Question

A superintendent of a school district was requested to present to the school board demographic data based on the schools within the district. One item that the superintendent had to present was the percent of students who were eligible for free or reduced price lunch (a commonly used proxy for socio-economic status). The following percents were reported for the 40 schools in the district: 53.7 52.4 73.1 49.6 58.4 54.7 54.7 45.0 74.7 79.4 47.2 52.4 21.4 37.5 76.0 67.3 27.1 84.5 39.9 44.9 27.2 31.1 42.9 44.7 24.1 61.4 43.6 58.9 38.1 58.4 34.6 64.9 55.6 56.5 58.8 41.4 35.6 68.1 34.3 75.5 Questions: 1. What is the value of the sample size for this analysis? 2. What is the mean percent of students receiving free or reduced price lunch for this district? 3. What is the median percent of students receiving free or reduced price lunch for this district? 4. What is the lowest percent of students receiving free or reduced price lunch for this district? 5. What is the highest percent of students receiving free or reduced price lunch for this district? 6. What is the value of the range? 7. What is the value of the standard deviation? 8. What is the value of the skewness statistic? 9. What are the values of the 25th, 50th, and 75th percentiles? 10. Present the results as they might appear in an article. This must include a table and narrative statement that provides a thorough description of the central tendency and distribution of the percent of students receiving free or reduced price lunch for this district. Note: The table must be created using your word processing program. Tables that are

Answer 1

1)

sample size = 40

2)

mean= sum of all terms/ number of terms
= 2049.6/40
= 51.24

3)
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
21.4   24.1   27.1   27.2   31.1   34.3   34.6   35.6   37.5   38.1   39.9   41.4   42.9   43.6   44.7   44.9   45.0   47.2   49.6   52.4   52.4   53.7   54.7   54.7   55.6   56.5   58.4   58.4   58.8   58.9   61.4   64.9   67.3   68.1   73.1   74.7   75.5   76.0   79.4   84.5

median = (52.4 + 52.4)/2
= 52.4

4)
min = 21.4
5)
max = 84.5

6)

range = max - min = 84.5 - 21.4 = 63.1