How can he assume SD of population equals to SD of sample means?

Question

I'm referring to this KhanAcademy video: https://youtu.be/bekNKJoxYbQ?t=445.

My question: How can he approximate the SD of the population to be equal to SD of the sample means? Isn't that SD of the sample means would be wayyy higher than the SD of the population?

Is this a wrong assumption, or is there any reason behind it?

Thanks.

Answer 1

He's not comparing the SD of the population to the SD of the sample means. He's saying that the SD of the population of all apple weights is approximately the SD of the sample of 36 apple weights, i.e. $\sigma\approx s$. The intuition is that the histogram of 36 weights should have a similar spread compared to the histogram of all 200,000 weights.