Use three significant figures (decimal places) when reporting answers that include decimals.

1. 6 points.Imagine that 400 students take a quiz that is worth 10 points. 5% of the students get 5 points, 10% get 6 points, 25% get 7 points, and 10% get 8 points, 40% get 9 points, and 10% get 10 points.

a. What is the mean score on the quiz? Include formula used to solve the problem.2 points.

b. What is the median score?1 point

c. What is the modal score (the mode)?1 point

d. If the lowest passing grade is 7, how many students (actual number, not percentage) passed the quiz? Show work.2 points.

2. 2 points.If a distribution of scores has a mean of 50 and a median of 30, which of the following is most likely to be true of the shape of the distribution?

a. It is positively skewed (skew to the right)

b. It is symmetrical

c. It is negatively skewed (skew to the left)

3.6 points. Imagine that I have the ability to take a survey in the future and I have collected a sample of 25 students in our class and found that their annual income (in thousands) in 2034 will be as follows: 60; 80; 100; 50; 75; 135; 110; 75; 90; 80; 125; 75; 70; 60; 90; 80; 60; 60; 75; 100; 75; 60; 90; 75; 70. (I apologize to all of you who will be making more than 135K, you just were not included in this sample.)

Show your work for each of the following (for repetitive calculations, such as relative frequency, you only have to show work for the first few repetitions):

Determine absolute and relative frequencies (i.e., proportions) of each value as well as the cumulative relative frequencies at each point. Fill out a table that follows the following format:

income (X)	Frequency (f)	Relative Frequency (p)	Relative Cumulative Frequency (p)

(Note: you should include as many rows as you need to display frequencies for each data value). Do not use "grouped frequencies" (as discussed in the textbook) in the rows of this table - in other words, do not group the data into class intervals. Instead, use one row for each value present in the dataset.

1 point. What is the median future income for this sample?

4.11 points. A researcher is interested in female labor participation rates. She uses 2023 data collected by the World Bank regarding the percentage of women who are economically active in a small sample of 32 countries. The data (slightly adapted) is:

Iraq 11%	Nicaragua 49%	Brazil 53%	China 61%
Syrian Arab Rep 14%	Turkmenistan 49%	Hungary 54%	Estonia 61%
Morocco 20%	Argentina 51%	Russia 54%	Australia 62%
Saudi Arabia 35%	Belgium 51%	Japan 55%	Congo D.R. 67%
Fiji 37%	Malaysia 52%	Brunei 55%	Vietnam 68%
Myanmar 40%	Mali 52%	Uruguay 56%	Iceland 70%
Italy 41%	Domin. Rep. 52%	United States 57%	Ethiopia 75%
Montenegro 49%	Spain 53%	Canada 61%	Madagascar 83%

1. 4 pointsDetermine the three measures of central tendency (mode 1 point, median 1 point, and mean 2 points) for this sample.

1. 7 points. Using Excel or other software or by hand, generate a histogram that displays this data in visualized form. Briefly describe in two or three sentences what the histogram shows

5.4 pointsResearchers will occasionally use a feeling thermometer to learn about opinions and concerns that respondents may have. The feeling thermometer has possible scores from 0 to 100 where 0 represents no concern at all and 100 represents extreme concern. Imagine a researcher wants to know if people are concerned with the potential effects of climate change. A sample of 500 responses are collected and the data can be summarized as follows:

Score	0	25	50	60	75	90	100
Rel Freq	0.14	0.03	0.03	0.05	0.25	0.2	0.3

Find the three measures of central tendency (mode 1 point, median 1 point, and mean 2 points)

Mode

Median

Mean