Unit 1
Kumpul, Kelas dan Susun Data
Kelas 3 Cerdik mahu memilih jus untuk hari sukan.
Mereka bertanya kepada kawan-kawan: jus apakah yang kamu suka?
Bagaimanakah mereka mengumpul, mengelas dan menyusun jawapan itu?
数据 = data；收集 = kumpul；分类 = kelas；整理 = susun
这一课学处理数据。3 Cerdik 班要为运动会选果汁，于是问同学喜欢哪一种。每个同学的回答就是一个数据。我们要做三件事：先收集回答，再按种类分开，最后整理成一张表，一看就知道哪种最多人喜欢。
例子：问 16 个同学，有人说橙汁、有人说苹果汁，这 16 个回答合起来就是一组数据。
注意：每个同学只算一次，同一个人问两次会让数目变多。
data = data; collect = kumpul; classify = kelas; organise = susun
This unit is about handling data. Class 3 Cerdik must choose juice for sports day, so they ask friends which juice they like. Every answer is one piece of data. We will collect the answers, sort them into kinds, and arrange them in a table so the favourite is easy to spot.
Example: asking 16 friends gives 16 answers such as orange or apple, and together they form one set of data.
Watch out: each friend is counted once; asking the same person twice makes the numbers too big.
Langkah 1
Cara mengumpul data
Memerhati · Soal selidik · Temu bual
👀 Memerhati
lihat dan catat
warna kereta yang lalu
warna kereta yang lalu
📝 Soal selidik
kawan isi borang
tanda ✓ pada pilihan
tanda ✓ pada pilihan
🗣️ Temu bual
tanya satu demi satu
catat jawapan
catat jawapan
Setiap jawapan = satu data
观察 = memerhati；问卷 = soal selidik；访谈 = temu bual
收集数据有三种常用方法。观察：站在一个地方看，看到一个就记一个，例如数学校门口经过的车是什么颜色。问卷：发一张表格给同学，让他们自己在选项上打勾。访谈：一个一个问同学，再把答案写下来。
例子：想知道同学怎样上学，可以发问卷让每人勾“走路、脚车、巴士、汽车”其中一个。
注意：问卷上每人只能勾一个选项，勾两个就不好分类。
observing = memerhati; questionnaire = soal selidik; interview = temu bual
There are three common ways to collect data. Observing means watching and writing down each thing you see, such as the colours of cars passing the school gate. A questionnaire is a form that friends fill in by ticking a choice. An interview means asking friends one by one and writing their answers.
Example: to find out how friends travel to school, hand out a form with walk, bicycle, bus and car, and each friend ticks one.
Watch out: each friend ticks only one choice, or the answers cannot be sorted.
Langkah 2
Mengelas dengan gundal
Pangkah satu data → lukis satu gundal · gundal ke-5 dilukis melintang
1 ikat = 5 · Merah: 5 + 1 = 6 · Biru: 4
计数字符 = gundal；划掉 = pangkah；一捆 = satu ikat
分类时一次只看一个数据：看第一辆车，把它划掉，再到它的颜色那一行画一竖。这样做下去，就不会漏数，也不会数两次。画到第五个时，不再画竖线，而是斜着划过前面四根，凑成一捆五。数的时候五个五个数，红色是一捆加一根，就是 6；蓝色 4 根，就是 4。
例子：13 个计数字符画成两捆再加三根，读作 5、10、11、12、13。
注意：第五根一定要斜划，画成五根竖线就很难一眼看出数目。
tally mark = gundal; cross out = pangkah; a bundle = satu ikat
When sorting, look at one piece of data at a time: take the first car, cross it out, then draw one line in the row for its colour. Going on like this means nothing is missed and nothing is counted twice. The fifth mark is not another upright line; it is drawn across the first four to make a bundle of five. Count in fives: red is one bundle and one line, so 6, and blue has 4 lines.
Example: 13 tally marks are two bundles and three lines, counted 5, 10, 11, 12, 13.
Watch out: the fifth mark must go across, because five upright lines are hard to read at a glance.
Cuba
Berapakah nilai gundal ini?
读计数字符 = baca gundal
图里有两捆，每捆是四根竖线加一根斜线，一共 5，所以两捆是 10。后面还有两根竖线，10 + 2 = 12。答案 12。如果把一捆只当成 4（忘了那根斜线），就会算成 10；把每捆当成 10 来数，就会错成 22。
例子：三捆加一根是 15 + 1 = 16。
注意：斜着的那一根也算一个，一捆永远是 5。
reading tally marks = baca gundal
The picture shows two bundles; each bundle has four upright lines and one line across, which makes 5, so two bundles make 10. Two more upright lines follow, and 10 + 2 = 12. The answer is 12. Counting a bundle as only 4 (forgetting the line across) gives 10, and counting each bundle as 10 gives 22.
Example: three bundles and one line make 15 + 1 = 16.
Watch out: the slanted line counts too, so a bundle is always 5.
Cara lain
Gundal atau tanda ✓
Kedua-dua cara memberi bilangan yang sama
| Warna | Tanda ✓ | Gundal | Bilangan |
|---|---|---|---|
| Merah | ✓✓✓✓✓✓ | 6 | |
| Biru | ✓✓✓✓ | 4 | |
| Putih | ✓✓✓✓✓✓✓✓✓✓✓ | 11 |
✓ dikira satu-satu · gundal dikira lima-lima
打勾 = tanda ✓；五个五个数 = kira lima-lima
除了计数字符，也可以每个数据打一个勾。两种方法得到的数目一样，红色都是 6、蓝色都是 4。不同的地方是：勾很多的时候，只能一个一个数，很容易数错；计数字符五根一捆，可以 5、10、15 这样跳着数，比较快。所以数据多的时候，用计数字符比较方便。
例子：白色 11 个勾要数 11 下；画成计数字符是两捆加一根，5、10、11 三下就数完。
注意：一个数据只打一个勾或画一根，不可以多画。
tick = tanda ✓; count in fives = kira lima-lima
Besides tally marks, we can put one tick for each piece of data. Both ways give the same number: red is 6 and blue is 4 either way. The difference is that a long row of ticks must be counted one by one, which is easy to get wrong, while tally marks come in bundles of five, so we can skip-count 5, 10, 15. With lots of data, tally marks are quicker.
Example: 11 ticks for white need 11 counts, but as tally marks they are two bundles and one line, counted 5, 10, 11.
Watch out: one piece of data gets exactly one tick or one line, never more.
Langkah 3
Susun data dalam jadual
Jus kegemaran 16 orang murid
OrenEpalOrenManggaTembikaiOrenEpalManggaOrenTembikaiManggaOrenEpalOrenManggaOren
| Jus | Gundal | Bilangan |
|---|---|---|
| Oren | 7 | |
| Epal | 3 | |
| Mangga | 4 | |
| Tembikai | 2 |
整理成表 = susun dalam jadual；种类 = kelas；数目 = bilangan
上面是 16 个同学的原始回答，乱乱的看不出什么。整理的方法：先写出所有种类（橙、苹果、芒果、西瓜），再一个一个回答去看，划掉一个就在那一种画一根计数字符，最后把每种的数目写在“Bilangan”一栏。整理好后，橙汁 7、苹果汁 3、芒果汁 4、西瓜汁 2，一看就清楚。
例子：如果再多一个同学说芒果，芒果那一行加一根，数目变成 5。
注意：表格里的数目加起来要等于问了多少人，这里是 7 + 3 + 4 + 2 = 16。
organise in a table = susun dalam jadual; class = kelas; number = bilangan
Above are the 16 raw answers, mixed up and hard to read. To organise them, first list every kind (orange, apple, mango, watermelon), then go through the answers one at a time, crossing each out and drawing one tally mark for its kind, and finally write how many in the Bilangan column. Now orange 7, apple 3, mango 4 and watermelon 2 can be seen at once.
Example: if one more friend says mango, the mango row gets one more line and becomes 5.
Watch out: the numbers in the table must add up to the number of people asked, here 7 + 3 + 4 + 2 = 16.
Cuba
Berapakah murid yang memilih warna Merah?
MerahKuningHijauMerahBiruKuningMerahHijauMerahBiruKuningMerahHijauMerah
从原始数据数一种 = kira satu kelas daripada data
这一题的 14 个回答里，要数“Merah”有几个。最稳的方法是从第一个开始，看到 Merah 就在纸上画一根计数字符，一路看到最后，不要跳着看。这样数出 Merah 一共 6 个。选 5 多半是漏看了一个，选 7 多半是有一个数了两次。
例子：同一组数据里，Kuning 有 3 个，Hijau 有 3 个，Biru 有 2 个。
注意：数完后把各种颜色加起来，6 + 3 + 3 + 2 = 14，跟总数一样才对。
counting one class in raw data = kira satu kelas daripada data
Among these 14 answers we must count how many say Merah. The safest way is to start from the first answer and draw a tally mark every time Merah appears, going all the way to the end without skipping. That gives 6 for Merah. Choosing 5 usually means one was missed, and 7 usually means one was counted twice.
Example: in the same data, Kuning appears 3 times, Hijau 3 times and Biru 2 times.
Watch out: add up all the colours afterwards, 6 + 3 + 3 + 2 = 14, which must match the total.
Cuba
Berdasarkan jadual jus, berapakah lebih murid yang suka jus Oren daripada jus Tembikai?
| Jus | Bilangan |
|---|---|
| Oren | 7 |
| Epal | 3 |
| Mangga | 4 |
| Tembikai | 2 |
多几个 = berapa lebih；相差 = beza
表格整理好以后，就可以用它回答问题。“多几个”要用减法：橙汁 7 个，西瓜汁 2 个，7 − 2 = 5，所以喜欢橙汁的多 5 个人。选 9 是把两个数加起来了；选 2 是只看了西瓜汁的数目。
例子：喜欢芒果汁的比苹果汁多 4 − 3 = 1 个。
注意：问“多几个”要大数减小数，不是相加。
how many more = berapa lebih; difference = beza
Once the table is ready, we can use it to answer questions. How many more means subtraction: orange has 7 and watermelon has 2, and 7 − 2 = 5, so 5 more pupils like orange. 9 comes from adding the two numbers, and 2 is just the watermelon count.
Example: mango is liked by 4 − 3 = 1 more pupil than apple.
Watch out: for how many more, take the smaller number from the bigger one; do not add them.
Padankan
Gundal dan bilangan
配对计数字符 = padankan gundal
每一组先数有几捆，一捆是 5，再加上后面单独的竖线。一捆加两根是 7；一捆加四根是 9；两捆加三根是 10 + 3 = 13；刚好一捆就是 5。四根竖线还没有斜划，表示只有 4，第五根划下去才变成一捆。
例子：两捆加一根是 11，三捆刚好是 15。
注意：不要把一捆看成 4 根，那根斜线也是一个数据。
matching tally marks = padankan gundal
For each group, first count the bundles, each worth 5, then add the single lines after them. One bundle and two lines make 7; one bundle and four lines make 9; two bundles and three lines make 10 + 3 = 13; one bundle alone is 5. Four upright lines with no line across mean only 4, and the fifth stroke turns them into a bundle.
Example: two bundles and one line make 11, and three bundles make exactly 15.
Watch out: a bundle is never 4; the slanted stroke is one piece of data as well.
Langkah 4
Semak jumlah
20 orang murid ditanya tentang sukan kegemaran
| Sukan | Gundal | Bilangan |
|---|---|---|
| Bola sepak | 9 | |
| Badminton | 7 | |
| Renang | 5 | |
| Jumlah | 21 ✗ |
Murid ditanya: 20 · 9 + 7 + 5 = 21 → ada data dikira dua kali
核对 = semak；总数 = jumlah；数两次 = dikira dua kali
表格做好了要核对：把每一类的数目加起来，应该等于问了多少人。这里问了 20 个同学，可是 9 + 7 + 5 = 21，多了 1，表示有一个回答被数了两次。如果加起来比 20 少，就是漏数了。发现不对就要重新数，一边数一边划掉。
例子：问 15 人，表格是 6、5、3，加起来 14，少 1，表示漏了一个回答。
注意：总数对不上时，不要随便改一个数字，要回到原始数据重新数。
check = semak; total = jumlah; counted twice = dikira dua kali
A finished table must be checked: add the numbers in every class, and the sum should equal the number of people asked. Here 20 pupils were asked, but 9 + 7 + 5 = 21, one too many, so one answer was counted twice. If the sum is smaller than 20, an answer was missed. When it does not match, count again, crossing out as you go.
Example: 15 people asked and a table of 6, 5 and 3 gives 14, one short, so one answer was missed.
Watch out: do not simply change a number to make it fit; go back to the raw data and recount.
Cuba
Sepatutnya 20 orang murid. Badminton dikira satu kali lebih. Berapakah bilangan Badminton yang betul?
| Sukan | Bilangan |
|---|---|
| Bola sepak | 9 |
| Badminton | 7 |
| Renang | 5 |
改正数目 = betulkan bilangan
刚才的表格总数是 21，但只有 20 个同学。题目说羽毛球多数了一次，所以羽毛球的数目要减 1：7 − 1 = 6。改好后 9 + 6 + 5 = 20，跟人数一样，表格就对了。选 8 是反而加了 1；选 7 是没有改。
例子：如果游泳少数了一次，就要把 5 加 1 变成 6。
注意：改正后一定要再加一次总数，确定等于人数。
correcting a number = betulkan bilangan
The table above adds up to 21, but there are only 20 pupils. The question says badminton was counted once too often, so its number must go down by 1: 7 − 1 = 6. After fixing it, 9 + 6 + 5 = 20, which matches, so the table is right. 8 adds 1 instead, and 7 leaves the mistake in place.
Example: if swimming had been missed once, its 5 would become 6.
Watch out: after correcting, add the column again to be sure it equals the number of pupils.
Ringkasan
Syabas!
kumpul → kelas (gundal) → susun (jadual) → semak
Kumpul data dengan memerhati, soal selidik atau temu bual. Kelas dengan gundal: gundal ke-5 melintang. Susun dalam jadual. Semak: jumlah mesti sama dengan bilangan data.
Latihan tambahan →