Grade Six Mathematics
Greetings, students! It's great to have you back for another edition of our weekly Mathematics Corner. I trust everyone is well. In our previous session, we delved into the calculation of averages for data sets. This week, we'll be exploring the calculation of mode and median. Without further ado, let's dive right in!
Mode Example 1 Exercise 1 Answers to last week’s exercise
The mode is a measure of central tendency, which helps us understand the most frequently occurring value in a given set of numbers.
How do you identify the mode?
Let us examine an example:
Let's start with a simple set of numbers: 3, 5, 2, 5, 1, 5, 4.
To find the mode, we look for the number that appears most often. In this set, the number 5 appears three times, while the other numbers appear only once. Therefore, the mode of this set is 5.
Now, let's try another example: 2, 4, 1, 2, 3, 4, 5.
To find the mode, we again look for the number that appears most frequently. Here, both 2 and 4 occur twice, and 1, 3, and 5 occur only once. In this case, the set is said to be bimodal because it has two modes (2 and 4).
Please note: If no number repeats, the set is called "uniform," and we say it has no mode.
In summary, finding the mode is like identifying the superstar of a group of numbers—the one that stands out by occurring more frequently than the others. Remember, a set can have no mode, one mode, or even more than one mode!
Now boys and girls, here is an exercise for you to complete:
Find the mode in each of the sets of data below by ordering the numbers and then finding the most common number.
4, 9, 5, 8, 1, 4, 10, 3 15, 23, 21, 35, 23, 28, 12 74, 72, 71, 72, 76, 74, 72 15, 6, 2, 13, 5, 5, 1, 7, 11 14, 18, 13, 12, 13, 15, 18, 18 9, 11, 5, 3, 5, 7, 9, 3, 6, 5 730, 734, 732, 730, 735, 737 9, 1, 5, 3, 3, 1, 2, 7, 3, 5, 8 58, 72, 64, 56, 58, 72, 58, 80 a) b) c) 4, 1, 1, 6, 5, 3 d) e) f) g) h) i) j) k) l) 814, 823, 818, 823, 820, 811 0.5, 0.3, 0.6, 0.3, 0.2, 0.9, 0.1
Excellent work, students!
Now, let’s move on to our next topic!
Median What is the median?
In simple terms, the median is like the middleman of a group of numbers—it helps us figure out the middle value when the numbers are arranged in order.
Let us examine two examples:
Example 1: Odd Number of Values
Suppose we have the following set of numbers: 3, 7, 1, 5, 9. To find the
median, first, we need to arrange the numbers from smallest to largest: 1, 3, 5, 7, 9
Now, look at the middle number—since there are five numbers, the third one, which is 5, is our median! In this case, 5 is the middle value that separates the lower half from the upper half.
Example 2: Even Number of Values
Now, let's consider a set with an even number of values: 2, 8, 4, 6. Again, let's arrange them from smallest to largest:
2, 4, 6, 8
Now, since there's no single middle number (because there's an even count), we need to find the average of the two middle numbers. Here, the middle numbers are 4 and 6. Add them together and divide by 2:
(4 + 6) / 2 = 10 / 2 = 5
So, the median is 5. This means that when the numbers are listed in order, 5 is right in the middle, separating the lower two values from the upper two values.
In summary, the median helps us find the middle value in a set of numbers. If there's an odd count, it's the middle number; if there's an even count, it's the average of the two middle numbers
Here’s an opportunity for you to work!
Exercise 2
Find the median of these data points. 16, 24, 8, 12, 19 13, 5, 2, 10, 8 15, 32, 53, 27, 11 89, 38, 94, 5 75, 29, 12, 17, 15 73, 91, 56, 24, 14, 17, 10 67, 13, 121, 86, 55, 22 142, 173, 129, 156, 181 257, 366, 305, 286, 182 362, 326, 263, 432 82, 106, 91, 115, 78, 83, 102
That’s all for today, boys and girls! Our column for this academic term comes to an end today. However, we will resume in the new academic term on January 14, 2024. Keep yourself safe and enjoy your Christmas break. Goodbye.