Module 6--Statistics: Measures of Central Tendency and/or Location Flashcards
What are the measure of Central Tendency?
Measures of Central Tendency
■ Provide information about the center of a distribution – Measures of central tendency are
specific measures of location that provide information about the center of a distribution or about
the most typical, representative value.
■ Mean, median, mode– Common measures of central tendency include the mode,
median and mean.
■ Three different approaches – These measures are based upon three different approaches that
help identify typical values for distribution.
■ No information about variance – Measures of central tendency do not give any information about
how varied or dispersed data are.
How do you determine the Mean?
Mean
■Arithmetic average – The mean is the arithmetic average.
■ x represents the mean – We use x (called “x bar”) to represent the mean.
Mean = Sum of all numbers
———————————-
Number count
x = Sum (x)
————————-
N
How do you calculate Mean in Excel?
Calculation of Mean (continued)
1. Select a blank cell and click the Insert Function (fx) button located just above the
column header.
- Select AVERAGE for mean.
- For Number1, click the small worksheet icon to the right of the field. A Function Arguments box
will pop up. - Use the mouse to select the data. Click and hold top cell, then drag to bottom cell. Release
the mouse button and then click to icon to the right of the field to accept the cell selection for
the data. - Leave Number2 blank because you have already selected all the data you wish to analyze.
- Click OK, and the results will appear in the selected cell.
* Formula: = AVERAGE(B6:B10)*
* Answer: 12.8
What is the Weighted vs Unweighted Mean?
Weighted vs. Unweighted Mean
The weighted mean gives more weight to the companies who have more people. The unweighted mean treats all three banks equally and disregards the number of people. The example shown on this
slide is therefore the unweighted mean, since we use the aggregated company data, and have no data on individual employee salaries in any of the 3 companies.
■ Weighted mean: obtained by weighting each value by the number of times that value has occurred in the set of data, and then averaging.
■ Unweighted mean: obtained without weighting each value by the number of times that value has occurred in the set of data. In some surveys, raw data are not disclosed.
* Instead, data are presented in summary form.
Example: Incumbents and average salaries given by company
■ The distinction between weighted and unweighted means then becomes important.
How do you calculate Weighted and Unweighted Mean? (page 151)
Calculation of Weighted and Unweighted Mean
■ Weighted mean – To calculate the weighted mean (find the mean salary of the incumbents),
multiply the number of incumbents by the means in each company, and divide the total number of
incumbents into the total of all the incumbents’ salary means.
■ Unweighted mean – To calculate the unweighted mean (find the mean salary in the companies),
divide the total number of companies into the total mean annual salary of incumbents.
How do you Use Means
■ Define for your audience – When you report a mean, define it for your audience.
* Explain clearly whether you are calculating a weighted or an unweighted mean, and why.
■ Know definition – When you read a mean, know its definition.
* Ask questions if you are not sure what kind of mean you are reading.
■ At least interval level data – As a general rule, you should have at least interval level data before
using the mean.
■ Influenced by outliers – Means are influenced by outliers, while medians and modes are not.
■ Most common – The mean is the most commonly reported measure of central tendency.
What is Median?
Median
The median corresponds to a point along an ordered distribution such that the same number of observations fall above and below this point. The median measures only the middle value, and totally
ignores the actual values – only determining the middle value when all of the values are placed in rank order. The median is a robust measure – it is unaffected by changes in actual values and is only
interested in their order.
■ Find the median number of bonus points earned for the following set of data: 32, 37, 38, 36, 40,
39 and 37.
■ Place the data into rank order.
■ Determine the median.
What is Mode?
■ The mode is the value that occurs most often among a data set.
Example:
Organizing data for analysis
■ Place the data into rank order.*
■ Group the data into intervals or common values.
What are the measures of locations?
Measures of Location
■ Based on same concept as median – Measures of location are based on the same concept used to
find the median.
* The median provides information about the central tendency of the distribution.
* Other measures of location represent other positions in the distribution.
■ Quartiles – In human resources management, we often use quartiles.
* P25, P50, and P75 are the upper limits of the 25th, 50th, and 75th percentiles.
* Q1, Q2, and Q3 are the upper limits of the 1st, 2nd, and 3rd quartiles.
* Triciles, quintiles and deciles are also commonly used.
■ Percentiles – Percentile bars, based on the 10th, 25th, 50th, 75th, 90th percentiles and the mean,
provide very useful visualizations of a distribution.
■ No information about variance – Measures of location offer no information about how varied or
dispersed the data are.
Measures of Location (continued)
■ Measures of location are very useful in setting pay philosophy.
■ A value that a given percent of the data is less than
Example: The 90th percentile is that value at which we have surpassed 90% of the data.
P75 = 75th percentile
P50 = 50th percentile (median)
P25 = 25th percentile
What are the Steps in Measures of Location
Measures of Location – Finding Percentiles
■ Step 1 – Locate the percentile in the rank order (right column)
Formula: rank order value = [(x ÷ 100) × n] + [1 - (x ÷ 100)]
Where:
x = the desired percentile (25th, 50th, etc.)
n = the number of cases in the list
■ Step 2 – Locate the value in the raw bonus points data (left column) that corresponds to the rankordered
position. Use the percentile result of Step 1 to interpolate the percentile in the raw data.
Interpolation is an exact value representing a remainder.
* Two-step formula:
a. Decimal remainder from Step 1
Percentile rank order – lower rank order
b. Percentile of raw data
Lower value + [(higher – lower) x decimal remainder]
What are Percentile Bars? (page 171)
Percentile Bars
■ The “bullseye” represents the mean.
■ In this example, the mean is bigger than the median.
■ The distance between the 25th percentile and the 50th percentile is smaller than the distance
between the 50th percentile and the 75th percentile.
■ These relationships among the various measures of central tendency or location will be helpful
when examining the symmetry or skewness of a distribution, as will be discussed in Module 8.
- What is the mode for the following set of numbers?
15, 18, 13, 19, 25, 24, 26, 14, 25, 35, 12, 99, 54, 13, 22, 19 and 13
A. 19
B. 26
C. 24
D. 13
D. 13
- What is the median of the following data?
Data: 7, 17, 3, 19, 13, 9, 7
A. 7
B. 9
C. 13
D. 11
B. 9
- What is interpolation?
A. A value that a given percent of the data is less than
B. An exact value representing a remainder
C. A whole number that represents the sum of a data set
D. A statistical representation of standard deviation
B. An exact value representing a remainder
- What are percentile bars?
A. A tool to help visualize the distribution of data
B. The value that occurs most often among a data set
C. Representations of the median salary in an organization’s pay grades
D. The most common method of representing unweighted means
A. A tool to help visualize the distribution of data
