5. Statistics ?
• Statistics is a branch of mathematics dealing with data
collection, organization, analysis, interpretation and
presentation.
https://en.wikipedia.org/wiki/Statistics
8. Importance of statistics
Measurement and evaluation are essential part of teaching
learning process.
• It makes the teaching learning process more efficient.
• You will become a better interpreter of educational data
by mastering the statistical concepts.
9. Cont.…
• It helps the teacher to predict the future performance of
the pupils.
• It enables the teacher to draw general conclusions.
• You can Improve your teaching strategy.
• It enables the teacher to summarize the results in a
meaningful and convenient form.
12. Types Of
Statistics
• Descriptive statistics
are simply numbers.
For example
percentages, numerals,
fractions and
decimals.
• These numbers are
used to describe or
summarize a larger
body numbers.
13. Tabulating Frequency Data
• The frequency tabulation is a very popular method for
summarizing data
• In frequency distribution table, we organize the collected data into
some classes or groups, and show the frequency in each group of
scores.
• The classroom teacher normally deals with a large amount of data
usually in form of test scores. As the data increase it becomes more
difficult to answer questions such as …..
14. Cont. ….
• How many people are above average?
• How many scored above the cut-off passing scores?
• Did most of the class do well on the test?
• What is the highest or lower score?
15. Frequency Distribution
• Frequency is how often something occurs.
• Suppose we obtain a set of numerical data like
• 72, 75, 77, 67, 81, 68, 65, 86, 73, 67, 69, 82, 76, 76, 70, 83, 71, 63, 72, 72,
61, 84, 64, 67.
• Step-I: Finding the Range:
• Range of the series of any score can be found out by subtracting the
lowest score from the highest. In the above set of scores, the range
of the distribution is (86-61)=25.
16. Cont.…
• Step-2: Determining the class interval
• There are two different rules for determining the class interval. The
First and easiest way is – the range is divided by the number of
classes desired, e.g.
• Where, i = class interval
• Here, i = 25 / 5 = 5
18. Question
• What is the range for the following set of numbers?
15, 21, 57, 43, 11, 39, 56, 83, 77, 11, 64, 91, 18, 37
Answer : 80
The range is the difference between the lowest and highest values.
The highest value is 91.
The lowest value is 11.
Therefore the range = 91 - 11 = 80
19. Question
• What is the range for the following set of numbers?
57, -5, 11, 39, 56, 82, -2, 11, 64, 18, 37, 15, 68
Answer = 87
The range is the difference between the lowest and highest values.
The highest value is 82.
The lowest value is -5.
Therefore the range = 82 - (-5) = 82+5 = 87
21. Example: Newspapers
These are the numbers of newspapers sold at a local shop over the last 10 days:
22, 20, 18, 23, 20, 25, 22, 20, 18, 20
Let us count how many of each number there is:
Papers Sold Frequency
18 2
19 0
20 4
21 0
22 2
23 1
24 0
25 1
It is also possible to group the values. Here they are grouped in:
Papers Sold Frequency
15-19 2
20-24 7
25-29 1
22. Question
Hockey team scored the following numbers of goals in their last
twenty matches:
3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 3
• Which number had the highest frequency?
• Answer : 3
23. Question
• Which letter occurs the most frequently in the following sentence?
THE SUN ALWAYS SETS IN THE WEST.
Answer : S
24. Fifty students of B.A. (Major) course obtained the following
scores in an achievement test. Tabulate the data in a
frequency distribution table
26. Answers
In the above example, the total no. of scores=50,
• Highest score=68
• Lowest score=21
• Range=68-21=47
• Hence, here 10 classes are sufficient.
• i=47/10=4.7 (approx.5)
34. Smooth Curve
Follow these two guidelines in constructing smooth curves:
• Be sure your score axis increases from left to right.
• Be sure the “tails” or ends of the curves come close to, but do not
touch, the baseline.
36. Two Major Characteristics Of Distribution
Symmetrical
• Each half of the distribution is
a mirror image of the other
side.
Asymmetrical
• This type f distribution has no
matching sides.
37. Check list
• Statistics
• List
• Simple frequency distribution
• Grouped frequency distribution
• Range
• Interval
• Lower limit
• Upper limit
• Frequency
• Midpoint
• Histogram
• Frequency polygon
• Smooth curve
• Symmetrical distribution
• Normal distribution
• Positively skewed distribution
• Negatively skewed distribution
38. Percentiles
• Percentile: the value below which a percentage of data falls.
Example: You are the fourth tallest person in a group of 20
80% of people are shorter than you:
That means you are at the 80th percentile.
Formula : R = P / 100* (N+1)
39. Example
• Find P25 and P50 in the following distribution of scores.
115, 112, 110, 108, 106, 104, 100, 100, 98, 96, 96, 94, 93, 91, 90, 88
• Answer: P25= 93.5 , P50= 99
• Formula : R = P / 100 (N+1)
40. Measures Of Central Tendency
• Mean
• Median
• Mode Mean Median Mode
The "average"
number
The middle
number
The most
frequent number
46. Median
• The median is the middle point in a dataset—half of the data points are smaller
than the median and half of the data points are larger.
• To find the median:
1. Arrange the data points from smallest to largest.
2. If the number of data points is odd, the median is the middle data point in the
list.
3. If the number of data points is even, the median is the average of the two
middle data points in the list.
47. Count ….
• Example 1
• 1,2,3,4,5
• Median is 3
• Example 2
• 0,1,2,3,4,5
• 2+3/2 = 5/2
• Median is 2.5
48. Activity
month Jan Feb March April May June July Aug Sep Oct Nov Dec
Temp 38 39 43 46 52 58 62 62 57 51 44 42
What is the median of these values?
49. Answer
• The median is the "middle" value
First arrange the temperatures in order:
38, 39, 42, 43, 44, 46, 51, 52, 57, 58, 62, 62
There are two temperatures in the middle: 46°F and 51°F
So the median is the mean of them
= (46 + 51) ÷ 2
= 48.5°F
50. Mode
• The mode is the most commonly occurring data point in a dataset.
• The mode is useful when there are a lot of repeated values in a
dataset.
• There can be no mode, one mode, or multiple modes in a dataset.
Example :
0,1,2,5,7,9,3,1,0,5,1,3,2,1,1
Answer 1
52. Count ….
Answer
The mode is the most frequently occurring average temperature =
62°F in July and August.
53. Skewed Data
• Data can be "skewed", meaning it tends to have a long tail on one
side or the other:
• Negative Skew
• No Skew
• Positive Skew
https://www.mathsisfun.com/data/skewness.html
