The below frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.From the data presented above, which one of the following is CORRECT?

Previously Asked in : Gate CE-forenoon season 2022 ||

mode > median > mean

mean > mode > median

mode > mean > median

median > mode > mean

Answer (Detailed Solution Below)

Option mode > median > mean is correct

Detailed Explanation :

Mean = \dfrac {f_1 x_1 \; + \; f_2 x_2 \,...... \,+ \; f_7 x_7 } { f_1 \;+\; f_2 + \;f_3 ..... \;+ \;f_7}

= \frac {3 \times 3 + 9 \times 4 + 11 \times 5 + 7 \times 6 + 14 \times 7 + 2 \times 8 + 4 \times 9} {3 + 9 + 11 + 7 + 14 + 2 + 4}

= \dfrac {292} {50} = 5.84

Median = \dfrac{ \left(\frac{n} {2}\right)^ {th} \; + \; \left (\frac {n} {2} \;+ \;1\right)^{th}} {2}

= \dfrac { \left(\frac {50}{2}\right)^{th} + \left ( \frac {50} {2} + 1\right) ^ {th}} {2}

= \dfrac {(25)^ {th} + (26)^{th}} {2}

= \dfrac {6 + 6} {2}

= 6

Mode = observation (data with high frequency)

= 7

Hence correct option is : Mode > Medium > Mean

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