This is an easy part about finding the mean of the sample and standard deviation

Question

This is an easy part about finding the mean of the sample and standard deviation of the sample in each sheet:

The first part of this question and its answer (and sheet 1 of data) is on this link:

https://www.chegg.com/homework-help/questions-and-answers/excel-file-bottom--25-pts-use-gaussian-distribution-model-monthly-temperature-data-state-c-q28070052

Now we will take some samples from the April dataset and use those samples to investigate the validity of the Central Limit Theorem.

4. Each of the first 50 rows of “Sheet 2” in the file contains a randomly selected sample of 5 April temperatures from Sheet 1. Compute the mean of each row (in this way, you are computing 50 sample means for sample size n=5). What are the mean and standard deviation of the set of 50 sample means (round to two decimal places)? What are the mean and standard deviation as predicted by the Central Limit Theorem (round to two decimal places)?

Sheet 2:

5. Repeat part (e) for the data in “Sheet 3”. Here, each of the first 50 rows contains a randomly selected sample of 10 April temperatures from Sheet 1.

Sheet 3:

6. Repeat part (e) for the data in “Sheet 4”. Here, each of the first 50 rows contains a randomly selected sample of 20 April temperatures from Sheet 1.

Sheet 4:

45.9 51.0 47.7 47.7 52.3 51.0 55.4 50.0 47.1 50.0 50.2 45.9 49.3 47.5 53.8 49.3 49.0 51.9 49.7 54.4 52.8 51.9 50.2 49.6 54.4 51.0 50.0 52.1 49.3 44.8 53.8 47.0 49.4 51.0 49.3 46.8 51.6 52.6 47.3 49.7 47.0 49.3 48.2 49.3 50.0 50.3 53.9 47.9 48.4 55.3 48.8 54.1 49.7 47.5 47.3 47.1 55.3 43.2 50.0 49.0 44.9 55.0 49.3 51.6 46.3 51.0 49.7 47.3 48.4 54.1 47.2 47.8 54.1 51.0 49.0 46.8 46.3 46.4 50.2 47.5 50.0 51.4 47.1 49.7 50.3 46.8 51.0 43.6 52.6 48.6 47.6 51.7 47.1 47.9 44.4 53.6 47.3 48.2 47.1 43.2 45.4 51.8 56.0 50.0 50.6 52.3 45.9 48.3 48.0 54.8 49.7 47.8 51.9 48.3 47.2 46.1 43.6 50.2 45.9 54.0 52.2 44.4 49.3 47.8 48.3 50.2 49.3 50.5 51.7 50.0 49.6 49.6 51.9 51.0 51.6 50.0 48.4 45.6 47.1 48.3 50.0 51.8 53.1 47.6 49.7 44.0 49.7 51.4 51.9 51.6 47.6 46.3 46.1 44.8 51.6 47.6 48.4 48.6 47.6 50.5 46.1 50.7 55.3 53.1 47.7 51.6 45.4 53.1 47.1 45.9 47.3 53.8 49.3 49.4 49.7 51.9 45.6 48.6 53.1 53.8 54.8 48.4 52.8 45.4 47.5 50.3 49.3 47.9 44.9 48.0 51.9 49.7 53.1 47.5 45.9 51.0 48.4 49.3 48.3 53.1 53.1 51.7 45.9 49.4 50.0 45.4 52.7 50.3 54.4 48.3 54.1 43.6 51.9 49.4 54.8 50.6 47.3 48.2 47.1 44.9 50.0 47.9 49.4 46.3 47.3 46.4 49.7 48.3 53.8 51.0 48.2 47.1 53.8 51.9 52.1 50.7 51.0 54.1 54.8 48.8 51.7 51.0 44.9 49.7 51.7 50.5 48.6 47.8 51.8 46.8

Explanation / Answer

The basic formulae are as follows:

Mean=sum(xi)/n SD=Sqrt(((xi-mean)^2)/n)

Central Limit Theorem:

Mean: ?x=? SD: ?x=?/?n

4. CLT mean=2475.82 sd=19.15556

5. CLT mean=2484.69 Sd=20.33321

6. CLT mean=2484.17 sd=20.69659

mean(?) SD(?) 48.92 2.63856 50.7 3.004996 49.34 2.993827 50.86 2.2832 51.78 1.947306 49.44 2.800536 50.1 2.511971 49.6 2.556365 48.76 1.17601 51.16 3.302726 49.48 2.762607 48.92 4.413275 49.42 4.064111 50.1 2.631539 49.82 2.798571 47.44 1.613382 49.7 1.589025 48.52 3.534402 47.74 2.612087 47.88 3.73055 50.76 3.803682 49.86 3.603193 48.98 1.875367 47.96 4.129528 48.4 2.811583 50.34 0.879204 50.74 1.089954 47.88 1.639207 50.44 2.105469 49.72 3.310136 47.28 2.610939 48.54 1.186592 50.58 3.775182 48.62 3.501 49.9 2.378024 50.6 3.434385 49.78 3.892557 48.08 2.03519 49.62 2.985297 50.02 2.033962 50.02 2.723417 50.22 3.554856 50.76 4.52471 47.62 2.060825 48.18 1.515586 49.84 2.795174 50.62 2.836723 51.88 2.505394 49.8 2.858321 49.1 2.029778

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