Chapter 11.10, Problem 19PPSE

Solution

a)

To explain: The set of values that appears to be distributed normally.

The second set of values appears to be normally distributed

Given:The given set of values

5
7
7
7
4
11
7
7
7
9
7
7

Concept used:

The data which is symmetrical appears to be normally distributed and it has values of mean, median, and mode all three the same.

Calculation:

With reference to the given data, the second set of values has most of the values 7, so the mode of the data is 7 and the mean and median are calculated as shown below

Mean of the data set is

  $\begin{array}{c}Mean=\frac{{\displaystyle \sum X}}{n}\\ =\frac{5+7+7+\mathrm{..}+7}{12}\\ =\frac{85}{12}\\ =7.083\end{array}$

The median is the middle data point when data is arranged in ascending order as shown below $45\text{ 7 7 7 7 7 7 7 7 }911$

The middle value of the set of values is the average of the middle values at the 6^th and 7^th position

  $Median=\frac{7+7}{2}=7$

Conclusion:The median and mode of the set of values are 7 and the mean is 7.083. As the mean, median, and mode of set of values are the same and there are two values above 7, two values below 7 and the remaining values are 7. Thus it can be concluded that the second set of values is normally distributed.

b)

To plot: The histogram for the set of values that appears to be distributed normally.

The histogram of the given data is shown below

  

Given:The given set of values

4

5

7

7

7

7

7

7

7

7

9

11

Plot:

Enter the data in excel in one column and the bins as shown below

  

In excel click on Data → Data analysis → select Histogram and click ok.

Enter the input data rage and bin range in the window and select the output range and click on the option for chart output as shown below

  

Once the histogram is generated right click on the histogram to format the data series and adjust the gap width to get the following histogram.

  

c)

To plot: The normal curve on the histogram plotted for the set of values that appears to be distributed normally.

The normal curve on the histogram of the given data is shown below

  

Given:The given set of values

4

5

7

7

7

7

7

7

7

7

9

11

Plot:

Right-click on the histogram and select the data to add the frequencies from the given data from the histogram output and name its series as normal as shown below

  

Now histogram with two bars for each data value is formed, right click on the histogram and change its chart type to scatterplot with the smooth line as shown below

  

Once clicked ok, the histogram with normal curve is generated as shown below