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DESCRIBING DATA WITH AVERAGES
 The most frequent number occurring in the
data set is known as the mode.
 Median: Given that the data collection is
arranged in ascending or descending order,
the following method is applied:
 If number of values or observations in the
given data is odd, then the median is given
by [(n+1)/2]th observation.
 If in the given data set, the number of values
or observations is even, then the median is
given by the average of (n/2)th and [(n/2)
+1]th observation.
 Mean is the most commonly used measure of
central tendency. It actually represents the
average of the given collection of data. It is
applicable for both continuous and discrete
data.
 It is equal to the sum of all the values in the
collection of data divided by the total
number of values.
 Ans Mean =7.8 Median =5 Mode=5
 Since Mean> Median --- Positively Skewed
 RANGE = MAXIMUM - MINIMUM
 IQR = 75%ILE – 25%ILE
 DEGREE OF FREEDOM = N-1
 Range
 It is the difference between the two extreme conclusions of the
distribution. In other words, the range is the difference between the
maximum and the minimum observation of the distribution.
 IQR
 The interquartile range defines the difference between the third and the
first quartile. Quartiles are the partitioned values that divide the whole
series into 4 equal parts. So, there are 3 quartiles. First Quartile is
denoted by Q1 known as the lower quartile, the second Quartile is
denoted by Q2 and the third Quartile is denoted by Q3 known as the upper
quartile. Therefore, the interquartile range is equal to the upper quartile
minus lower quartile.
Averages and Variability.pdf
Averages and Variability.pdf
Averages and Variability.pdf
Averages and Variability.pdf

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Averages and Variability.pdf

  • 2.  The most frequent number occurring in the data set is known as the mode.
  • 3.  Median: Given that the data collection is arranged in ascending or descending order, the following method is applied:  If number of values or observations in the given data is odd, then the median is given by [(n+1)/2]th observation.  If in the given data set, the number of values or observations is even, then the median is given by the average of (n/2)th and [(n/2) +1]th observation.
  • 4.  Mean is the most commonly used measure of central tendency. It actually represents the average of the given collection of data. It is applicable for both continuous and discrete data.  It is equal to the sum of all the values in the collection of data divided by the total number of values.
  • 5.
  • 6.
  • 7.
  • 8.  Ans Mean =7.8 Median =5 Mode=5  Since Mean> Median --- Positively Skewed
  • 9.
  • 10.  RANGE = MAXIMUM - MINIMUM  IQR = 75%ILE – 25%ILE  DEGREE OF FREEDOM = N-1
  • 11.  Range  It is the difference between the two extreme conclusions of the distribution. In other words, the range is the difference between the maximum and the minimum observation of the distribution.  IQR  The interquartile range defines the difference between the third and the first quartile. Quartiles are the partitioned values that divide the whole series into 4 equal parts. So, there are 3 quartiles. First Quartile is denoted by Q1 known as the lower quartile, the second Quartile is denoted by Q2 and the third Quartile is denoted by Q3 known as the upper quartile. Therefore, the interquartile range is equal to the upper quartile minus lower quartile.