Question

For the following data distribution, find the value that best defines the central tendency of the distribution and characterize the distribution.

{23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38}

Answer 1

Explanation:

The given data set is:

23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38

firstly arrange the given data set in ascending order, we have

1, 7, 12, 14, 17, 18, 18, 23, 23, 23, 23, 24, 27, 28, 29, 32, 33, 38, 43

Now, Mode is the observation point which occurs frequently in the given data set, thus

Mode=23

Mean is given as:

`Mean=(sum of observations)/(total no. of observations)`

`Mean=(433)/(19)=22.7`

`Mean`≈
`23`

Median of the given data set is the middle value of the given set, thus

Median=23

Hence, the value that would best describe the central tendency is 23. Since, the values to the left of 23 are more scattered than those to its right, the distribution exhibits negative.

Answer 2

To characterize the distribution, the data have to be put into a frequency distribution graph.

After graphing the data, the distribution is a bit skewed to the right although it could be considered symmetrical.
Here are the values that define the central tendency:
mean = 22.79
median = 23
mode = 23

The three are almost equal. So, the distribution can be classified as symmetrical.