Question

CHAPTER 3: Describing Data with Averages

Key Terms

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Measures of central tendency --- General term for the various averages.

Modes --- The value of the most frequent observation.

Bimodal --- Describes any distribution with two obvious peaks.

Median --- The middle value when observations are ordered from least to most, or vice versa.

Population --- A complete set of observations.

Sample --- A subset of observations from a population.

Sample mean --- The balance point for a sample, found by dividing the total value of all observations in the sample by the sample size.

Sample size --- The total number of observations in the sample.

Population mean --- The balance point for a population, found by dividing the total value of all observations in the population by the population size.

Population size --- The total number of observations in the population.

Text Review

            There are several types of average, all known as (1)_____________________________

____________________________. The most frequently occurring observation is an average called the (2)_________________. It is understood as the most (3)_______________________.

Sometimes a distribution will have more than one mode. If there are two peaks, distributions are referred to as (4)___________________. If there are more than two peaks, the distribution is referred to as (5)_____________________. The occurrence of more than one mode may indicate (6)________________________________ in the data set.

            When observations are ordered from least to most, the middle value is the (7)_________. The median has a percentile rank of (8)______________. The median reflects the (9)_________ of an observation, not the position. The most common of the averages is the (10)_____________. Adding all the observations and then dividing by the number of observations will yield the (11)_______________. This calculation can be done without ordering the data or organizing it. The symbol for the sample mean is (12)____________. Another important symbol for the sample mean is the one for “the sum of,” (13)________________. The symbol (14)__________________ represents any unspecified observation. The mean serves as the balance point for a distribution. This is true because the sum of all observations, expressed as positive and negative deviations from the mean, always equals (15)_______________. Statisticians actually deal with types of means. One is the means of a complete set of observations or (16)_______________________.

The other is a (17)_________________ mean, or the mean of a subset of observations from a population. These two means are distinguished by different symbol but are calculated by the same formula. Similar values of the mode, median, and mean will usually indicate that the distribution is (18)_________________________________. In this case, any of the measures of central (19)_______________________ can be used to describe the distribution. If a distribution is skewed by extreme observations, the values of the three measures of (20)_______________________________ differ considerably. Since the (21)__________ and the (22)___________

are not sensitive to extreme observations, the (23)________________ should be reported along with the median. Accordingly, large differences between the mean and the median signal a (24)__________________ distribution. If the mean is larger than the median, the distribution will be (25)________________skewed, but if the median is larger than the mean, the distribution will be (26)________________skewed. Overall, the (27)__________________ is the most preferred average.

For qualitative data, the (28)________________ is always appropriate. However, the (29)_____________________ is only appropriate if the data can be ordered. Conventional usage prescribes that the term “average” usually refers to the (30)______________________.

Answer 1

            There are several types of average, all known as (1) Measures of Central Tendency. The most frequently occurring observation is an average called the (2) Mode. It is understood as the most (3) popular..

Sometimes a distribution will have more than one mode. If there are two peaks, distributions are referred to as (4) bimodal. If there are more than two peaks, the distribution is referred to as (5) mutimodal. The occurrence of more than one mode may indicate (6) heterogeneity in the data set.

            When observations are ordered from least to most, the middle value is the (7) median The median has a percentile rank of (8) 50%.. The median reflects the (9) midway of an observation, not the position. The most common of the averages is the (10) mean. Adding all the observations and then dividing by the number of observations will yield the (11) mean. This calculation can be done without ordering the data or organizing it. The symbol for the sample mean is (12) xbar. Another important symbol for the sample mean is the one for “the sum of,” (13) xi/n. The symbol (14) xirepresents any unspecified observation. The mean serves as the balance point for a distribution. This is true because the sum of all observations, expressed as positive and negative deviations from the mean, always equals (15) 0. Statisticians actually deal with types of means. One is the means of a complete set of observations or (16) population mean..

The other is a (17) sample mean, or the mean of a subset of observations from a population. These two means are distinguished by different symbol but are calculated by the same formula. Similar values of the mode, median, and mean will usually indicate that the distribution is (18) symmetrical.. In this case, any of the measures of central (19) tendency can be used to describe the distribution. If a distribution is skewed by extreme observations, the values of the three measures of (20) central tendency differ considerably. Since the (21) median and the (22) Interquartile range

are not sensitive to extreme observations, the (23) Interquartilerange should be reported along with the median. Accordingly, large differences between the mean and the median signal a (24) skewed distribution. If the mean is larger than the median, the distribution will be (25) positively skewed, but if the median is larger than the mean, the distribution will be (26) negatively skewed. Overall, the (27) mean is the most preferred average.

For qualitative data, the (28) mean is always appropriate. However, the (29) median is only appropriate if the data can be ordered. Conventional usage prescribes that the term “average” usually refers to the (30) mean.