# Category: Basic Statistics

Introduction to statistics

## MCQs Basic Statistics 12

This quiz contains MCQs about Basic Statistics with answers covering variable and type of variable, Measure of central tendency such as mean, median, mode, Weighted mean, data and type of data, sources of data, Measure of Dispersion/ Variation, Standard Deviation, Variance, Range, etc. Let us start the MCQs Basic Statistics Quiz.

MCQs about Introductory Statistics

1. The height of a student is 60 inches. This is an example of ____________?

2. Suppose data are normally distributed with a mean of 120 and a standard deviation of 30. Between what two values will approximately 68% of the data fall?

3. For the given data $2, 3, 7, 0$, and $-8$, the G.M. will be:

4. According to the empirical rule, approximately what percent of the data should lie within $\mu \pm 2\sigma$?

5. Which of the following is not a measure of central tendency?

6. Data in the Population Census Report is:

7. Which of the following measure does not divide a set of observations into equal parts?

8. Which of the following divides a group of data into four subgroups?

9. Which one is the not measure of dispersion?

10. Consider the following grouped data. What is the sample variance of these data?

11. The interquartile range is which of the following?

12. The sum of squares of deviations from mean is:

13. Which one of the following is the class frequency?

14. If a distribution is abnormally tall and peaked, then it can be said that the distribution is:

15. Which branch of statistics deals with the techniques that are used to organize, summarize, and present the data:

16. Which of the following describe the middle part of a group of numbers?

17. Which of the following is written at the top of the table?

18. Which one is the formula of mid-range?

19. If a Curve has a longer tail to the right, it is called

20. If the mean of the two observations is 10.5, then the median of these two observations will be:

21. In positively skew cure which relation is ______.

22. Which of the following is not based on all the observations?

23. According to Chebyshev’s theorem, if a population has a mean of 80 and a standard deviation of 35, at least what proportion of the values lie between 30 and 130?

24. The mean of a distribution is 23, the median is 24, and the mode is 25.5. It is most likely that this distribution is:

25. Which one of the following is not included in measures of central tendency?

26. Which dispersion is used to compare the variation of two series?

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Basic statistics deals with the measure of central tendencies (such as mean, median, mode, weighted mean, geometric mean, and Harmonic mean) and measure of dispersion (such as range, standard deviation, and variances).

Basic statistical methods include planning and designing the study, collecting data, arranging, and numerical and graphically summarizing the collected data.

Basic statistics are also used to perform statistical analysis to draw meaningful inferences.

A basic visual inspection of data using some graphical and numerical statistics may give some useful hidden information already available in the data. The graphical representation includes a bar chart, pie chart, dot chart, box plot, etc.

Companies related to finance, communication, manufacturing, charity organizations, government institutes, simple to large businesses, etc. are all examples that have a massive interest in collecting data and measuring different sorts of statistical findings. This helps them to learn from the past, noticing the trends, and planning for the future.

## MCQs Skewness & Kurtosis 11

This quiz contains MCQs Skewness and Kurtosis covering the shape of the distribution, Measures of central tendency such as mean, median, mode, Weighted mean, data and type of data, sources of data, Measures of Dispersion/ Variation, Standard Deviation, Variance, Range, etc. Let us start the MCQs Skewness Quiz.

Please go to MCQs Skewness & Kurtosis 11 to view the test

Basic statistics deals with the measure of central tendencies (such as mean, median, mode, weighted mean, geometric mean, and Harmonic mean) and measure of dispersion (such as range, standard deviation, and variances).

Basic statistical methods include planning and designing the study, collecting data, arranging, and numerical and graphically summarizing the collected data.

Basic statistics also used to perform statistical analysis to draw meaningful inferences.

A basic visual inspection of data using some graphical and numerical statistics may give some useful hidden information already available in the data. The graphical representation includes a bar chart, pie chart, dot chart, box plot, etc.

Companies related to finance, communication, manufacturing, charity organizations, government institutes, simple to large businesses, etc. are all examples that have a massive interest in collecting data and measuring different sorts of statistical findings. This helps them to learn from the past, noticing the trends, and planning for the future.

There are various graphical and numerical ways that are used to check the skewness of the data. Skewness is the lack of symmetry in distribution.

## Variance: A Measure of Dispersion

Variance is a measure of the dispersion of a distribution of a random variable. The term variance was introduced by R. A. Fisher in 1918. The variance of a set of observations (data set) is defined as the mean of the squares of deviations of all the observations from their mean. When it is computed for the entire population, the variance is called the population variance, usually denoted by $\sigma^2$, while for sample data, it is called sample variance and denoted by $S^2$ in order to distinguish between population variance and sample variance. Variance is also denoted by $Var(X)$ when we speak about the variance of a random variable. The symbolic definition for population and sample variance is

$\sigma^2=\frac{\sum (X_i – \mu)^2}{N}; \quad \text{for population data}$

$\sigma^2=\frac{\sum (X_i – \overline{X})^2}{n-1}; \quad \text{for sample data}$

It should be noted that the variance is in the square of units in which the observations are expressed and variance is a large number compared to observations themselves. The variance because of its nice mathematical properties, assumes an extremely important role in statistical theory.

Variance can be computed if we have standard deviation as the variance is square of standard deviation i.e. Variance = (Standard Deviation)$^2$.

Variance can be used to compare dispersion in two or more sets of observations. Variance can never be negative since every term in the variance is squared quantity, either positive or zero.
To calculate the standard deviation one has to follow these steps:

1. First find the mean of the data.
2. Take difference of each observation from mean of the given data set. The sum of these differences should be zero or near to zero it may be due to rounding of numbers.
3. Square the values obtained in step 1, which should be greater than or equal to zero, i.e. should be a positive quantity.
4. Sum all the squared quantities obtained in step 2. We call it sum of squares of differences.
5. Divide this sum of squares of differences by total number of observation if we have to calculate population standard deviation ($\sigma$). For sample standard deviation (S) divide the sum of squares of differences by total number of observation minus one i.e. degree of freedom.
Find the square root of the quantity obtained in step 4. The resultant quantity will be standard deviation for given data set.

The major characteristics of the variances are:
a)    All of the observations are used in the calculations
b)    Variance is not unduly influenced by extreme observations
c)    The variance is not in the same units as the observation, the variance is in the square of units in which the observations are expressed.

Read more about Measure of Dispersion

## Levels of Measurement (Scale of Measure)

The levels of measurement (scale of measures) have been classified into four categories. It is important to understand these levels of measurement since these levels of measurement play an important part in determining the arithmetic and different possible statistical tests that are carried on the data. The scale of measure is a classification that describes the nature of the information within the number assigned to a variable. In simple words, the level of measurement determines how data should be summarized and presented. It also indicates the type of statistical analysis that can be performed. The four-level of measurement are described below:

1) Nominal Level of Measurement (Nominal Scale)

At the nominal level of measurement, the numbers are used to classify the data (unordered group) into mutually exclusive categories. In other words, for the nominal level of measurement, observations of a qualitative variable are measured and recorded as labels or names.

2) Ordinal Level of Measurement (Ordinal Scale)

In the ordinal level of measurement, the numbers are used to classify the data (ordered group) into mutually exclusive categories. However, it does not allow for a relative degree of difference between them. In other words, for the ordinal level of measurement, observations of a qualitative variable are either ranked or rated on a relative scale and recorded as labels or names.

3) Interval Level of Measurement (Interval Scale)

For data recorded at the interval level of measurement, the interval or the distance between values is meaningful. The interval scale is based on a scale with a known unit of measurement.

4) Ratio Level of Measurement (Ratio Scale)

Data recorded at the ratio level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale. Almost all quantitative variables are recorded on the ratio level of measurement.

### Examples of level of measurements

Examples of Nominal Level of Measurement

• Religion (Muslim, Hindu, Christian, Buddhist)
• Race (Hispanic, African, Asian)
• Language (Urdu, English, French, Punjabi, Arabic)
• Gender (Male, Female)
• Marital Status (Married, Single, Divorced)
• Number plates on Cars/ Models of Cars (Toyota, Mehran)
• Parts of Speech (Noun, Verb, Article, Pronoun)

Examples of Ordinal Level of Measurement

• Rankings (1st, 2nd, 3rd)
• Marks Grades (A, B, C, D)
• Evaluation such as High, Medium, Low
• Educational level (Elementary School, High School, College, University)
• Movie Ratings (1 star, 2 stars, 3 stars, 4 stars, 5 stars)
• Pain Ratings (more, less, no)
• Cancer Stages (Stage 1, Stage 2, Stage 3)
• Hypertension Categories (Mild, Moderate, Severe)

Examples of Interval Level of Measurement

• Temperature with Celsius scale/ Fahrenheit scale
• Level of happiness rated from 1 to 10
• Education (in years)
• Standardized tests of psychological, sociological, and educational discipline use interval scales.
• SAT scores

Examples of Ratio Level of Measurement

• Height
• Weight
• Age
• Length
• Volume
• Number of home computers
• Salary

For further details visit: Level of measurements