The Le ngth a xis is shown below. Choos e the b est sc ale for this axis. What should the values of A and B be?

<br /><br />In given tabular data, the maximum value for length is 119 cm and the minimum value is 72 cm. In the graph axis provided, we must accommodate the aforementioned ranges at maximum and minimum respectively. <br /><br />We will first calculate the range of the Length values:<br /><br />\( Range = Maximum- Minimum = 119-72 = 47 \)<br /><br />Range representing and dividing the values across the scale mean the gaps exhibited in the axis upgrading should neither be too large (Leads to a compressed representation ) nor too small (Leads to an extended hard to comprehend visually diagram).<br /><br />Since we need values of A and B, we import the sheet across a universal/Homogeneous division say into 5.fields (You may choose more number of fields hypothetically, but larger the pieces more jaggy conversion Id has to maintain )<br /><br />Then we will find each field length purely quantitatively describe the interval as :<br /><br />\( length = Range/5 = 47/5=9.4 \) <br /><br />To facilitate graph drawing use usually Round off the obtained Range.<br /><br />Round off (lower integer) normal mathematical compliance we use, round off the length.<br />\( rounded length ≈ 9 \)<br /><br />\( ((rounded length) * graph fields ) + minBound ≤ actual U\_bound == (9*5) + 72)<br /> <br />= 117 . that is just optimal as greater<br /> <br />So, the Increasing splice will: cm 72 , 81, 90 , 99, 108, 119 <br /><br />=> Integral low round off rounded value incurred error close to ACCEPTed <br />`A = 72 cm` and `B = 119 cm`. This means you will choose the starting point A as the smallest number in the dataset and choose B as the largest number in the dataset going by accordance to in-betweens subdivisions increment distributing and Framing by 9(closely rounded off value). <br />Strictly Having `A=72 cm` and next typical increments happen by you can still insist to optimize Rounded length = say 10 the ,`B = 72+50 = 122 cm`. However strictly never ask for going over space in terms of values:<br />`A = 72 cm` (Perfect no underscale/quantisation error)<br />`B = 119 cm` (this boundary never faces underscale/quantisation error but Ideal Means)<br />Agency of choosing A, B in upper minima and Maxima at those easy integrable and visually analog signals aliasing free Numbers convolute Lesser with dataset making hierarchy visually remembering.<br />Hence, The best scale for this axis should be from `72 cm` to `119 cm`.