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Question
Mode = ?
Options
`x_k + h · {((f_(k - 1) - f_k))/((2f_k - f_(k - 1) - f_(k + 1)))}`
`x_k + h · {((f_k - f_(k - 1)))/((2f_k - f_(k - 1) - f_(k + 1)))}`
`x_k + h · {((f_k - f_(k - 1)))/((f_k - 2f_(k - 1) - f_(k + 1)))}`
`x_k + h · {((f_k - f_(k - 1)))/((f_k - f_(k - 1) - 2f_(k + 1)))}`
MCQ
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Solution
`bb(x_k + h · {((f_k - f_(k - 1)))/((2f_k - f_(k - 1) - f_(k + 1)))})`
Explanation:
For a grouped (continuous) frequency distribution the mode is given by Mode = lower limit of modal class + `h * (f_"modal" - f_"prev")/(2 f_"modal" - f_"prev" - f_"next")`.
Identifying xk as the lower limit, h as class width, fk as modal frequency, `f_{k - 1}` the preceding frequency and `f_{k + 1}` the succeeding frequency gives the expression.
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