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Q.

The exam results of 250 students are listed below. Determine the mean.

Class interval0-910-1920-2930-3940-49
Frequency0262436
Class interval50-5960-6970-7980-8990-99
Frequency4755402713

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a

50.12

b

90.31

c

60.82

d

75.12

answer is C.

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Detailed Solution

The sum of the values of all the observations =f1x1+f2x2++fnxn, and the number of observations =f1+f2++fn.

So, the mean x¯ of the data is given by

x¯=f1x1+f2x2++fnxnf1+f2++fn

 Mean = Total ( midvalue × frequency ) Totalfrequency 

Class intervalMid-valueFrequency.Mid-value $\times$ frequency
0-94.500
10-1914.5229
20-2924.56147
30-3934.524828
40-4944.5361602
50-5954.5472561.5
60-6964.5553547.5
70-7974.5402980
80-8984.5242281.5
99-9994.5131228.5
  25015205

 Mean = Total ( midvalue × frequency ) Totalfrequenct =15205250=60.82

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