Central t endency student

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Central t endency student

  1. 1. RANGE ANDMEASURES OF CENTRAL TENDENCYRange and measures of central tendency(mean, median and mode) are values thatsummarize a set of data. They are usefulwhen analyzing data.
  2. 2. Range -the difference between the greatestand the least values in a data set DAILY HIGH TEMPERATURES (FOR ANY GIVEN DATE) OVER THE LAST DECADE1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 59 50 49 13 40 46 50 53 58 47To find the range of the daily high temperatures,subtract the least value from the greatest value. 59 - 13 = 46
  3. 3. Mean -(or average) the sum of a set ofdata divided by the number of data DAILY HIGH TEMPERATURES (FOR ANY GIVEN DATE) OVER THE LAST DECADE1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 59 50 49 13 40 46 50 53 58 47To find the mean, find the sum of the data 59+50+50+13+40+46+50+53+58+57=465and divide it by the number of data. 465 10=46.5The mean for daily high temperature over the lastdecade is 46.5 , or approximately 47 .
  4. 4. Median -the middle value of a data set DAILY HIGH TEMPERATURES (FOR ANY GIVEN DATE) OVER THE LAST DECADE1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 59 50 49 13 40 46 50 53 58 47To find the median, place all the data innumerical order, then find the middle number. Ifthere are two middle numbers, find the mean (oraverage) of the two middle numbers. 13 40 46 47 49 50 50 53 58 59 49+50=99 99 2=49.5
  5. 5. Mode -the most common value in a dataset DAILY HIGH TEMPERATURES (FOR ANY GIVEN DATE) OVER THE LAST DECADE1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 59 50 49 13 40 46 50 53 58 47To find the mode, find the most common value.It helps to place data in numerical order to findthe mode. 13 40 46 47 49 50 50 53 58 59If there is not a value which appears more oftenthan another, then there is no mode.
  6. 6. OutliersSometimes there are extreme values that areseparated from the rest of the data. Theseextreme values are called outliers. Outliers affectthe mean.Daily High Temperatures (for any given date) Over the Last Decade1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 59 50 49 13 40 46 50 53 58 47The daily high temperature in 1996 is the outlier. Mean 59+50+49+13+40+46+50+53+58+57=494 465 10=46.5
  7. 7. Because outliers can affect the mean, the medianmay be better measures of central tendency. Youmight consider the median to best represent theexpected temperature. Median 13 40 46 47 49 50 50 53 58 59 49+50=99 99 2=49.5
  8. 8. Sometimes the mode is more helpful whenanalyzing data. If you were trying to determinewhat clothes to wear for a day trip, you mightbase your decision on the mode temperaturebecause the mode temperature is thetemperature which occurred most often. 13 40 46 47 49 50 50 53 58 59
  9. 9. Dropping the outlier may help when determiningthe mean. 59+50+49+13+40+46+50+53+58+57=494 465 10=46.5 40+46+47+49+50+50+53+58+59=452 452 9=50.2When the 13 outlier is dropped, the averagedaily temperature increases by more than 4 to50.2 , which is closer to both the median of49.5 and the mode of 50 .
  10. 10. You Try It!Jessica’s test scores in Algebra for the firstsemester are 93, 79, 88, 77, 92, 88, 80, 34, 84,88. Calculate the range, mean, median, andmode. Then make and explain a prediction fornext semester’s test scores.Predictions will vary:
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