The average weights in kilograms of babies born on a maternity ward are given below. Part a) Write this data on a stem and leaf diagram. Part b) One of the babies is selected at random. What is the probability that the baby will weigh less than three kilograms?
Now in order to actually answer part a) and write the data as a stem and leaf diagram, we first need to add something to our diagram before we begin. And that first thing we need to add is our key, because this tells us how the actual stem and leaf diagram is going to work and what it will represent.
So in our key, I’ve actually just chosen a value. So I’ve done two line six, so we’ve got our stem being two and our leaf is six. This is gonna be equal to 2.6, because this seems like it will work looking at the values that we’ll have. Next, I’ve written our stem numbers, which are two, three, and four. And the reason we’ve got these ones is because actually if you look back at the numbers we’ve got for the weights, then the only units we’ve got are two, three, or four.
Now what we need to do is actually write in our results, so our numbers from the data. And whenever we do this, we need to make sure it’s actually ordered. So we go from smallest to biggest. So our smallest value is 2.6, so I’ll write this into our stem and leaf diagram as two. And then as we said, that’s gonna be our stem, then our line, and then six is the leaf. Our next smallest value is 2.9. So we’ve written in the nine, and that’s because these two are the only ones below three.
So then we have two 3.0s, so I’ll write in two zeros. We’ve got one 3.2, two 3.3s, three 3.4s, two 3.5s, no 3.6s, but then we’ve got two 3.7s, a 3.8, and then two 3.9s. Then finally, we can move on to our fours. Well, first of all, we’ve got 4.1. Then there’s a 4.5 and finally a 4.8. Okay, so we’ve written all in and they’re actually all ordered. And actually, I’ve crossed through them as I’ve done them so we can see that actually we’ve used all the numbers.
And the other way we could actually check to make sure that we’ve actually got all the values is to actually count them up. Well, if we look at our dataset, we can see that actually it’s a four-by-five grid. So therefore, we’ve got 20 bits of data. And when we count our bits of data, we see, yes, we’ve got 20 of them in our stem and leaf diagram, so we haven’t missed any. So this is now completed stem and leaf diagram, remembering important point: don’t forget your key.
Okay, now let’s move on to part b). So in part b), we actually want to look to see what is the probability that the baby will weigh less than three kilograms if one of the babies is selected at random. Well, if we look at our stem and leaf diagram, we can see that there are two babies that are less than three kilograms.
So therefore, we can say that the probability the baby is gonna weigh less than three kilograms, and that’s what I’ve shown here with this bit of notation, so we’ve got 𝑃 and then less than three kilograms. And this probability is gonna be equal to two over 20. And that’s because actually it says there are two babies that are less than three kilograms when we look at our data or when we look at the stem and leaf diagram. And actually, we’ve already worked out that there’re 20 babies in total. So we can say two out of 20. We’ll write that as a fraction as two over 20.
Well, you would in fact get the marks for the answer two over 20. However, just to tidy up, we’re actually gonna simplify. And we can do that by dividing the numerator and the denominator by two, which is gonna give us one over 10 or one-tenth. So therefore, we can say that the probability that the baby will weigh less than three kilograms is one-tenth or two over 20.