上一片里，中位数靠“排队站中间”回答了“一般水平是多少”。可有些时候，我们真正想问的是一句更简单的话：哪个出现得最多？运动鞋店备货，就得先回答它。Last leaf, the median answered “what’s typical” by standing in the middle of a queue. But sometimes the real question is simpler: which one shows up the most? A sneaker shop has to answer that before it stocks up.
第 1 步：数一数：谁出现最多Step 1: Count: who shows up most
小算盘机器人接了新活儿——帮运动鞋店看最近卖出的鞋码。The little abacus robot has a new job — checking which sizes the sneaker shop sold lately.
机器人把卖出的鞋码一张张摊开：39、38、39、40、39、42、39。数一数：39 出现了 4 次，比谁都多——39 就是这组数据的众数（mode）。店长马上下单：39 码多进几双。The robot lays out the sold sizes one by one: 39, 38, 39, 40, 39, 42, 39. Count them: 39 appears 4 times — more than any other value. So 39 is the mode of this data set. The manager instantly orders more size 39.
你可能会想：要是两种东西卖得一样多，谁算“最多”？You might wonder: if two things sell equally well, which one counts as “most”?
第 2 步：可能不止一个Step 2: Not always one: there can be several
机器人又去帮冰淇淋摊数口味：香草和巧克力各卖出 9 份，并列第一——这组数据有两个众数，叫双众数。要是每种口味都只出现过一次，那就一个众数也没有。众数是数出来的：可能一个、两个，也可能没有。Off to the ice-cream stand next: vanilla and chocolate each sold 9 — a tie at the top. This set has two modes. And if every flavour appeared exactly once, it would have no mode at all. The mode is counted: one, two, or none.
一个个数太慢，有没有更快的办法？Counting one by one is slow — is there a faster way?
第 3 步：一眼看出：最高的那根柱子Step 3: Spot it fast: the tallest bar
把票数画成柱状图，众数就是最高的那根柱子，并列最高就并排站。班委投票、儿歌热榜、超市销量……都靠这一眼。下一片我们就去细看统计图表。Draw the votes as a bar chart and the mode is simply the tallest bar; ties stand side by side. Class votes, hit-song charts, supermarket sales — one glance is enough. Next leaf, we take a closer look at charts.
🎮 数频次：点出众数（30 秒）🎮 Count the frequency: tap the mode (30 seconds)
看每组数据，数一数各出现了几次，再点出它的众数；第 3 组有两个众数，两个都要点中。For each set, count how often each value appears, then tap its mode. Set 3 has two modes — tap both.
一句话记住它：众数 = 一组数据里出现次数最多的那个；可能一个、可能多个，也可能一个都没有。Remember it in one line: the mode is the value that appears most often — there may be one, several, or none at all.
众数是“数出来”的：数每个值出现了几次The mode is counted, not computed: count how often each value appears并列最多时，几个并列值都是众数（双众数）If several values tie at the top, they are all modes柱状图里最高的柱子就是众数，一眼看出In a bar chart the mode is the tallest bar — spot it at a glance
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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