The Normal Frequency Curve
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The Normal Frequency Curve

Figure 118.2 is the frequency distribution of a certain variable x. Is this frequency distribution a normal frequency curve if 78.9 % of the data lie within one standard deviation of the mean?

The strings: S7P6A64 (Grouping - Multi-criteria).

The math:
Pj Problem of Interest is of type grouping (multi-criteria). Grouping is at the heart of statistics. The grouping may be permutational or combinational, single criterion or multi-criteria grouping.

No. The frequency distribution is not a normal frequency curve because 78.9 % lie within one standard deviation on either side of the mean.
Normal frequency curves are varied. However, they are all characterized by their mean and standard deviation. Irrespective of the value of the mean and standard deviation, 68.2 % of the data lie within one standard deviation (σ) on either side of the mean; 95.4 % of the data lie within 2σ on either side of the mean and 99.8 % lie within 3σ on either side of the mean.

Mean = arithmetic average = [f1x1 + f2x2 ... fnxn]/n
Where fi is the number of xi in the data. i = 1, 2,...n.

Standard deviation σ = [Σi [fi(xi - mean)2]/n]1/2. i = 1, 2,...n.

Math

Blessed are they that have not seen, and yet have believed. John 20:29