For each of the following distributions, decide whether it ispossible to find th

Question

For each of the following distributions, decide whether it ispossible to find the mean and/or the median.Explain youranswers.

a)           Grade                  Frequency
             40-49                       5
             50-59                      18
             60-69                       27
             70-79                       15
             80-89                        6

b)          IQ                         frequency
           less than90                  3
          90-99                          14
          100-109                       22
          110-119                       19
           more than119                7

c)        Weight                     frequency
            100 orless                41
             101-110                  13
             111-120                   8
              121-130                  3
               131-140                  1

Explanation / Answer

Median: the median formula can be used only for continuousclasses without any gaps, i.e., for exclusive type classification.If we are given a frequency distribution in which classes are ofinclusive type with gaps, then it must be converted into acontinuous exclusive type frequency distribution without any gapsbefore applying median formula. It is not at all affected by extreme values. (a) classinterval midpoint f fx 40-49 44.5 5 222.5 50-59 54.5 18 981 60-69 64.5 27 1741.5 70-79 74.5 15 1117.5 80-89 84.5 6 507 71 4569.5 For this distribution, both median and mean are possible (b) class interval f cum.freq Class -boundaries less than 90 3 3 Below 89.5 90-99 14 17 89.5-99.5 100-109 22 39 99.5-109.5 110-119 19 58 109.5-119.5 morethan 119 7 65 119.5 and above N=65 class interval f cum.freq Class -boundaries less than 90 3 3 Below 89.5 90-99 14 17 89.5-99.5 100-109 22 39 99.5-109.5 110-119 19 58 109.5-119.5 morethan 119 7 65 119.5 and above N=65 For this distribution, only median is possible (c) ci f cum.freq Class-boundaries 100 orless 41 41 Below 100.5 101-110 13 54 100.5-110.5 111-120 8 62 110.5-120.5 121-130 3 65 120.5-130.5 131-140 1 66 130.5 and above N=66 For this distribution, both median and mean are notpossible classinterval midpoint f fx 40-49 44.5 5 222.5 50-59 54.5 18 981 60-69 64.5 27 1741.5 70-79 74.5 15 1117.5 80-89 84.5 6 507 71 4569.5

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