Statistics_Gpc_Chapter 3 Numerically Summarizing Data

Front 1

Name three measures of the central tendency of data.

Back 1

Three measures of the central tendency of data are: mean, median, and mode.

Front 2

How do you calculate the arithmetic mean (mean) of a variable?

Back 2

The arithmetic mean (mean) of a variable is computed by finding the sum of all the values of the variable in the data set and dividing the sum by the number of observations.

Front 3

What symbol is used for the mean of population data and what is the formula?

Back 3

The symbol used is µ, and the formula is: µ = (Σxi)/N, where N is the size of the population.

Front 4

What symbol is used for the mean of sample data and what is the formula?

Back 4

The symbol used is x-bar, and the formula is: x-bar = (Σxi)/n, where n is the size of the sample.

Front 5

What is the median of a variable data?

Back 5

The median of a variable is the value that lies in the middle of the data when arranged in ascending order. We use M to represent the median

Front 6

How is the median of variable data determined?

Back 6

First arrange the values in ascending order.

If there is an odd number of data values, take the value in the middle.

If there is an even number of values, take the average of the two middle values.

Front 7

What is a parameter?

Back 7

A descriptive measure of a population.

Front 8

What is a statistic?

Back 8

A descriptive measure of a sample

Front 9

What is the mode of variable data?

Back 9

The mode is the variable value that occurs most frequently in the data. The data may be bimodal, multimodal, or there may be no mode.

Front 10

Which of the three measures of central tendency is/are resistant to extreme values?

Back 10

The median and mode are resistant to extreme values. The mean can be significantly influenced by extreme values.

Front 11

What does it mean for a numerical summary, such the median, to be resistant to extreme values?

Back 11

A numerical summary of data is said to be resistant if extreme values (very large or small) relative to the data do not affect its value substantially.

Front 12

If we collect data and the mean is substantially smaller than the median, what is the likely shape of the distribution?

Back 12

Skewed left

Front 13

If we collect data and the mean and the median are close in value, what is the likely shape of the distribution?

Back 13

Symmetric

Front 14

If we collect data and the mean is substantially larger than the median, what is the likely shape of the distribution?

Back 14

Skewed right

Front 15

Name four measures that describe the dispersion or spread of variable data.

Back 15

Four measures that describe the dispersion or spread of variable data are: 1) Range, 2) Variance, 3) Standard Deviation, and 4) Interquartile Range.

Front 16

How is the Range of variable data defined?

Back 16

The range, R, of a variable is the difference between the largest data value and the smallest data values.

R = Largest Data Value – Smallest Data Value

Front 17

How is variance computed for population data?

Back 17

The population variance of a variable is the sum of squared deviations about the population mean divided by the number of observations in the population, N.

Front 18

What symbol is used for population variance?

Back 18

The population variance is symbolically represented by σ^2 (lower case Greek sigma squared)

Front 19

What is the formula for calculating population variance?

Back 19

σ^2 = Σ (xi – µ)^2/N

Front 20

How is SAMPLE variance determined?

Back 20

The sample variance is computed by finding the sum of squared deviations about the SAMPLE mean and then dividing this result by n – 1.

Front 21

What symbol is used for sample variance?

Back 21

The sample variance is symbolically represented by s^2.

Front 22

Give the formula for calculating sample variance.

Back 22

The formula for calculating sample variance is:
s^2 = Σ (xi – x-bar)^2/(n – 1)

Front 23

How does the polulation variance compare to the population standard deviation?

Back 23

The population standard deviation is obtained by taking the square root of the population variance.

Front 24

What symbol is used for population standard deviation?

Back 24

The population standard deviation is denoted by
the Greek letter σ.

Front 25

How does the sample standard deviation compare to the sample variance?

Back 25

The sample standard deviation is obtained by taking the square root of the sample variance.

Front 26

What symbol is used to represent the sample standard deviation?

Back 26

The sample standard deviation is denoted by the symbol "s".

Front 27

Give the formula used to compute sample standard deviation.

Back 27

The formula used to compute sample standard deviation is;

s = SQRT[Σ (xi – x-bar)^2/(n – 1)]

Front 28

According to the Empirical Rule, if a distribution is roughly bell-shaped, what percentage of the data values should fall within ± 1 standard deviation of the mean?

Back 28

According to the Empirical Rule, if a distribution is roughly bell-shaped, approximately 68% of the data will lie within ± 1 standard deviation of the mean.

That is, 68% of the data should fall between, µ – 1σ and µ + 1σ

Front 29

According to the Empirical Rule, if a distribution is roughly bell-shaped, what percentage of the data values should fall within ± 2 standard deviation of the mean?

Back 29

According to the Empirical Rule, if a distribution is roughly bell-shaped, approximately 95% of the data will lie within ± 2 standard deviation of the mean.

That is, 95% of the data should fall between, µ – 2σ and µ + 2σ.

Front 30

According to the Empirical Rule, if a distribution is roughly bell-shaped, what percentage of the data values should fall within ± 3 standard deviation of the mean?

Back 30

According to the Empirical Rule, if a distribution is roughly bell-shaped, approximately 99.7% of the data will lie within ± 3 standard deviation of the mean.

That is, 99.7% of the data should fall between, µ – 3σ and µ + 3σ.

Front 31

What is a z-score and what is it used for?

Back 31

The distance that a value is from the mean in terms of the number of standard deviations.

Z-scores are used to standardize data and to compare relative positions.

Front 32

How is a z-score calculated?

Back 32

For population data, to convert a value, X, into a z-score, the formula is: Z = (X – µ)/σ.

For sample data, to convert a value, X, into a z-score, the formula is: Z = (X – X-bar)/s.

Front 33

How is the kth percentile defined?

Back 33

The kth percentile, denoted, Pk, of a set of data is a value such that k percent of the observations are less than or equal to the value.

Front 34

What are Quartiles?

Back 34

Quartiles divide data sets into fourths, or four equal parts.
The 1st quartile, denoted Q1, divides the bottom 25% the data from the top 75%. Therefore, the 1st quartile is equivalent to the 25th percentile.
The 2nd quartile divides the bottom 50% of the data from the top 50% of the data, so that the 2nd quartile is equivalent to the 50th percentile, which is equivalent to the median.
The 3rd quartile divides the bottom 75% of the data from the top 25% of the data, so that the 3rd quartile is equivalent to the 75th percentile.

Front 35

What is the Interquartile Range?

Back 35

The interquartile range, denoted IQR, is the range of the middle 50% of the observations in a data set. That is, the IQR is the difference between the first and third quartiles and is found using the formula
IQR = Q3 – Q1

Front 36

How is the interquartile range used in identifying outliers?

Back 36

Fences serve as cutoff points for determining outliers. The IQR is used to determine the upper and lower fences as follows:
Lower fence = Q1 – 1.5(IQR)
Upper fence = Q3 + 1.5(IQR)

Front 37

What is the "5-Number Summary"?

Back 37

1. Minimum Value
2. Q1
3. Median
4. Q3
5. Maximum Value

Front 38

How is a boxplot used?

Back 38

The boxplot is primarily used to identify possible outliers.

It can also be used to determine whether a distribution is roughly symmetric, skewed left or skewed right.