1 Measures of Central Tendency “Measures of central tendency (averages) are statistical constants which enable us to figure out in a single effort the significance of the whole.” (Prof Bowley)
The main objectives of measure of central tendency are
To reduce data in a single value.
To make easy comparisons between data.
There are different types of averages; each has its own business applications.
1. Arithmetic Mean
2. Median
3. Mode
4. Geometric Mean
5. Harmonic Mean
1.1 Arithmetic Mean
1.1.1 Definition
Most important measure of location is the mean or average value, for a variable. The mean provides a measure of central location for the data. If the data are for a sample, the mean is denoted by; if the data are for a
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(David R. Anderson et al)
1.2.2 Business Applications of Median
Median is positional measures of central tendency. The median salary gives a value close to the average salary commonly paid, without taking the extreme values into consideration. There are mainly used in the qualitative cases like honesty, intelligence, ability, etc. These are also suitable for the problems of distribution of income, wealth, investment, etc. (www.publishyourarticles.net)
1.2.2.1 Example The U.S. Census Bureau finds the median household income. According to the U.S. Census Bureau, "median household income" is defined as "the amount which divides the income distribution into two equal groups, half having income above that amount, and half having income below that amount." (www.ehow.com)
1.3 Mode
1.3.1 Definition
The mode is defined as the element that appears most frequently in a given set of elements. Mode can also be defined as the element with the largest frequency in a given data set. (www.wyzant.com)
1.3.2 Business Applications of Mode
The mode is the most important when an analysis is looking for what happens most often. In analyzing prices, most of the sales occur at a particular list price or possibly at a reduced, sale price. While there may have been sales at other prices, very few customers will have paid an average or a mean price. Those values are therefore
1. For the following scores, find the mean, median, and the mode. Which would be the most appropriate measure for this data set?
· How were measures of central tendency used in the study? Did the study use the most appropriate measure of central tendency for the given data? Why or why not?
4. Give the mean for the median column of the Worksheet. Is this estimate centered about the parameter of interest (the parameter of interest is the answer for the mean in question 2)
median household income of $36,327 and showed 29.2% of them living in poverty in 2013
The mean for the median column of the worksheet is 3.6Yes, the estimate is centered about the parameter of interest.
5. When is it more appropriate to use the median as a measure of center rather than the mean? Why?
Mean would be the most appropriate measure of central tendency to describe this data. This is because the mean is the average of all scores in the data set. If Dr. Williams were to graph the data into a bell shaped distribution, then the mean would be in the center where most of the scores are located. The mean is calculated using all information of the data set, and is the best score to use if you want to predict an individual score.
1. For the following scores, find the mean, median, and the mode. Which would be the most appropriate measure for this data set?
There was also a difference between the median income of a male and the one of a female.While males had a median income of $39,581, the females had a median income of $28,488.
The last variable chose was number of prior drug convictions. The mean was .33 the median was 0 and the mode was 0. The mode is the most appropriate measure for this set of data because 957 people have had 0 prior drug convictions out of 1160. The next closest choice was 1 prior conviction with
Median: 3, 5, 11, 12, 13, 15, 19, 35, 42, 65 = 13 + 15 = 28/2 = 14
C. The researchers analyzed the data as though it were at the interval/ratio level since they calculated means (the measure of central tendency that is appropriate only for interval/ratio level data) and standard deviations (the measure of dispersion for interval/ratio data) to describe their study variables.
“A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data (Laerd Statistics, 2013).” In terms of statistical data, the measurements could be mean, median, and mode. “The mean is equal to the sum of all the values in the data set divided by the number of values in the data set, the median is the middle score for a set of data that has been arranged in order of magnitude, and the mode is the most frequent score in our data set (Laerd Statistics, 2013).” BIMS can benefit from this type of statistical data because the company can get a good picture of the satisfaction
This boxplot displays this information in a graphical format. The box represents the lower quartile of $30,250 (25% of incomes are less than this value), the median of $42,000, and the upper quartile of $54,750 (25% of incomes are greater than this value).
Determining the mean and the median of the checking accounts for Century National Bank, we are trying to find the single value that will represent all 60 checking accounts in our sample. That single value will be measure of central tendency.