Question

Data Set: 5, 9, 11, 14, 15, 17, 19, 23

-Construct a frequency table using 5 as a starting point and a class of width 7

-Construct a relative frequency histogram. Include the midpoints and boundary points

- Find the mean, Variance, and standard deviation without a graphing calculator of the sample data

Data Set:

5, 9, 11, 14, 15,

17, 19, 23

Data Set:

5, 9, 11, 14, 15,

17, 19,

Data Set:

5, 9, 11, 14, 15,

17, 19, 23

Answer 1

In this case we have to construct the frequency table of the data with set of values 5,9,11,14,15,17,19,23 with 5 as a starting point and 7 as a width of class of interval. Here, we have class of equal width of 7 and the class is created in such a way that the in each class lower limit is included in the class where as upper limit excluded so in 5-12 class of width 7, 5 is included and 12 excluded. Then, we have given the frequency table as

The frequency histogram with labels and mid point of the class is given below

Now, we obtain the mean using the frequency table. For this let us consider

For given class and the frequency table, we have the mean and variance as

Therefore we first calculate the mean using the above table.

Once we have obtained the mean the variance can be obtained by making use of the table below

Using the formula and the above table we have variance and standard deviation as