


Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
How to calculate various measures of central tendency and dispersion, including the mean, median, mode, upper and lower quartiles, range, variance, and standard deviation. It provides step-by-step instructions and examples for each measure.
Typology: Lecture notes
1 / 4
This page cannot be seen from the preview
Don't miss anything!
Formula:
∑
Measures that indicate the approximate center of a distribution are called measures of central tendency. Measures that describe the spread of the data are measures of dispersion. These measures include the mean, median, mode, range, upper and lower quartiles, variance, and standard deviation.
The mean of a set of data is the sum of all values in a data set divided by the number of values in the set. It is also often referred to as an arithmetic average. The Greek letter (“mu”) is used as the symbol for population mean and the symbol ̅ is used to represent the mean of a sample. To determine the mean of a data set:
Consider the data set: 17, 10, 9, 14, 13, 17, 12, 20, 14
∑
The mean of this data set is 14.
The median of a set of data is the “middle element” when the data is arranged in ascending order. To determine the median:
middle.
points, meaning the two center values should be added together and divided by 2.
Consider the data set: 17, 10, 9, 14, 13, 17, 12, 20, 14
Step 1: Put the data in order from smallest to largest. 9, 10, 12, 13, 14, 14, 17, 17, 20
Step 2: Determine the absolute middle of the data. 9, 10, 12, 13, 14 , 14, 17, 17, 20
Note: Since the number of data points is odd choose the one in the very middle.
The median of this data set is 14.
C. Finding the Mode
The mode is the most frequently occurring measurement in a data set. There may be one mode; multiple modes, if more than one number occurs most frequently; or no mode at all, if every number occurs only once. To determine the mode:
Consider the data set: 17, 10, 9, 14, 13, 17, 12, 20, 14
Step 1: Put the data in order from smallest to largest. 9, 10, 12, 13, 14, 14, 17, 17, 20
Step 2: Look for any number that occurs more than once. 9, 10, 12, 13, 14 , 14 , 17 , 17 , 20
Step 3: Determine which of those occur most frequently. 14 and 17 both occur twice.
The modes of this data set are 14 and 17.
D. Finding the Upper and Lower Quartiles
The quartiles of a group of data are the medians of the upper and lower halves of that set. The lower quartile , Q1, is the median of the lower half, while the upper quartile, Q 3 , is the median of the upper half. If your data set has an odd number of data points, you do not consider your median when finding these values, but if your data set contains an even number of data points, you will consider both middle values that you used to find your median as parts of the upper and lower halves.
Consider the data set: 17, 10, 9, 14, 13, 17, 12, 20, 14
Step 1: Put the data in order from smallest to largest. 9, 10, 12, 13, 14, 14, 17, 17, 20
Step 2: Identify the lower half of your data. 9, 10, 12, 13, 14, 14, 17, 17, 20
Step 3: Identify the upper half of your data. 9 , 10, 12, 13, 14, 14, 17, 17, 20
Step 4: For the lower half, find the median. 9, 10, 12, 13 Since there are an even number of data points in this half, you will find the median by summing the two in the center and dividing by two. This is Q 1.
Step 5: For the upper half, find the median. 14, 17, 17 , 20 Since there are an even number of data points in this half, you will find the median by summing the two in the center and dividing by two. This is Q 3.
Q 1 of this data set is 11 and Q 3 of this data set is 17.
Step 2: Subtract the mean from each data value. 17 – 14 = 3 ; 10 – 14 = -4 ; 9 – 14 = -5 ; 14 – 14 = 0
13 – 14 = -1 ; 17 – 14 = 3 ; 12 – 14 = -2 ; 20 – 14 = 6 ; 14 – 14 = 0
Step 3: Square these values. 32 = 9 ; (-4)^2 = 16 ; (-5)^2 = 25 ; 0^2 = 0 ; (-1)^2 = 1 ; 3^2 = 9 ; (-2)^2 = 4 ; 6^2 = 36
Step 4: Add these values together. 9 + 16 + 25 + 0 + 1 + 9 + 4 + 36 = 100
Step 5: There are 9 values in our set, so we will divide by 9 – 1 = 8. = 12.
Note: This is your variance.
Step 6: Square root this number to find your standard deviation. (^) √ = 3.
The variance is 12.5 and the standard deviation is 3.536.
G. Using the TI-
the key. Select Edit…
Sample Standard Deviation Population Standard Deviation Number of data values
Lower Quartile
Median Upper Quartile Smallest data value
Largest data value
These could be subtracted to find the range.