RESEARCH STATISTICS QUESTIONS
AND ANSWERS WITH SOLUTIONS 2024
Chapter 3 - ANSWER DESCRIPTIVE STATISTICS, PROBABILITY, AND MEASURE OF CENTRAL TENDENCY
descriptive Statistics - ANSWER computed to reveal characteristics of the sample and to describe study
variable
How to describe a sample - ANSWER create a frequency distribution of the variable or variable being
studied
- is a plot of one variable, whereby the x-axis consists of possible values of that variable , and the y - axis
is tally of each value
Inferential Statistics - ANSWER computed to draw conclusions and make inferences about the greater
population, based on the sample data set.
Bi Modal - ANSWER having or providing two modes, ,methods, systems, etc.
-having 2 values/categories that have highest occurrence and are equal frequencies
Central Tendency - ANSWER indicator of center of data
-nominal variable= categorical differences EX: gender (tendency of samples of given measurement to
cluster around some central value.
Measures of Central tendency are descriptive statistics.
Statistics represent measures of central tendency are mean, median and mode (all are representations
or descriptions of the center or middle of a frequency distribution
mean= arithmetic average of all of the values of a variable.
median= exact middle value ( or average of the middle two values if there is an even number of
observations)
mode= most commonly occurring value in a data set. can have more than one mode in a sample.
in a normal curve, mean, median and mode are equal or approximately equal
,Multimodal - ANSWER having more than 2 modes
Unimodal - ANSWER When distribution only has one mode
-the frequencies progressively decline as they move away from the mode. Symmetrical distributions are
usually uni modal.
bimodal - ANSWER means you have not defined your population if you find a bimodal
Mode - ANSWER most frequently occurring measure (value or category) in (distribution) data
Mean - ANSWER called location parameter
most frequent central tendency but requires interval and ratio data
-sum of values divided by total # of observations
Median - ANSWER for ordinal, interval and ratio data, value in middle when you line up all measured
values in order from least to most, 50th percentile value.
-data that is rank ordered (ordinal, interval and ratio)
has second measure of central tendencies :median
Range - ANSWER difference between maximum value and minimum value of variable in distribution
probability - ANSWER chance that particular outcome will occur after an event
**long-run relative frequency EX: dice/100 rolls
Standard Deviation - ANSWER average distance of values from variable mean. Large SD = spreading
among variable in data set is large.
FORMULA :
, -1st find mean (average) then place in formula then square root (check mark with x)
-FORMULA to create SD variable with population data;
Long-Run relative frequency - ANSWER
frequency distribution - ANSWER lists all poss. outcomes of experiment and tallies # of times each
outcome occurs. Tallies are then graphed to make them easier to visualize and comprehend
Probability Distribution - ANSWER graphs the prob. of all poss. outcomes of var. instead of frequency.
Shows prob. of all poss outcomes of var. looks alot like frequency, but represent 2 very distinct concepts.
Sampling Distribution - ANSWER plots (actual) realized frequencies of a statistic versus range of possible
values that statistics can take
-
Normal Distribution - ANSWER probability dist. where mean, median and mode are equal with a bell-
shaped distribution curve.
-68% of area under curve falls with in one SD of mean, 95% of area under curve falls it within two DS of
mean, increasing mean makes curve shift to right, decreasing ships curve to left, decreasing variance
makes graph look taller and skinnier, increasing variance = shorter and fatter
-the theoretical normal curve is symetrical and unimodal and has continuous values.
mean, median and mode are equal
theoretical normal curve - ANSWER