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Chapter 17: Problem 5

Find the mean of the data set. $$ 5,2,19,6,5,2 $$

Short Answer

Expert verified
Answer: The mean of the data set is 6.5.

Step by step solution

01

Sum the values in the set

To find the sum, simply add all the values in the set together: $$ 5+2+19+6+5+2 = 39 $$
02

Count the number of values in the set

The given data set contains 6 values, which can be confirmed by counting each of the values: 5, 2, 19, 6, 5, and 2.
03

Divide the sum by the number of values

Now that we have the sum of the values (39) and the number of values (6), we can find the mean by dividing the sum by the number of values: $$ \text{Mean} = \frac{\text{Sum}}{\text{Number of values}} = \frac{39}{6} = 6.5 $$ So, the mean of the given data set is 6.5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Data Set
A "data set" is simply a collection of numbers or values. These can represent any kind of observable data, such as test scores, temperatures, or counts. In our example, we have a data set:
  • 5
  • 2
  • 19
  • 6
  • 5
  • 2
This set contains six numbers. Data sets can vary in size, ranging from just a few values to thousands or even millions, depending on the context.
In data analysis, the mean is often used to find the central tendency, or average, of a data set. This helps to summarize the data with a single value that represents it well.
Calculating the Sum of Values
The "sum of values" refers to the total obtained when you add all the numbers in a data set together. This step is foundational for calculating the mean.
To calculate the sum in our example, you add each number one by one:
  • Start with the first number: 5
  • Add the second number: 5 + 2 = 7
  • Continue adding: 7 + 19 = 26
  • Add the next: 26 + 6 = 32
  • Next: 32 + 5 = 37
  • Finally: 37 + 2 = 39
So, the sum of the values is 39. This step ensures that you accurately compile the data, making it ready for the next steps in calculating the mean.
Identifying the Number of Values
The "number of values" simply refers to how many individual numbers you have in your data set. For our example data set 5, 2, 19, 6, 5, and 2, the number of values is 6.
This count is crucial because, when calculating the mean, you divide the sum of the values by this number. Dividing the sum by the count gives a sense of each number's contribution to the total.
To ensure accuracy, always double-check the number of values by counting them one by one, particularly in larger data sets. This practice helps to avoid small mistakes that could lead to incorrect results in the mean calculation.

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Most popular questions from this chapter

The clutch size of a bird is the number of eggs laid by the bird. Table 17.7 shows the clutch size of six different birds labeled (i)-(vi). What is the (a) Mean clutch size? (b) Standard deviation of these clutch sizes? $$ \begin{array}{c|c|c|c|c|c|c} \hline \text { Bird } & \text { (i) } & \text { (ii) } & \text { (iii) } & \text { (iv) } & \text { (v) } & \text { (vi) } \\ \hline \text { Clutch size } & 6 & 7 & 2 & 3 & 7 & 5 \\ \hline \end{array} $$

Find the standard deviation of the data set. Five readings each equaling 120 , three readings each equaling 130 , two readings each equaling 140 , four readings each equaling 150 , and 1 reading equaling \(160 .\)

Suppose you record the hours of daylight in Tucson, Arizona, each day for a year and find the mean amount. (a) What do you expect for an approximate mean? (b) How would your data compare with a student doing the same project in Anchorage, Alaska? (c) How would your standard deviation compare with a student doing the same project in Anchorage, Alaska?

Suppose you record the hours of daylight each day for a year in Tucson, Arizona, and find the mean. (a) What do you expect for an approximate mean? (b) How would your data compare with a student doing the same project in Anchorage, Alaska? (c) How would your mean compare with a student doing the same project in Anchorage, Alaska?

Table 17.19 gives the vehicle occupancy for people driving to work in 1990 as determined by the US Census. For instance, 84,215,000 people drove alone and 12,078,000 people drove in 2 -person car pools. Picking at random, what is the probability, given as a percentage, that: (a) A commuter drives to work alone? (b) A vehicle carries 4 or more people?$$ \begin{array}{c|c|c|c|c|c|c|c} \hline \text { Occupancy } & 1 & 2 & 3 & 4 & 5 & 6 & 7+ \\ \hline \text { People, } 1000 \mathrm{~s} & 84,215 & 12,078 & 2,001 & 702 & 209 & 97 & 290 \\ \hline \end{array} $$
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