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The formula for variance is:

Mathematics

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Step-by-step solution

2 steps
  1. Calculate the variance (s2s^2).

    The formula for variance is:

    s2=∑fx2N−(∑fxN)2s^2 = \frac{\sum fx^2}{N} - \left(\frac{\sum fx}{N}\right)^2

    Substitute the given values:

    s2=10468.980−(90980)2s^2 = \frac{10468.9}{80} - \left(\frac{909}{80}\right)^2

    Perform the division:

    s2=130.86125−(11.3625)2s^2 = 130.86125 - (11.3625)^2

    Calculate the square:

    s2=130.86125−129.00640625s^2 = 130.86125 - 129.00640625

    Subtract the values:

    s2=1.85484375 (g/100ml)2s^2 = 1.85484375 \text{ (g/100ml)}^2

    Rounding to two decimal places:
    The variance is 1.85 (g/100ml)2\boxed{1.85 \text{ (g/100ml)}^2}.

  2. Calculate the range.

    The range is estimated as the difference between the upper class boundary of the highest class and the lower class boundary of the lowest class.

    Upper class boundary of 14.0-14.9: 14.9+0.05=14.9514.9 + 0.05 = 14.95
    Lower class boundary of 8.0-8.9: 8.0−0.05=7.958.0 - 0.05 = 7.95

    Calculate the range:

    Range=14.95−7.95=7.0 g/100ml\text{Range} = 14.95 - 7.95 = 7.0 \text{ g/100ml}

    The range is 7.0 g/100ml\boxed{7.0 \text{ g/100ml}}.

    b) Step 1: Identify the classes with haemoglobin levels less than 11.0 g/100ml.
    The classes with haemoglobin levels less than 11.0 g/100ml are:

    • 8.0-8.9
    • 9.0-9.9
    • 10.0-10.9
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