Stats-Chapter 4

Dana examined the GRE verbal scores of 10 first-year graduate students in her creative writing class to see the variability. Dana found the variance to be 135. What is the standard deviation? 3.674 11.619 13.5 18,225

11.619

The variance calculated on 32 scores is equal to 42.24. What is the standard deviation? 1.32 units 1.32 units squared 6.50 units 6.50 units squared

6.50 units

Measures of central tendency and variability are calculated to describe the nature of charitable giving each year. These figures are computed for the "average" American citizen. Which of these is a possible value for the variance in dollars given? -$147.56 $147.56 (not it) $138.45 to $147.26 $147.56 squared dollars

???

Which of these is NOT a reason to use the interquartile range instead of the range? The range includes the smallest-to-largest observations and may be unreliable. The interquartile range can help assess skew better than the range can alone. The interquartile range is not based on the minimum and maximum scores. (not it) The interquartile range is more likely to account for outliers.

????

A deviation from the mean

A deviation from the mean is the amount that a score in a sample differs from the mean of the sample; also called a deviation.

How do Greek letters refer to numbers?

Based on populatons (µ)

A multimodal distribution

It has more than two modes, or most common scores.

A unimodal distribution

It has one mode, or most common score.

A bimodal distribution

It has two modes, or most common scores.

Variability

It is a numerical way of describing how much spread there is in a distribution.

Central tendency

It refers to the descriptive statistic that best represents the center of a data set, the particular value that all the other data seem to be gathering

Symbol for mean square (referring to the average of the squared deviations).

MS

Symbols that represent variance

SD^2 , s^2 , and MS.

Symbols that represent the standard deviation squared

SD^2 and s^2 ,

Mathematical definition of variance

STEP 1: Subtract the mean from every score. We call these deviations from the mean. STEP 2: Square every deviation from the mean. We call these squared deviations. STEP 3: Sum all of the squared deviations. This is often called the sum of squared deviations, or the sum of squares for short. STEP 4: Divide the sum of squares by the total number in the sample (N).

How to find the interquartile range

Step 1: Calculate the median. Step 2: Look at all of the scores below the median. The median of these scores, the lower half of the scores, is the first quartile, often called Q1 for short. Step 3: Look at all of the scores above the median. The median of these scores, the upper half of the scores, is the third quartile, often called Q3 for short. Step 4: Subtract Q1 from Q3. The interquartile range, often abbreviated as IQR, is the difference between the first and third quartiles: IQR =Q3−Q1.

The first quartile

The first quartile marks the 25th percentile of a data set.

Formula for variance

The formula for variance is: To calculate N variance, subtract the mean (M) from every score (X) to calculate deviations from the mean; then square these deviations, sum them, and divide by the sample size (N). By summing the squared deviations and dividing by sample size, we are taking their mean. NOTE: THE BOOK DOESN'T SHOW N-1!!! JUST "N"

Basic formula for standard deviation

The most basic formula for standard deviation is: SD = SD 2 . We simply take the square root of the variance.

Statistics

The numbers based on samples taken from a population are called statistics; M is a statistic.

Parameters

The numbers based on whole populations are called parameters; µ is a parameter.

How does standard deviation relate to variance

The standard deviation is simply the square root of the variance: It represents the typical deviation of a score from the mean.

The standard deviation

The standard deviation is the square root of the average of the squared deviations from the mean; it is the typical amount that each score varies, or deviates, from the mean.The beauty of the standard deviation—compared to the variance—is that we can understand it at glance.

Sum of sqaures

The sum of squares, symbolized as SS, is the sum of each score's squared deviation from the mean.

The third quartile

The third quartile marks the 75th percentile of a data set.

full standard deviation formula

To determine standard deviation, subtract the mean from every score to calculate deviations from the mean. Then, square the deviations from the mean. Sum the squared deviations, then divide by the sample size. Finally, take the square root of the mean of the squared deviations.

When the mean is presented in research articles, it is most often accompanied by the _____ as a measure of variability. range variance standard deviation interquartile range

standard deviation

The _____ is equal to the square root of the _____. variance; standard deviation standard deviation; variance central tendency; mean mean; central tendency

standard deviation; variance

Variance

Variance is the average of the squared deviations from the mean. When something varies, it must vary from (or be different from) some standard. That standard is the mean. So when we compute variance, that number describes how far a distribution varies around the mean.

Interquartile range

Whenever there are outliers, the range will be an exaggerated measure of the variability. Fortunately, we have an alter- native to the range: the interquartile range. The interquartile range is a measure of the distance between the first and third quartiles. As we learned earlier, the median marks the 50th percentile of a data set.

Measures of central tendency and variability are calculated to describe the nature of charitable giving each year. These figures are computed for the "average" American citizen. In that case, the mean calculated would be taken as: a population parameter. a measure of variability. a sample statistic. part of a five-number summary.

a population parameter.

How do Latin letters refer to numbers?

based on samples (M)

The number of avalanche fatalities in Colorado for the last nine seasons was reported as 7, 1, 6, 6, 7, 5, 8, 2, 3. What type of distribution do the numbers represent? unimodal bimodal multimodal nonmodal

bimodal

The range as a measure of variability is problematic because: it does not represent the spread of the distribution. calculations of the range are frequently full of errors. it is expressed in squared units. it relies on the most extreme scores, which could be outliers.

it relies on the most extreme scores, which could be outliers.

When looking at a distribution of data with a possible outlier, it is important to keep in mind the range of all scores because an extremely high or low outlier may skew the _____of the data set. parameters sum of squares mean mode

mean

When data are based on a nominal scale of measurement, what measure of central tendency should be used? mean median mode variance

mode

The numerical summary characteristics of a population are called _____, while the numerical summary characteristics of a sample are called _____. parameters; variance parameters; statistics statistics; parameters statistics; sum of squares

parameters; statistics

Simplest measure of variability

range

What measure of variability is the square root of the average of the squared deviations from the mean? variance standard deviation range central tendency

standard deviation

Which measure of variability is the average of the squared deviations from the mean? variance standard deviation range central tendency

variance