<< Chapter < Page Chapter >> Page >

  • For the following problems, recall that value = mean + (#ofSTDEVs)(standard deviation) . Verify the mean and standard deviation or a calculator or computer.
  • For a sample: x = x ¯ + (#ofSTDEVs)( s )
  • For a population: x = μ + (#ofSTDEVs)( σ )
  • For this example, use x = x ¯ + (#ofSTDEVs)( s ) because the data is from a sample

  1. Verify the mean and standard deviation on your calculator or computer.
  2. Find the value that is one standard deviation above the mean. Find ( x ¯ + 1s).
  3. Find the value that is two standard deviations below the mean. Find ( x ¯ – 2s).
  4. Find the values that are 1.5 standard deviations from (below and above) the mean.
    • Clear lists L1 and L2. Press STAT 4:ClrList. Enter 2nd 1 for L1, the comma (,), and 2nd 2 for L2.
    • Enter data into the list editor. Press STAT 1:EDIT. If necessary, clear the lists by arrowing up into the name. Press CLEAR and arrow down.
    • Put the data values (9, 9.5, 10, 10.5, 11, 11.5) into list L1 and the frequencies (1, 2, 4, 4, 6, 3) into list L2. Use the arrow keys to move around.
    • Press STAT and arrow to CALC. Press 1:1-VarStats and enter L1 (2nd 1), L2 (2nd 2). Do not forget the comma. Press ENTER.
    • x ¯ = 10.525
    • Use Sx because this is sample data (not a population): Sx=0.715891
  1. ( x ¯ + 1s) = 10.53 + (1)(0.72) = 11.25
  2. ( x ¯ – 2 s ) = 10.53 – (2)(0.72) = 9.09
    • ( x ¯ – 1.5 s ) = 10.53 – (1.5)(0.72) = 9.45
    • ( x ¯ + 1.5 s ) = 10.53 + (1.5)(0.72) = 11.61
Got questions? Get instant answers now!

Try it

On a baseball team, the ages of each of the players are as follows:

21; 21; 22; 23; 24; 24; 25; 25; 28; 29; 29; 31; 32; 33; 33; 34; 35; 36; 36; 36; 36; 38; 38; 38; 40


Use your calculator or computer to find the mean and standard deviation. Then find the value that is two standard deviations above the mean.

μ = 30.68

s = 6.09
( x ¯ + 2 s ) = 30.68 + (2)(6.09) = 42.86.

Got questions? Get instant answers now!

Explanation of the standard deviation calculation shown in the table

The deviations show how spread out the data are about the mean. The data value 11.5 is farther from the mean than is the data value 11 which is indicated by the deviations 0.97 and 0.47. A positive deviation occurs when the data value is greater than the mean, whereas a negative deviation occurs when the data value is less than the mean. The deviation is –1.525 for the data value nine. If you add the deviations, the sum is always zero . (For [link] , there are n = 20 deviations.) So you cannot simply add the deviations to get the spread of the data. By squaring the deviations, you make them positive numbers, and the sum will also be positive. The variance, then, is the average squared deviation.

The variance is a squared measure and does not have the same units as the data. Taking the square root solves the problem. The standard deviation measures the spread in the same units as the data.

Notice that instead of dividing by n = 20, the calculation divided by n – 1 = 20 – 1 = 19 because the data is a sample. For the sample variance, we divide by the sample size minus one ( n – 1). Why not divide by n ? The answer has to do with the population variance. The sample variance is an estimate of the population variance. Based on the theoretical mathematics that lies behind these calculations, dividing by ( n – 1) gives a better estimate of the population variance.

Questions & Answers

what is the frequency
okoh Reply
Frequency is the number of all object which is comes from population or sample size
Faiqa
Denoted by f
Faiqa
number of all objects?
Amir
frequency is the rate of occurrence of an object
Leek
Explain nominal and ordinal variables
Oyinlola
 nominal variables are those variable which is used to “name,” a series of values.
Amir
while  ordinal scales provide good information about the order of choices,for example in a customer satisfaction survey.
Amir
what is the difference between Mean and Varience?
Amir
Sum of total object, divided by number of object is called mean
Faiqa
variance?
Amir
faiqa U didn't clear me.Sorry
Amir
what is df in statistics
Oyinlola
degre of freedom
Amir
Acquits the accused when in fact,he is ennocent
Barbie Reply
what is statistics
scholar Reply
statistics is a mathematical sciences which deals with collection,presentation and analysis the numerical data
CH
statistics is a tools who convert data into information
CH
method of collection of data
Abdul Reply
problems of find mean and standard deviation with drawing curve
Kukkuzz Reply
describe the methods of calculation of sample
Anuradha Reply
what are the various uses of statistics in education
Buhari Reply
Survey, Public allocation of federal funds, business analysis and consumer data, the lotto, government programs and special services.
Willard
probability sampling
Rosy Reply
dicuss probability sampling
Rosy
given that a sample is normally distributed with M=10 sd=8 determine
Rosy
disscuss probability sampling
Rosy
Discuss probability sampling
Rosy
What is mean
Rosy
Probability sampling is based on the fact that every member of a population has a known and equal chance of being selected. For example, if you had a population of 100 people, each person would have odds of 1 out of 100 of being chosen. With non-probability sampling, those odds are not equal.
Willard
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.  To calculate it:  • add up all the numbers, • then divide by how many numbers there are. Example: what is the mean of 2, 7 and 9? Add the numbers: 2 + 7 + 9 = 18 Divide by how many numbers, 3 you
Willard
get 6
Willard
guidelines of designing a table
Anuradha
you can find that information on this website there is a lot of information. It's about interpreting what the concept of information & data you are getting from the graph and understanding how to read the graph and analyze the information. ***understandinggraphics.com/design/data-table-design/
Willard
find X and Y so that the ordered data set has a mean of 38 and median of 35 17, 22, 26, 29, 34, X, 42, 67 , 70, Y
Mohamed
Frequency find questions
Rimsha Reply
?
Rosy
What is nominal variable
olusola Reply
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
how I get the mcq
Mukesh Reply
please what is data mining
Josephine Reply
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
All Reply
f(x)=cx(1-x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
Akeem Reply

Get the best Introductory statistics course in your pocket!





Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask