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Measures of central tendency in Stat.pptx

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This document discusses measures of central tendency, including the mean, median, and mode. It provides examples of calculating each measure using sample data sets. The mean is the average value calculated by summing all values and dividing by the number of data points. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequently occurring value. Examples are given to demonstrate calculating the mean, median, and mode from sets of numeric data.

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MEASURES OF CENTRAL TENDENCY NIGHAT KANWAL
OBJECTIVES At the end of presentation the learner's would be able to:  Describe the measures of central tendency  Discuss the mean, median and mode with examples  Enlist the distribution shapes of the data
MEASURES OF CENTRAL TENDENCY A measure of central tendency is a single value that attempt to describe a set of data by identify the central position within the set of data . As such, measure of central tendency are sometimes called measure of central location . The most common of central tendency are Mean Median mode
MEAN The statistical mean refers to the mean or average that is used to derived the central tendency of the data in question. This is also known as arithmetic average. The mean can be used for both continuous and discrete numeric data. Mean assumes numerical values and requires interval data. The mean cannot be calculated for categorical data, as the value cannot be summed. Mean affected by high or low values (outliers).
MEAN CALCULATED BY The mean is the sum of the value of each observation in a data set divided by the number of observation.
CALCULATING THE MEAN FOR DRIVING SPEED OF CARS Example : Find the mean driving speed for 6 different cars on the same highway. 66 mph, 57 mph, 71 mph, 54 mph, 69 mph, 58 mph Formula: Sum of the value/ number of cases Solution: 66 + 57 + 71 + 54 + 69 + 58 = 375 375/6 Answer: The mean driving speed is 62.5 mph.
MEDIAN • The median represents the middle of the ordered sample data • When the sample size is odd, the median is the middle value • When the sample size is even, the median is the midpoint of the two middle values • Median requires ordering of values and can be used with both interval and ordinal data • Median not effected by outliers.
EXAMPLE Find the median value of the set of numbers {4, 12, 15, 3, 7, 10}. First, arrange the numbers in order from least to greatest. 3, 4, 7, 10, 12, 15 We have an even number of terms in our set, so we must take the average of the two middle terms. Formula = M1 + M2 / 2 = 7+10/2 =8.5 Our median is 8.5
MODE • The mode is the value that occur most frequently • It is the least useful of the three measures of central tendency
EXAMPLE The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode? 8, 11, 9, 14, 9, 15, 18, 6, 9, 10 Solution: Ordering the data from least to greatest, we get: 6, 8, 9, 9, 9, 10, 11 14, 15, 18 Answer: The mode is 9.
Measures of central tendency in Stat.pptx
Measures of central tendency in Stat.pptx
REFERENCES  (n.d.). Retrieved from mean, median, mode and range (examples solutions, worksheet, videos): http:/www.onlinemathlearning.com  frost, j. (n.d.). statistics by Jim. Retrieved from https:/statisticsbyjim.com.
Measures of central tendency in Stat.pptx
Measures of central tendency in Stat.pptx

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Measures of central tendency in Stat.pptx

  • 2. OBJECTIVES At the end of presentation the learner's would be able to:  Describe the measures of central tendency  Discuss the mean, median and mode with examples  Enlist the distribution shapes of the data
  • 3. MEASURES OF CENTRAL TENDENCY A measure of central tendency is a single value that attempt to describe a set of data by identify the central position within the set of data . As such, measure of central tendency are sometimes called measure of central location . The most common of central tendency are Mean Median mode
  • 4. MEAN The statistical mean refers to the mean or average that is used to derived the central tendency of the data in question. This is also known as arithmetic average. The mean can be used for both continuous and discrete numeric data. Mean assumes numerical values and requires interval data. The mean cannot be calculated for categorical data, as the value cannot be summed. Mean affected by high or low values (outliers).
  • 5. MEAN CALCULATED BY The mean is the sum of the value of each observation in a data set divided by the number of observation.
  • 6. CALCULATING THE MEAN FOR DRIVING SPEED OF CARS Example : Find the mean driving speed for 6 different cars on the same highway. 66 mph, 57 mph, 71 mph, 54 mph, 69 mph, 58 mph Formula: Sum of the value/ number of cases Solution: 66 + 57 + 71 + 54 + 69 + 58 = 375 375/6 Answer: The mean driving speed is 62.5 mph.
  • 7. MEDIAN • The median represents the middle of the ordered sample data • When the sample size is odd, the median is the middle value • When the sample size is even, the median is the midpoint of the two middle values • Median requires ordering of values and can be used with both interval and ordinal data • Median not effected by outliers.
  • 8. EXAMPLE Find the median value of the set of numbers {4, 12, 15, 3, 7, 10}. First, arrange the numbers in order from least to greatest. 3, 4, 7, 10, 12, 15 We have an even number of terms in our set, so we must take the average of the two middle terms. Formula = M1 + M2 / 2 = 7+10/2 =8.5 Our median is 8.5
  • 9. MODE • The mode is the value that occur most frequently • It is the least useful of the three measures of central tendency
  • 10. EXAMPLE The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode? 8, 11, 9, 14, 9, 15, 18, 6, 9, 10 Solution: Ordering the data from least to greatest, we get: 6, 8, 9, 9, 9, 10, 11 14, 15, 18 Answer: The mode is 9.
  • 13. REFERENCES  (n.d.). Retrieved from mean, median, mode and range (examples solutions, worksheet, videos): http:/www.onlinemathlearning.com  frost, j. (n.d.). statistics by Jim. Retrieved from https:/statisticsbyjim.com.