode (Most Common Value):

The mode is the value that appears most frequently in the data. In this case, there are multiple values with the same highest frequency, so there may be multiple modes. The modes are 3, 4, and 7.

4. Range (Difference Between Maximum and Minimum Values):

Range = Maximum Value - Minimum Value

Maximum Value = 15

Minimum Value = 0

Range = 15 - 0

Range = 15

The range of ages of entry is 15.

5. Standard Deviation (Measure of Data Spread):

To calculate the standard deviation, we need to calculate the variance first. Then, take the square root of the variance.

Variance = Σ(xi - Mean)² / N

where Σ represents the sum, xi are individual values, Mean is the mean calculated earlier, and N is the number of values.

Variance = [(0-7.5)² + (1-7.5)² + ... + (15-7.5)²] / 16

Variance = [1202.5] / 16

Variance = 75.15625

Standard Deviation = √(Variance)

Standard Deviation ≈ √(75.15625)

Standard Deviation ≈ 8.66 (rounded to two decimal places)

The standard deviation is approximately 8.66.

6. Unusual Values and Outliers:

To identify unusual values or outliers, you can use a measure like the z-score, which quantifies how far a data point is from the mean in terms of standard deviations. Values that are more than 2 standard deviations away from the mean can be considered potential outliers.

Calculate the z-score for each data point:

Z = (xi - Mean) / Standard Deviation

Any data point with a |Z| > 2 can be considered an unusual value or potential outlier.

Note: The presence of outliers should be interpreted in the context of the data and the specific analysis being conducted.