Statistics Mean,media,mode, variance

1. Descriptive Statistics
Measure of Central Tendency
Measure of Dispersion
Measure of Distribution

2. Measure of Central Tendency:
Ungrouped Data
 Provides information about the center or
middle part of a group of numbers.
 Includes mean, median, mode, quartiles,
percentiles etc.

3. Mode
 Most frequently occurring value in a set of data.
 Less popular than mean and median
 Use to find out the value with highest demand in business.
How to determine the mode in a data set
 Order the values from minimum to maximum and locate the value which occurs the most.
 3,4,5,5,6,6,6,6,6,7,7,7,8,8,9,9,9,10,10,11,12 Mode=6
 3,4,5,5,5,5,6,6,6,6,8,8,9,9,9, 10, 11, 11, 12 Mode = 5 and 6 (Bimodal)
 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18 Mode = none

4. Median
 Middle value in an ordered array of numbers.
 For an array with an odd number of terms, the median is the
middle number
 For an array with an even number of terms, the median is an
average of the two middle numbers
 Steps to determine the median:
 Step1: Arrange the observation in an ascending/descending order
 Step2: For an odd number of terms, find the middle term
 Step3: For an even number of terms, the average of middle two
terms

5. Median Example: Calculate the median of the following example:
34 72 39 55 24 26 75 23 35 51 82 66 69 85 56 70 76 89 26 41
Step1:Arrange inascendingorder
2324262634353941515556666970727576828589
Step2:Themiddlevaluesare55and56
Step3:Medianis(55+56)/2= 55.5
Median is not affected by theextreme values
Median is not reflecting theinformation about all the numbers.

6. Mean
Arithmetic mean is the
average of a group of
members.
Computed by dividing
the sum of the numbers
by the total numbers.

7. Meanisaffectedbyallthevaluesinthedataset.
Meanisbadlyaffectedbytheoutliersortheextremevaluesinthe
dataset.

8. Percentiles
 99 values (dividers) which divide the
data into 100 equal parts.
 nth percentile means that n % of the
data is below than value. For example
87th percentile means 87% of the values
are lower than this number.
Percentiles are widely used in tests
such as CAT, JEE, GRE etc. The results of
these exams are reported in percentile
form along with raw scores.

9. Quartiles
Are measure of central tendency that divide a
group of data into four equal parts.
These quartiles are denoted as Q1, Q2 and Q3.
Q1 is 25th percentile, Q2 is 50th percentile and Q3
is 75th percentile.


10. Measure of Variability-
Ungrouped data
Describe the dispersion or
spread of the data set.
Provides significant information
along with measure of central
tendency.

11. Range and Interquartile range
Range is the difference between the largest value of a data set and the smallest value of the
data set.
Easy to compute
Not considered as a good measure as it considers the extreme values of the dataset.
Interquartile range is the difference between first quartile and third quartile of a dataset
i.e. Interquartile Range = Q3 - Q1
It indicates the range of 50% of the dataset.

12. Mean Absolute deviation
 Average of the absolute values of the deviations around the mean for a set of
numbers

13. Variation
 Average of the squared deviations from the mean for a set of numbers

14. Standard Deviation
 Square root of the variance

15. Chebyshev’s Theorem:
Helps in estimating the approximate percentage of values that lie within
a given number of standard deviation from the mean of a set of data if
the data is normally distributed.

16. Chebyshev’s theorem
statesthatatleast1–1/k2valueswillfallwithin+standarddeviationofthe
meanregardlessoftheshapeofthedistribution
Assuming the average weight of 56 kg and standard deviation of 10 kg.
Estimate that how much proportion of the population lie within the
range of mean + 2 * SD
a. If the distribution is normal.
b. If the distribution is not normal.

17. Z-Scores
is a numerical measurement used in statistics of a value's relationship to
the mean (average) of a group of values, measured in terms of standard
deviation from the mean.
If a Z-score is 0, it indicates that the data point's score is identical to the
mean score.
A Z-score of 1 would indicate a value that is one standard deviation
from the mean.
Z-scores may be positive or negative, with a positive value indicating the
score is above the mean and a negative score indicating it is below the
mean.

19. Coefficient of Variation
Is the ratio of standard deviation to the mean expressed in
percentage
𝐶𝑉 =
𝜎
𝜇
(100)
CV is a relative comparison of a SD to the mean.

20. Skewness

21. Kurtosis

22. Mean – Grouped data

23. Median Grouped Data

24. Box Plot Diagram

25. Thankyou