Question

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Hours Worked Last Week Frequency Cumulative Percentage Percentage 3 9.4 9.4 2 6.3 15.6 1 3.1 18.8 1 3.1 21.9 30 9.4 31.3 3.1 34.4 40 14 43.8 78.1 6.3 84.4 50 2 3.1 87.5 1 55 3.1 90.6 1 60 3.1 93.8 1 96.9 64 3.1 1 70 3.1 100.0 1 Total 32 100.0 1. What is the level of measurement, mode, and median for "hours worked last week"? 2. Construct quartiles for weeks worked last year. What is the 25th percentile? The 50th percentile? The 75th percentile? Why don't you need to calculate the 50th percentile to answer this question? 4. GSS 2014 respondents were asked, "Some people say the following things are important for being truly American. Others say they are not important. How important do you think each of the following is-to be a Christian?" Responses were measured on a 4-point scale: very important, fairly important, not very important, and not important at all Important to Be a Christian Frequency Very important 136 Fairly important 49 Not very important 89 Not important at all 118 Total 392 1. What is the modal category? 2. Calculate the median category for this variable. 3. Identify which categories contain the 20th and 80th percentiles. 5. Monitoring the Future is a longitudinal study of the behaviors and attitudes of American secondary school students. Data from the 2014 survey are presented, measuring the frequency of eating breakfast (an indicator of a healthy lifestyle) by student race. The table features a different format, presenting frequencies and percentages in a single column.

Answer 1

Solution: For the distribution of "Number of hours worked last week"

1) i) The level of measurement is ordinal as the number of hours worked is arranged in increasing order.

ii) The mode value is 40 hours

iii) The median value is 40 hours( both in terms of cumulative frequency as well as cumulative percentage)

2) The quartiles for "Number of hours worked last week" are

Q₁= variable value corresponding to cumulative frequency $\geqslant$ 1*(N+1/4)^th value = 30 hours

Q₂= variable value corresponding to cumulative frequency $\geqslant$ 2*(N+1/4)^th value = 40 hours

Q₃= variable value corresponding to cumulative frequency $\geqslant$ 3*(N+1/4)^th value = 50 hours

P₂₅= variable value corresponding to cumulative frequency $\geqslant$ 25*(N+1/100)^th value = 30 hours

P₅₀= variable value corresponding to cumulative frequency $\geqslant$ 50*(N+1/100)^th value = 40 hours

P₇₅= variable value corresponding to cumulative frequency $\geqslant$ 75*(N+1/100)^th value = 50 hours

Here the median value = 50th percentile value. Hence we do not need to compute 50th percentile.

Solution for question 4:

1. The modal category is "very important"

2. The median category is "not very important"

3. The "very important" category contains 20th percentile and the "not important at all" category contains the 80th percentile.

regarding the question 5, no data has been provided.

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