CH 7 Flashcards
Dr. Ritter’s quiz scores for his Intro to Stat class:
Score / Frequency / Percent (%) 9 1 5 8 1 5 7 2 10 6 6 30 5 7 35 4 3 15
Which value would be the largest in this distribution of scores?
(A) The mode
(B) The mean
(C) The median
(D) Unable to determine
(B) The mean
*Mode is the most frequent score, which is 5.
Median is the middle score, which is 5.5 (between a score of 5 and 6).
Mean is the arithmetic average, which is 5.7
**Typically, in a skewed distribution, the mean is pulled out into the tail of the distribution. Thus, with a positively skewed distribution, such as this one, the mean is generally larger than the median and mode. In a negatively skewed distribution, the mean is generally smaller than the median and mode.
Which measure is NOT dependent on the value of every score?
(A) Standard deviation
(B) Range
(C) Mean
(D) Variance
(B) Range
To calculate the range, you only need the smallest and largest scores along with the interval width. The other three measures use every value in the distribution to calculate!
There is one type of data that should be presented using a bar graph rather than a histogram (even though the book says it’s okay to use a histogram for this type of data). Unfortunately, our book does not differentiate between bar graphs and histograms, but you should know the difference when you see them. The answer is explicitly stated on the powerpoints and in the lectures! Which type of variable should use a bar graph or bar chart (or pie chart)?
(A) nominal
(B) ordinal
(C) interval
(D) ratio
(A) nominal
*Nominal data should be displayed using a bar graph rather than a histogram because the numbers assigned to the variables are categorical (not continuous) and do not have an ordered, relational effect.
**In bar graphs, we separate the bars to show that the data are not continuous. While histograms will have bars that touch showing that the data are continuous.
The values of four out of a sample of five deviation scores are: -5, +2, +4, -2
The value of the !fth deviation score is:
(A) -1
(B) +1
(C) +2
(D) 0
(B) +1
*The sum of a set of deviation scores must add up to zero.
Thus, (-5) + (+2) + (+4) + (-2) + (?) = (-1) + (?) = 0
The answer would be +1.
Classify the following based on the type of measurement scale: Number of minutes to complete a test.
(A) nominal
(B) ordinal
(C) interval
(D) ratio
(D) ratio
*We would select ratio because the number of minutes to complete a test has an absolute zero starting place (it would be impossible to complete a test in -3.5 minutes), and the minutes are equal units of measurement.
Subject / ACT score 1 20 2 27 3 30 4 19 5 26 6 16 7 23 8 31
What is the total N for this population?
(A) 5
(B) 8
(C) 30
(D) 15
(B) 8
Subject / ACT score 1 20 2 27 3 30 4 19 5 26 6 16 7 23 8 31
Calculate the mean ACT score for our population?
(A) 21
(B) 23
(C) 24
(D) 28
(C) 24
*192 / 8 = 24
Subject / ACT score 1 20 2 27 3 30 4 19 5 26 6 16 7 23 8 31
Calculate the variance for our population?
(A) 4.5
(B) 25.5
(C) 36
(D) 204
(B) 25.5
*Variance is calculated by summing the squared deviation scores then dividing by N.
ACT score / Deviation / Deviation Squared 20 -4 16 27 3 9 30 6 36 19 -5 25 26 2 4 16 -8 64 23 -1 1 31 7 49 Sum: 0 204
204 / 8 = 25.5
You are recording the type of primary learning disability for each student in a special needs classroom. The variable you are collecting is what type of measurement scale?
(A) nominal
(B) ordinal
(C) interval
(D) ratio
(A) nominal
*The types of primary learning disabilities might be classified under areas such as visual, auditory, physical, behavioral… They would be categorical in nature with no continuous ranking. Thus, this would be a nominal variable.
Use the following observations to identify the median: 8, 9, 6, 4, 9, 10
(A) 4
(B) 6
(C) 8
(D) 8.5
(D) 8.5
*The median is the middle score: 8, 9, 6, 4, 9 becomes 4, 6, 8, 9, 9, 10 where 8 and 9 are the middle scores.
Thus the median would be 8.5.
Calculate the mean of the following data: 8, 9, 6, 4, 9, 10
(A) 6
(B) 6.52
(C) 7.67
(D) 9
(C) 7.67
*The mean is the arithmetic average of the set of scores: (8 + 9 + 6 + 4 + 9 + 10) / 6 = 46 / 6 = 7.67
Identify the mode of the following set of scores: 8, 9, 6, 4, 9, 10
(A) 6
(B) 7
(C) 8
(D) 9
(D) 9
*The mode is the most frequently occurring score, which would be 9 in this set.
Compute the standard deviation of the following population of scores: 10, 3, 8, 6, 9, 4, 9
(A) 2.51
(B) 2.71
(C) 6.29
(D) 7.33
(A) 2.51
- The deviation scores would be 3, -4, 1, -1, 2, -3, 2.
- The squared deviation scores would be 9, 16, 1, 1, 4, 9, 4.
- The average of the squared deviation scores is 44/7 = 6.29.
- The square root of 6.29 is 2.51. This is the standard deviation.
Which of the 3 measures of central tendency must be equal in a perfectly normal distribution?
(A) mean and median
(B) mean and mode
(C) median and mode
(D) mean, median, and mode
(D) mean, median, and mode
*If a distribution is a perfect normal distribution, then all three measures of central tendency will be the same.
The purpose of descriptive statistics are to:
(A) enable us to organize, summarize, and describe our observations.
(B) allow us to infer information about the sample to the population.
(C)test statistical hypotheses.
(A) enable us to organize, summarize, and describe our observations.
*Descriptive statistics are procedures for describing the data. Inferential statistics will provide evidence to allow us to generalize or infer to a population using statistical hypothesis testing.
