Averages & spread

Data displays

<p>A grouped table tells us how many observations lie in each interval, but not their individual values. Use each class midpoint to estimate the values in that class.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Quantity</strong></th><th style="text-align: center; --cell-justify: center"><strong>Calculation</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Class midpoint, \(m\)</td><td style="text-align: center; --cell-justify: center">\(m=\dfrac{\text{lower boundary}+\text{upper boundary}}{2}\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Estimated mean</td><td style="text-align: center; --cell-justify: center">\(\overline{x}\approx\dfrac{\sum fm}{\sum f}\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Estimated standard deviation</td><td style="text-align: center; --cell-justify: center">\(\sigma\approx\sqrt{\dfrac{\sum fm^2}{\sum f}-\left(\dfrac{\sum fm}{\sum f}\right)^2}\)</td></tr></tbody></table></div></div>
<p>Enter the midpoints as the calculator values and the class frequencies as their frequencies. Check the total frequency before reading the mean and population standard deviation.</p>
<p>For a histogram with equal class intervals, adjoining bars can use frequency as their height. The horizontal axis shows the class boundaries. Keep all class widths equal in this chapter.</p>
<p>A grouped table usually cannot give the exact mean, standard deviation, smallest value or largest value. State which results are estimates and explain what information has been lost.</p>

A grouped table tells us how many observations lie in each interval, but not their individual values. Use each class midpoint to estimate the values in that class.

Enter the midpoints as the calculator values and the class frequencies as their frequencies. Check the total frequency before reading the mean and population standard deviation.

For a histogram with equal class intervals, adjoining bars can use frequency as their height. The horizontal axis shows the class boundaries. Keep all class widths equal in this chapter.

A grouped table usually cannot give the exact mean, standard deviation, smallest value or largest value. State which results are estimates and explain what information has been lost.

Grouped data

Grouped data

Quantity	Calculation
Class midpoint, \(m\)	\(m=\dfrac{\text{lower boundary}+\text{upper boundary}}{2}\)
Estimated mean	\(\overline{x}\approx\dfrac{\sum fm}{\sum f}\)
Estimated standard deviation	\(\sigma\approx\sqrt{\dfrac{\sum fm^2}{\sum f}-\left(\dfrac{\sum fm}{\sum f}\right)^2}\)