Question

1. Decide the best measurement of central tendency for each data set. Justify your answer.

Note: Do not compute the measurements of central tendency; just decide which the best measure in each

case is.                                                                                                                                     a) Letter grades:                 A, B, B, A, C, C, C, D, F, B.
Explain why:

Answer 1

A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value.In statistics, the three most common measures of central tendency are:

1. Mean
2. Median
3. Mode.

Each of these measures calculates the location of the central point using a different method.

Choosing the best measure of central tendency depends on the type of data you have.

• When you have a symmetrical distribution for continuous data, the mean, median, and mode are equal. In this case, analysts tend to use the mean because it includes all of the data in the calculations.
• However, if you have a skewed distribution, the median is often the best measure of central tendency.
• When you have ordinal data, the median or mode is usually the best choice.
• For categorical data, you have to use the mode.

Here in this case we have a Categorical data (i.e data which may be divided into groups) . Hence here the best measure of central tendency would be mode. The mode is the most commonly occurring value in a distribution.

Consider the above dataset:-  A, B, B, A, C, C, C, D, F, B.

Make a frequency table for the given data:

Value	Frequency
A	2
B	3
C	3
D	1
F	1

The most commonly occurring value is B and C therefore the mode of this distribution is B and C.

Here we have 2 modes (this is known as bimodal if there are two modes).One of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency.

If no number in a set of numbers occurs more than once, that set has no mode:

Advantages and Disadvantages of the Mode

Advantages:

• The mode is easy to understand and calculate.
• The mode is not affected by extreme values.

Disadvantages:

• The mode is not defined when there are no repeats in a data set.
• The mode is not based on all values.
• The mode is unstable when the data consist of a small number of values.
• Sometimes data have one mode, more than one mode, or no mode at all.