The Essential Statistics Formula Sheet

Statistics, the study of data, plays a crucial role in society. Almost all the generalized information, summarizations, and insights you come across in newspapers & the Internet are statistical information. The undeniable importance, all-pervasiveness and potency of statistics make it an integral aspect of academics. However, statistics aren’t that easy, and many pupils require statistics homework & statistics assignment help quite frequently.

If you are struggling with your stat formulae, this handy statistics formula sheet can help. It has all the formulae you need to solve every generic stat problem that comes your way.

Salient Statistics Formulas For Everyone

Some Key Terms

Statistical science generally studies a population. A population can be a collection of any entity, from people to objects, or a set of any data. To study a population, we select a sample, where sampling involves selecting an appropriate subset and studying to gain more information about the population. The characteristics of a sample are representative of the population.

A statistic is data that represents a property of the sample. And a parameter informs us about a property of the population.

Now, some of the most common and crucial formulas in descriptive statistics measure the location of the data. Common measures of location are quartiles and percentiles.

• PERCENTILES

  in stats are measures that indicate a number below which a percentage of data observations fall.

• QUARTILES

  are special percentiles. The first quartile is the same as the 25^thpercentile, and the third quartile is also the 75^th And the median is both the second quartile and the 50^th percentile. More on the median later.
• The MEDIAN is a number that’s near the centre of the data. It can be considered the middle value but need not be part of the data set.

Consider the following set: 1, 11.5, 6, 7.2, 4, 8, 9, 10, 6.8, 8.3, 2, 2, 10, 1 Ordering them from smallest to largest, we have: 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5. As there are 14 observations, the medina will lie between the seventh and eighth elements. Therefore, we add the two values together to find the median and divide the sum by two.

The median for the above data set is:

Median= (6.8+7.2)/2=7

A median value of 7 signifies that half of the values are less than seven, and half are greater than seven.

• Quartiles separate a data set into quarters. The first quartile Q₁is the middle value of the lower half of the data, and the third quartile Q₃ is the middle value of the upper half of the data. And the median is the second quartile Q₂ of the entire data set.

Let's now look at measures of the center of the data.

The two most widely used measures of locating the data centre are MEAN (AVERAGE) and the median.

• To calculate the mean of a sample of 50 entries, we add the values of all 50 entries together and divide the sum by 50.
• To find the median, follow the process mentioned previously or find the number that splits the entire set equally in two halves.

The most common measure of variation or spread is the STANDARD VARIATION. It is a measure for determining how far data values are from the mean. It also provides a numerical approximation of the overall amount of variation intrinsic to the data set.

• If x is a number in the data set, then the difference “x - mean” is its DEVIATION. There will be as many deviations as items in a data set. These deviations are used to calculate the standard deviation.  

x – x’ is the deviation value for a sample, and x - m values for the population. x’ is thus the sample mean, while m is the population mean.

Procedures to calculate the standard deviation depend on whether the values represent the entire population or are just data from a sample. So again, the calculations are pretty similar but not the same.

S represents the sample standard deviation, while the Greek letter represents the population standard deviation.

• To calculate the standard deviation, we first need to find the VARIANCE. Variance is the average of the squares of the deviations.

• s²is the POPULATION VARIANCE, and s is the POPULATION STANDARD DEVIATION, that is, the square root of the sample variance. Similarly, s² is the SAMPLE VARIANCE and s, the SAMPLE STANDARD DEVIATION.

Formula for Sample Standard Deviation: s = Ö [Σ(x-x’)²/ (n-1)] or s = Ö [Σ f(x-x’)²/ (n-1)]

Formula For Population Standard Deviation: s = Ö [Σ(x-x’)²/ N] or Ö [Σ f(x-x’)²/ N]

Where N is the total number of items in a population and n is the number of items in the sample. Inferential statistics uses probability to infer about populations. The sub-branch is often used to predict outcomes and events. 

• The intersection of two events, A and B, is A ∩ B, and the union of two events is A ∪
• For any event A, 0 <= P(A) <=1
• For two events, A and B, P (A ∪B) = P(A) + P(B) – P (A ∩ B)
• If A and B are mutually exclusive (cannot both occur), then P (A ∪B) = P(A) + P(B)
• A and B are independent if and only if P (A ∩ B) = P(A) P(B)
• CONDITIONAL PROBABILITY of A given B is given as

P(A|B) = P (A ∩ B)/P(B), only when P(B) is not equal to 0

BAYES THEOREM is central to conditional probability and a primary concept in inferential statistics. Note that the conditional probability of an event is obtained with additional information that some related or independent event has already occurred. Bayes theorem extends that for a more accurate calculation of probability value.

One key thing to remember is that we are dealing with sequential events in scenarios where the Bayes theorem is applicable. In that context, the terms prior probability and posterior probability are used.

• Prior probability is the initial probability value before any additional information is obtained. The posterior probability is the revised value after using additional information.
• If we have two events, A and B, and we have info about the conditional probability of A given B, that is, P(A|B), then using Bayes Theorem, we can find the probability of B given A with the formula

P(B|A) = P(A|B) P(B) / P(A|B) P(B) + P(A|B’) P(B’)

Where B’ is the probability of B not occurring.

That’s all the space we have for today. Hope this statistics formula sheet aids you big time in solving your assignments. However, if you are looking for expert statistics homework & assignment help, Tophomeworkhelper.com has the brightest bunch of experts on standby!

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