100 random samples were taken from a large population. A particular numerical characteristic of sampled items was measured. The results of the measurements were as follows: 45 measurements were between 0.859 and 0.900 0.901 was observed once 0.902 was observed three times 0.903 was observed twice 0.904 was observed four times The smallest value was 0.859, and the largest value was 0.958. The sum of all 100 measurements was 91.170. Except those noted, no measurements occurred more than twice. What is the median of the measurements

Answer:

The median is [tex]Median = 0.903[/tex]

Step-by-step explanation:

From the question we are told that  

   The sample size is n =  100

   The  [tex]1^{st} \to 45^{th}[/tex] measurements is  [tex]= 0.859 \to 0.900[/tex]

    Generally since that after 0.900 we have  0.901 , then the

     [tex]46^{th} \ measurement \ is \ 0.901[/tex]

in the same manner the  [tex]47^{th} \ measurement \ is \ 0.902[/tex],

Given that 0.902  was observed three times it means that

                                         [tex]47^{th},48^{th},49^{th} \ measurement \ is \ 0.902[/tex],

Given that 0.903  was observed two times it means that

                                          [tex]50^{th},51^{th} \ measurement \ is \ 0.903[/tex],

Given that 0.903  was observed four times it means that

                                         [tex]52^{nd},53^{rd},54^{th},55^{th} \ measurement \ is \ 0.904[/tex],

Given that the highest measurement is  0.958 then then the  [tex]56^{th} \to 100^{th} \ measurement \ is \ between \ 0.905 \to 0.958[/tex]

Generally the median is is mathematically represented as

            [tex]Median = \frac{ [\frac{n^{th}}{2}] + [(\frac{n}{2})^{th} + 1 ]}{2}[/tex]

=>        [tex]Median = \frac{ [\frac{100^{th}}{2}] + [(\frac{100}{2})^{th} + 1 ]}{2}[/tex]

=>        [tex]Median = \frac{ [50^{th}] + [51^{th} ]}{2}[/tex]

=>        [tex]Median = \frac{ 0.903 + 0.903}{2}[/tex]

=>        [tex]Median = 0.903[/tex]

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