** Range: **It is the provided meacertain of just how spreview apart the values in a data set are. It is measured as= (highest possible worth — lowest value) of the variable.

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Range = Max- Min

**Range**

2. *Variance*

Variance is calculated by taking the distinctions between each number in the data set and the expect, then squaring the distinctions to make them positive, and ultimately dividing the sum of the squares by the number of values in the data collection.

**Variance**

For any Sample, **always the amount of deviations from mean or average is equal to 0.** This is just one of the constraint we have actually on any sample data.

Variance is meacertain to quantify degree of dispersion of each observation from suppose worths.

Advanteras and Disbenefits of Variance*Advantages*:

a. Statisticians use variance to check out just how individual numbers relate to each various other within a data collection, fairly than making use of broader mathematical techniques such as arranging numbers right into quartiles.

b. The advantage of variance is that it treats all deviations from the expect the same regardless of their direction. The squared deviations cannot sum to zero and give the appearance of no variability at all in the data.

*Disadvantages*:

a. One drawago to variance is that it provides added weight to outliers, the numbers that are much from the intend. Squaring these numbers can skew the data.

The drawearlier of variance is that it is not conveniently taken. Users of variance frequently employ it primarily in order to take the square root of its value, which indicates the typical deviation of the data set.

*Degree of Freedom*

Degree of Degrees of liberty of an estimate is **the variety of independent pieces of information that got in calculating the estimate**. It’s not quite the very same as the number of items in the sample. In order to obtain the df for the estimate, you have to subtract 1 from the variety of items. Let’s say you were finding the intend weight loss for a low-carb diet. You might usage 4 human being, offering 3 levels of liberty (4–1 = 3), or you might use one hundred world through df = 99.

n= no. of items in your set.

Degree of Freedom = n-1

**Degree of Freedom for Population**

Consider a populace of dimension ’N’. Tright here are no constraints on any type of population. So the level of populace remains ’N’ only.

**Degree of Freedom for Sample**

Consider a sample of size’n’ , and also there is constantly constraint on every sample i.e. amount of deviation = 0. So max degree of liberty for any kind of sample is (n-1).

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n=1000

df= (1000–1)

df= 999

*Variance of Population:*

**Population variance** (σ2) tells us how data points in a specific **population** are spread out. It is the average of the distances from each data allude in the **population** to the intend, squared.