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Create a frequency table with cumulative frequency and sums for fi, fi Xi, and fi X_i2.

Mathematics

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Answer

∑fi=30\sum f_i = \mathbf{30}

∑fiXi=90\sum f_i X_i = \mathbf{90}

∑fiXi2=342\sum f_i X_i^2 = \mathbf{342}

Step-by-step solution

5 steps

Here is the completed frequency table and the required sums.

  1. Calculate the Cumulative Frequency (CFCF).

    The cumulative frequency for each row is the sum of the frequencies up to that row.

  2. Calculate fiXif_i X_i.

    Multiply each frequency (fif_i) by its corresponding value (XiX_i).

  3. Calculate Xi2X_i^2.

    Square each value (XiX_i).

  4. Calculate fiXi2f_i X_i^2.

    Multiply each frequency (fif_i) by its corresponding squared value (Xi2X_i^2).

  5. Calculate the sums.

    Sum the values in the fif_i, fiXif_i X_i, and fiXi2f_i X_i^2 columns.

    The completed table is:

    XifiCFfiXiXi2fiXi2133313212152444836211895445262016805026025063291836108713074949∑3090342\begin{array}{|c|c|c|c|c|c|} \hline X_i & f_i & CF & f_i X_i & X_i^2 & f_i X_i^2 \\ \hline 1 & 3 & 3 & 3 & 1 & 3 \\ 2 & 12 & 15 & 24 & 4 & 48 \\ 3 & 6 & 21 & 18 & 9 & 54 \\ 4 & 5 & 26 & 20 & 16 & 80 \\ 5 & 0 & 26 & 0 & 25 & 0 \\ 6 & 3 & 29 & 18 & 36 & 108 \\ 7 & 1 & 30 & 7 & 49 & 49 \\ \hline \sum & \mathbf{30} & & \mathbf{90} & & \mathbf{342} \\ \hline \end{array}

    The required sums are:

    • ∑fi=30\sum f_i = \boxed{\mathbf{30}}
    • ∑fiXi=90\sum f_i X_i = \boxed{\mathbf{90}}
    • ∑fiXi2=342\sum f_i X_i^2 = \boxed{\mathbf{342}}
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