variables & research
A researcher counts how many toys each child shares with a friend. What is the variable being measured?
The number of toys shared
Which graph is commonly used to display the frequency of numerical data grouped into continuous intervals?
Histogram
Calculate the mean of 2, 4, 6, 8.
5
In a normal distribution, approximately what percentage of scores falls between the mean and one standard deviation above the mean?
~34%
What feature distinguishes an experiment from an observational study?
An experiment involves manipulating an independent variable; an observational study does not
A researcher asks students to rate their happiness as low, medium, or high. What level of measurement is this?
Ordinal
A dataset contains the values 1, 2, 2, 3, 3, 3. What is the frequency of the value 3?
3
Find the median of 2, 7, 8, 3, 7, 4, 9, 6
6.5
Approximately what percentage of scores falls within two standard deviations of the mean in a normal distribution?
~95%
What is one common mistake that can make a bar graph misleading?
The y-axis does not start at 0
A researcher investigates whether listening to music affects memory test performance. Identify the independent variable and dependent variable.
IV: Music condition. DV: Memory test performance.
In a sample of 20 students, 5 report sleeping fewer than six hours. What is the relative frequency of those students?
0.25, or 25%
Calculate the range of 12, 5, 18, 9, 14
13
A distribution has a mean of 50 and a standard deviation of 10. What is the z-score for a score of 70?
2
A pie chart has slices representing 35%, 30%, 25%, and 20% of a whole. What is wrong with this graph?
It adds up to 110%, not 100%
A researcher records the number of hours each student sleeps per night. Is this nominal, ordinal, interval, or ratio?
Ratio
A researcher groups scores into the intervals [0–2), [2–4), [4–6). What interval does a score of exactly 4 belong to?
[4-6)
A dataset has a variance of 25. What is its standard deviation?
5
A score has a z-score of −2 in a distribution with a mean of 30 and a standard deviation of 5. What is the original score?
20
In statistics, what does N generally represent?
the sample size
A researcher records students’ college majors, ranks their stress from 1 to 5, and measures their temperatures in Celsius. Identify the level of measurement for each variable.
College major = nominal
stress ranking = ordinal
Celsius temperature = interval
A researcher wants to show how the average stress level of students changes over five weeks. Which graph would be most appropriate?
Line graph
Calculate the sample standard deviation for 2, 4, 4, 6.
~1.63
A student's z-score is −1.5. What does this mean about their score relative to the distribution's mean?
Their score is 1.5 standard deviations BELOW the mean
A researcher finds a relationship between sleep and happiness and concludes that sleeping more definitely causes happiness. What is wrong with this conclusion?
Correlation does not prove causation. Other variables may explain the relationship