Explain the difference between a simple random sample and a systematic sample.

Mathematics

1 answer:

Stells [14]3 years ago

5 0

Answer:

Step-by-step explanation:

Simple random sampling otherwise called probability sampling involves selecting a subset of a part of a population in which each member of the population has equal chances of being selected while systematic sampling involves the use of sampling interval which is determined by dividing the population by the sample size and a random starting point is selected. for example let say we have a population of 1000 people and we want to systematically select 50 people, 1000 / 50 = 20, it means after choosing a random starting point, we select every 20th person after the starting point until the desire sample size has been attained.

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We are given a sequence of five non-zero numbers, where the sum of each term and its neighboring terms is 15 or 25. Find the sum

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We have a sequence that meets the given criteria, and with that information, we want to get the sum of all the terms in the sequence.

We will see that the sum tends to infinity.

So we have 5 terms;

A, B, C, D, E.

We know that the sum of each term and its neighboring terms is 15 or 25.

then:

A + B + C = 15 or 25
B + C + D = 15 or 25
C + D + E = 15 or 25

Now, we want to find the sum of all the terms in the sequence (not only the 5 given).

Then let's assume we write the sum of infinite terms as:

$a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + ...$

Now we group that sum in pairs of 3 consecutive terms, so we get:

$(a_1 + a_2 + a_3) + (a_4 + a_5 + a_6) + ...$

So we will have a sum of infinite of these, and each one of these is equal to 15 or 25 (both positive numbers). So when we sum that infinite times (even if we always have the smaller number, 15) the sum will tend to be infinite.

Then we have:

$(a_1 + a_2 + a_3) + (a_4 + a_5 + a_6) + ... \to \infty$