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Statistics

All 6 textbook questions with direct answer previews. Open any question for simple explanations and exam-ready answers.

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6
Q1

State the direct method formula for mean of grouped data.

For grouped data, xˉ=∑fixi∑fi\bar{x}=\frac{\sum f_i x_i}{\sum f_i}, where xix_i is the class mark and fif_i is the frequency.
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Q2

Explain the assumed mean method for grouped data.

Choose an assumed mean aa, compute di=xi−ad_i=x_i-a, then use xˉ=a+∑fidi∑fi\bar{x}=a+\frac{\sum f_i d_i}{\sum f_i}.
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Q3

When is the step-deviation method useful? State its formula.

It is useful when class marks have a common factor in their deviations. Let ui=xi−ahu_i=\frac{x_i-a}{h}. Then xˉ=a+h∑fiui∑fi\bar{x}=a+h\frac{\sum f_i u_i}{\sum f_i}.
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Q4

State the formula for mode of grouped data and define the terms.

Mode =l+f1−f02f1−f0−f2×h=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h, where ll is lower limit of modal class, hh is class size, f1f_1 modal class frequency, f0f_0 preceding frequency, and f2f_2 succeeding frequency.
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Q5

State the formula for median of grouped data.

Median =l+n2−cff×h=l+\frac{\frac n2-cf}{f}\times h, where ll is lower limit of median class, nn total frequency, cfcf cumulative frequency before median class, ff median class frequency, and hh class size.
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Q6

What is an ogive? How can median be found graphically?

An ogive is a cumulative frequency curve. Median can be found by locating n2\frac n2 on the cumulative frequency axis, drawing a horizontal line to the ogive, and then dropping a perpendicular to the data axis.
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