(begin{array}{c|c} Class Intervals & 0 – 2 & 3 – 5 & 6 – 8…

(begin{array}{c|c} Class Intervals & 0 – 2 & 3 – 5 & 6 – 8 & 9 – 11 & \ hline Frequency & 3 & 2 & 5 & 3 &end{array})
Find the mode of the above distribution.
  • A.
    9
  • B.
    8
  • C.
    10
  • D.
    7
Correct Answer: Option D
Explanation

Mode = L1 + ((frac{D_1}{D_1 + D_2}))C
D1 = frequency of modal class – frequency of the class before it
D1 = 5 – 2 = 3
D2 = frequency of modal class – frequency of the class that offers it
D2 = 5 – 3 = 2
L1 = lower class boundary of the modal class
L1 = 5 – 5
C is the class width = 8 – 5.5 = 3
Mode = L1 + ((frac{D_1}{D_1 + D_2}))C
= 5.5 + (frac{3}{2 + 3})C
= 5.5 + (frac{3}{5}) x 3
= 5.5 + (frac{9}{5})
= 5.5 + 1.8
= 7.3 (approx) = 7

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