Population Mean and Standard Deviation:



Population Mean and Standard Deviation:

Until this point, we have mainly been working with random samples. However, we can work with the entire population, by computing the population mean (μ, Greek letter mu) and the population standard deviation (σ, Greek letter sigma).

Formulas:

μ = Σx (population mean)

N

σ = √ Σ (x – μ)2 (population standard deviation)

N

Where N is the number of data values in the population, x represents the individual data values of the population, μ is the same formula as x bar (sample mean), σ is the same as the formula for s (sample standard deviation).

To compute these two formulas by hand we will once again construct a computation table to guide us along the way. Our table will look like this:

|x |x - μ |(x – μ)2 |

| | | |

| | | |

| | | |

|Σx = | |Σ(x – μ)2 = |

Using the calculator we will just go through the same routine that we used for sample standard deviation, using 1-VAR STATS.

Examples:

1) Bill has been training for the upcoming track season. He has been running the mile daily for the past two weeks. His times were as follows (in minutes): 8.7 8.9 7.4 6 8.9 10 12.2 11.3 9.3 5.1 12.3 12 15.8 8.6

a) Calculate the population mean and population standard deviation.

2) The following amounts of people arrive at Cherry Valley every morning for 2 weeks to order a TCS hero and waffle couch: 5 8 9 7 22 13 10 1 5 6 9 15 4 17

a) Calculate the range, mode, median, and mean.

b) Calculate the population mean and population standard deviation.

3) The recent prices of SFP stock are indicated: 54.3 56.2 57.2 49.5 55.5 56.0 59.9 60.2 51.3 66.6 55.2 62.3 55.4 57.3

a) Calculate the range, mode, and median

b) Calculate the sample mean and sample standard deviation.

c) Calculate the population mean and population standard deviation.

4) Linda often travels for her company. She has been tracking the amount of time she spends in the airport each month. She has recorded the following amounts (in hours): 55 26 33 19 10 15 12 88 45 65 25 23

a) Calculate the range, mode, and median.

b) Calculate the sample mean and sample standard deviation.

c) Calculate the population mean and population standard deviation.

5) On a recent exam, 20 students received the following scores: 86 77 99 100 86 86 82 95 99 100 87 72 66 63 88 64 76 89 91 73

a) Calculate the range, mode, and median.

b) Calculate the sample mean and standard deviation.

c) Calculate the population mean and population standard deviation.

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