Using the data on the “National Cancer Institute Data” Excel spreadsheet, calculate the descriptive statistics indicated below for each of the Race/Ethnicity groups. Refer to your textbook and the Topic Materials, as needed, for assistance in with creating Excel formulas

Alternative Expert Answer and Explanation

Measures of Central Tendency: Mean, Median, and Mode

This paper will elaborate on the descriptive statistical analysis for lung and bronchus cancer for the different racial groups as contained in the National Cancer Institute (2018). The data compiled was from the years 2000 to 2015.

Mean

Mean, also known as average, is the total summation of the values given divided by the number of items in a data set (Grove & Gray, 2018). The following is a mean for the different racial groups:

Mean = Σ/n. where Σ is the total sum of the rate per 100,000, and n is the number of years (16 years).

American Indian / Alaska Native (includes Hispanic)

Mean = 692.4/16 = 43.275

Asian / Pacific Islander (includes Hispanic)

Mean = 616.2/16 = 38.5125

Black (includes Hispanic)

Mean = 1121.1/16 = 70.06875

Hispanic (any race)

Mean = 503.9/16= 31.49375

White (includes Hispanic)

Mean = 1003.6/16=62.725

 Median

Median is defined as the middle number in a data set (Grove & Gray, 2018). Given that the data set used by this paper contains an even number of items, one can get the median by calculating the average of the two middle numbers. The median for the following racial groups is calculated as follows

American Indian / Alaska Native (includes Hispanic)

Median = (43.1+44.6)/2 = 43.85

Asian / Pacific Islander (includes Hispanic)

Median = (38.8+39)/2 = 38.9

Black (includes Hispanic)

Median = (71.2+71.6)/2 =71.4

Hispanic (any race)

Median = (32+32.2)/2 =32.1

White (includes Hispanic)

Median = (63.9+65.2)/2 = 64.55

Mode

Mode is defined as the most repeated number in a data set. In case a modal value can’t be established, one is supposed to group the data values, and using the following formula; the modal value for the group can be identified.

Mode = L + (fm − fm-1) / ((fm − fm-1) + (fm − fm+1)) × W

where:

• L is the lower-class boundary of the modal group
• fmis the frequency of the modal group
• fm-1is the frequency of the group before the modal group
• fm+1is the frequency of the group after the modal group
• w is the group width

American Indian / Alaska Native (includes Hispanic)

Data Groups 31-40 frequency = 6, 41-50 frequency = 9, 51-60 frequency = 1

The modal estimation for this population group is

Mode = 41+ (9 − 6) / ((9 − 6) + (9 − 1)) × 10 = 41 +3/11 x 10 = 43.73

Ans = 43.73

Asian / Pacific Islander (includes Hispanic)

The mode for this population group is 36,6

Black (includes Hispanic)

Data Groups 55-60 frequency = 2, 61-65 frequency =3, 66-70 frequency =2, 71-75 frequency =6, 76–80 frequency = 3

The modal estimation for this population group is

Mode = 71+ (6 − 2) / ((6 − 2) + (6 − 3)) × 5 = 71 +4/7 x 10 = 76.71

Ans = 76.71

Hispanic (any race)

The mode for this population group is 34.1

White (includes Hispanic)

The mode for this population group is 65.8

Measures of Variation:

Variance

Variance is the measurement of how numbers are distributed in a given data set. The following is a formula used to calculate variance;

Σ (Xi – μ) 2 / n.

Where:

Σ is summation of the items

n is the total number of items in the data set.

Xi is the individual figures in the data