Moving Between Tables and Graphs

A table is useful when you need an exact recorded entry. A graph is useful when you want to see a pattern. Moving between them allows us to combine both advantages. But the journey can lose precision: a decimal table entry may be rounded for plotting, and a point read by eye is often only an estimate.

We will use average rainy days, monthly births, and a historical price table. These examples also teach a second skill: choosing the right calculation. Sometimes we need a sum, sometimes a mean, and sometimes the difference between the first and last values.

Plotting Average Rainy Days

The table gives average numbers of rainy days in each month. An individual month has a whole-number count of rainy days, but an average across several years can be fractional. For example, counts of 2, 3, and 4 days have mean 3, while counts of 2, 2, and 3 have mean 7/3 days.

Use the original decimals for calculations when available. For a hand-drawn graph, you can round each value to the nearest whole day, provided you state that choice. A displayed zero after rounding might represent a small positive average; it does not necessarily mean it never rained.

Reading a Graph Back into a Table

The chapter supplies New Delhi’s rainy-day series as a graph rather than as numbers in the table. To recover a value, move from the month up to the point, then across to the vertical scale. Do not read the height from the picture’s edge or estimate before checking the tick interval.

The following redraw uses approximate whole-day readings. The graph suggests about 10 rainy days in July and August, around 4 in June and September, and mostly 0–2 in other months. Near a rounding boundary, another careful reader may reasonably choose a neighbouring whole number.

Monthly Births and Annual Totals

The chapter’s birth graph uses M to mean million. A point at 1.7M represents about 1,700,000 births. July 2017 is approximately at that level. The plotted series extends from around April 2017 to around March 2020; the labelled six-month ticks are not the only months represented.

To estimate births during 2019, read the twelve monthly points from January through December 2019 and add them. Averaging them would give births per month instead. Because the graph readings are approximate, an estimated annual total should also be reported approximately.

Comparing Historical Prices

The following table records January retail prices of iodised salt in the supplied historical dataset. Each column is one place and each row is one year. The three-series graph selects Gujarat, Uttar Pradesh, and West Bengal to keep the comparison readable.

A price is not a count to add across years when asking how much it increased. For an increase from 2016 to 2025, subtract the 2016 price from the 2025 price. A series may have the greatest final price but a smaller increase than another series that started much lower.

Compare Before and After Rounding

Use Mangaluru’s monthly values to explore the effect of rounding.

1. Add the original decimals.
2. Round each monthly value to the nearest whole number, taking .5 upward.
3. Add the rounded values and compare the totals.

The original sum is 112.1, while the rounded monthly values sum to 113. Rounding each entry first can produce a different result from rounding the final sum. Keep the original values for calculations when possible.