正解The correct answer is ア. First, read the number of female members for each age group from the graph. Those in their 20s: 15 → 35 → 50; those in their 30s: 25 → 75 → 115; those in their 40s: 75 → 53 → 220; those in their 50s: 44 → 45 → 138 (from the left, the 10-to-14, 14-to-18, and 18-to-22 time slots). What ア compares is the following two increase rates. (1) Those in their 30s, comparing the 10-to-14 and 14-to-18 time slots ... (75 − 25) ÷ 25 = 2.0, that is, an increase of 200% (3 times as many). (2) Those in their 40s, comparing the 14-to-18 and 18-to-22 time slots ... (220 − 53) ÷ 53 ≈ 3.15, that is, an increase of about 315% (about 4.2 times as many). Since an increase of 315% is larger than an increase of 200%, the increase rate of those in their 40s is larger. The key point is that increase rates are compared not by the difference in the number of people, but by the ratio to the original value. Intuitively, those in their 40s gained 167 people on top of the original 53 (the increase is about 3.2 times the original value), whereas those in their 30s gained only 50 people on top of the original 25 (the increase is 2 times the original value); therefore, in terms of increase rate, those in their 40s exceed those in their 30s. It helps to grasp it this way, by comparing the sizes of the ratios.
×Incorrectイ
When the 10-to-14 and 14-to-18 time slots are compared, the increase rate of each age group is as follows: those in their 20s, 15 → 35, an increase of about 133%; those in their 30s, 25 → 75, an increase of 200%; those in their 40s, 75 → 53, a decrease of about 29%; those in their 50s, 44 → 45, an increase of only about 2%. The largest increase rate is that of those in their 30s, and those in their 50s are almost flat, going from 44 people to 45 (the smallest among the three age groups that increased). Therefore this option is wrong.
×Incorrectウ
When the 14-to-18 and 18-to-22 time slots are compared, the increase rates are as follows: those in their 20s, 35 → 50, an increase of about 43%; those in their 30s, 75 → 115, an increase of about 53%; those in their 40s, 53 → 220, an increase of about 315%; those in their 50s, 45 → 138, an increase of about 207%. The largest is those in their 40s, not those in their 30s. For those in their 30s, both the increase in the number of people (40) and the increase rate are on the smaller side among the four age groups, so this option is wrong.
×Incorrectエ
Those in their 40s decreased from 75 people in the 10-to-14 time slot to 53 people in the 14-to-18 time slot, so it is not the case that every age group keeps increasing. The overall height of the stacked bars (159 → 208 → 523) does grow as the time slot gets later, but that is about the totals, which is a separate matter from the trend of each age group that makes up the breakdown. Applying an overall trend directly to the components of the breakdown is a typical mistake.
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Increase rate (rate of change) = (later value − earlier value) ÷ earlier value. The size of the increase in the number of people (a difference) and the increase rate (a ratio) are different things; when comparing increase rates, match up ratios in the form of “by how many times the original value it increased”. Always read carefully whether an option is talking about the “increase rate” or the “number of people”.
In a stacked bar chart, the overall height of a bar represents the total, and each segment inside the bar represents a component of the breakdown. Even when the total is increasing, part of the breakdown may be decreasing, so when a question asks about the breakdown, such as by age group, read the value of each segment to make the judgment.