Central tendency and spread homework answers

Rough Draft Qualitative Research Critique And Ethical Considerations

Summary and Descriptive Statistics

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SUMMARY AND DESCRIPTIVE STATISTICS 5

Summary and Descriptive Statistics

Measures of Central Tendency

The measures of central tendency include the mean, the mode, and the median. They describe the center point of a data set (Aldous, 2016). For this data, we calculate the measures of central tendency for the race/ethnic groups. We use the AVERAGE, MEDIAN, and MODE functions in Excel to calculate the mean, median, and mode, respectively. The following is a summary for the measures:

American Indian / Alaska Native (includes Hispanic)

Asian / Pacific Islander (includes Hispanic)

Black (includes Hispanic)

Hispanic (any race)

White (includes Hispanic)

Mean

43.275

38.5125

70.06875

31.49375

62.725

Median

43.85

38.9

71.4

32.1

64.55

Mode

N/A

36.6

N/A

34.1

65.8

From the table above, the Black (includes Hispanic) has the highest mean rate per 100,000 among the ethnic groups while Hispanic (any race) has the lowest mean rate per 100,000. Similarly, the Black (includes Hispanic) has the highest median rate per 100,000 among the ethnic groups while Hispanic (any race) has the lowest mean rate per 100,000. American Indian / Alaska Native (includes Hispanic) and the Black (includes Hispanic) do not have a mode, while the mode for the Asian / Pacific Islander (includes Hispanic), Hispanic (any race), and White (includes Hispanic) have modes of 36.6, 34.1, and 65.8, respectively.

Measures of Dispersion

They include the variance, the standard deviation, and the range. They measure how the data is spread (Aldous, 2016). In this case we measure the sample values assuming the data is a sample. The following is the summary:

American Indian / Alaska Native (includes Hispanic)

Asian / Pacific Islander (includes Hispanic)

Black (includes Hispanic)

Hispanic (any race)

White (includes Hispanic)

Sample Variance

27.71933333

5.679833333

45.42895833

8.399291667

26.162

Sample Standard deviation

5.264915321

2.383240091

6.740100766

2.898153148

5.114880253

Range

19.7

7.8

21.6

9

15.6

From the values, Black (includes Hispanic) have the highest variance, standard deviation, and range while Asian / Pacific Islander (includes Hispanic) have the lowest variance, standard deviation, and range of the rates per 100000. This means Blacks (includes Hispanic) have the largest spread of the rates per 100,000 while Asian / Pacific Islander (includes Hispanic) have the smallest spread of the rates per 100,000.

References

Aldous, D.J. (2016). Descriptive Statistics. New Rochelle, N.Y: Magnum Publishing