# Question: Which of the following is not a measure of central tendency?

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Contents

`Answer:`

## General guidance

Concepts and reason

Measures of central tendency:

• Mean

• Median

• Mode

Measures of variation:

• Standard deviation

• Range

• Inter quartile range (IQR) Fundamentals

Mean: Mean is the most commonly used measure of central tendency. It is the average of all the observations in the data set. In other words, the mean is obtained by summing the observed numerical values of a variable in a set of data and then dividing the total by the number of observations involved.

Median: Median divides the observations into two equal parts. It represents the middle value for a set of observations when they are arranged in order of magnitude.

The middle data value when the data are entered in ascending order is termed as median. That is, the observation is located at the middle

Mode: The mode is the data value that occurs with the greatest frequency or repeated value.

Standard deviation: The mean is the average of all samples. The variance is the average of the squared differences from the mean. And the standard deviation refers to the square root of the variance. Standard deviation refers to how closely the samples are located to the mean. In other words, standard deviation refers to how much the values in the distribution vary from the mean value of that distribution. Larger the variability around the mean, the larger will be the standard deviation.

Symmetric distribution:

A symmetricdistribution can be defined as one in which the upper half is a mirror image of the lower half of the distribution. If a vertical line is drawn through the mean of the distribution depicted by a histogram or a polygon, the lower half could be “folded over” and would coincide with the upper half of the distribution. Symmetric distribution can be defined as the distribution which is balanced equally around the mean. The upper half and the lower half of the distribution are equal.

For a symmetric distribution, Mode = Median = Mean. Show more First Step | All Steps | Answer Only

## Step-by-step

### Step 1 of 2

The incorrect options are identified below:

The central tendency measures represent the center value for the given data. The central tendency measures are mean, median and mode. Hence, the options (1), (2) and (4) are incorrect.Explanation | Hint for next step

The incorrect options are identified by observing the central tendency measures as mean, median and mode.

Use the concept of central tendency and measures of variation to identify the correct option.

### Step 2 of 2

The correct option is identified below:

The central tendency measures are mean, median and mode. The range represents the variation method. That is, the range is not central tendency value. Hence, the option (3) is correct.

The range is not a measure of central tendency.
Explanation | Common mistakes

The correct option is identified by observing the central tendency measures as mean, median and mode and the variation measures are range, standard deviation and variance.

Identifying range as central tendency value is wrong here. Because, the range is the measure of variation.