Which measures of central tendency are not affected by extremely low or extremely high values quizlet?

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Terms in this set (10)

Arithmetic Mean

Computed by adding all values of the variable in the data set and dividing by the # of observations. Known as the Mean.

Value such that a histogram of the data is perfectly balanced, with equal weight on each side of the mean

Population Arithmetic Mean (pronounced mew)

Computed using all the individuals in a population. Known as a Parameter.

Sample Arithmetic Mean (pronounced x-bar)

Computed using sample data. Known as a statistic.

Greek and Roman Symbols

N= population size
n= sample size
Greek Sigma ="add the terms"
i=shows that various values are distinct and does not serve as a math operation
M=Median
Mew symbol = Population Mean
x-bar symbol= Sample Mean

Median

Value that lies in the middle of the data when arranged in ascending order

Mode

The most frequent observation of the variable in a data set.

If there is only 1 instance of each variable, there is no Mode.
A data set can have more than one mode (Bimodal or Multimodal) A set that is multimodal is usually not reported.

Measures of Central Tendency

1) Mean (uses all the data;
Best used for Quantitative data and frequency distribution that is roughly symmetrical)

2)Median (relies only on the position of the data;
Best used for Quantitative data when frequency distribution is skewed right or left )
3) Mode (used for Qualitative data;
used for quantitative data when "most frequent" observation is desired measure)

When is a statistic Resistant?

If extreme values (very large or small) relative to the data do not affect its value substantially.
The Median is resistant - the Mean is not
(extreme values DO make a difference in the Mean)

Relation between Mean, Median, and Distribution Shape

Skewed right - Mean substantially larger than Median.
Skewed left - Mean substantially smaller than Median.
Symmetric - Mean roughly equal to Median (we would use the Mean in this case)

NOTE: Guidelines that work well for continuous data, but when using discrete data, they may not apply in all cases.

Measure of Central Tendency for data that are Nominal

Only the Mode can be computed, not Mean or Median.

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Which measures of central tendency are not affected by extremely low or extremely high values?

The three common measures of central tendency are the mean, the median and the mode. The mean gives each element of a data set equal weight. When there are no extreme numbers in the data set (no very low or very high numbers), the mean is a good choice for a measure of central tendency.

Which of the following measures of central tendency is not affected by extreme values in the sample data set?

Median is the middle most value of a given series that represents the whole class of the series.So since it is a positional average, it is calculated by observation of a series and not through the extreme values of the series which. Therefore, median is not affected by the extreme values of a series.

Which of these measures of central tendency is not affected by extreme or deviant value?

Properties of Median Median is the score or class in the distribution wherein 50% of the score fall below it and another 50% lie. 2. Median is not affected by extreme or deviant values.

Which measure of central tendency should be avoided when extreme values affect the data?

Answer. When there are extreme numbers in the data set (very low or very high numbers), the median is a good choice for a measure of central tendency. The extreme numbers have less effect (or no effect at all) on the median.