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From Karnataka Open Educational Resources
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hypotheses.
hypotheses.
== Textbook ==
Please click here for Karnataka and other text books.
# Karnataka text book for Class 10, Chapter 06 - Statistics
# NCERT text book for class 10, Chapter 14 - Statistics
# Page No 279-298 of Temilnadu text book for class 10 - Statistics
== Additional Information ==
=== Useful websites ===
STATISTICS IS FUN.
# This website has many powerful videos based on statistical inferences on important social issues [http://gapminder.org/videos/the-joy-of-stats/#.U8JbOzf_QjA click here]
# For wikipedia link [https://en.wikipedia.org/wiki/Wikipedia:Statistics click here]
# For video lessons on Statistics [http://www.neok12.com/Statistics.htm click here]
# youtube videos on statistics
= Mind Map =
= Mind Map =
* A teacher may ask “How many hours of TV by students on TV' to get an idea of what children are learning from TV at home and how it supplements (or affects) the learning in the school
* A teacher may ask “How many hours of TV by students on TV' to get an idea of what children are learning from TV at home and how it supplements (or affects) the learning in the school
# Specialised equipment (rainwater gauges to measure rainfall in a place, various medical equipment that collect information about different biological processes)
# Specialised equipment (rainwater gauges to measure rainfall in a place, various medical equipment that collect information about different biological processes)
'''England beat India
'''England beat India'''
by 6 wickets (D/L). '''England won the toss and decided to field
by 6 wickets (D/L). '''England won the toss and decided to field'''
{| border="1"
{| border="1"
304 for 6 (50.0 overs)
304 for 6 (50.0 overs)
|-
|-
241 for 4 (32.2 overs)
241 for 4 (32.2 overs)
|}
|}
'''India
'''India'''
1st Innings - Close'''
1st Innings - Close
{| border="1"
{| border="1"
|
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Name
Name
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|
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-
-
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Runs
Runs
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Balls
Balls
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4s
4s
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6s
6s
|-
|-
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P Patel
P Patel
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c Bresnan
c Bresnan
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b Swann
b Swann
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'''19'''
'''19'''
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39
39
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0
0
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0
0
|-
|-
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Rahane
Rahane
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c Finn
c Finn
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b Dernbach
b Dernbach
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'''26'''
'''26'''
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47
47
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3
3
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0
0
|-
|-
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Dravid
Dravid
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-
-
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b Swann
b Swann
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'''69'''
'''69'''
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79
79
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4
4
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0
0
|-
|-
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Kohli
Kohli
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hit wicket
hit wicket
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b Swann
b Swann
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'''107'''
'''107'''
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93
93
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9
9
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1
1
|-
|-
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Raina
Raina
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c Bresnan
c Bresnan
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b Finn
b Finn
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'''15'''
'''15'''
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15
15
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0
0
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1
1
|-
|-
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Dhoni
Dhoni
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not out
not out
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-
-
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'''50'''
'''50'''
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26
26
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5
5
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2
2
|-
|-
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Jadeja
Jadeja
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c Bopara
c Bopara
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b Dernbach
b Dernbach
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'''0'''
'''0'''
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1
1
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0
0
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0
0
|-
|-
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Ashwin
Ashwin
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not out
not out
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-
-
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'''0'''
'''0'''
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0
0
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0
0
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0
0
|-
|-
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'''Extras'''
'''Extras'''
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-
-
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6w 1b 11lb
6w 1b 11lb
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'''18'''
'''18'''
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-
-
|-
|-
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'''Total'''
'''Total'''
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-
-
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for 6
for 6
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'''304'''
'''304'''
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-
-
|}
|}
{| border="1"
{| border="1"
|
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Bowler
Bowler
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Overs
Overs
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Maidens
Maidens
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Runs
Runs
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Wickets
Wickets
|-
|-
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Bresnan
Bresnan
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9.0
9.0
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0
0
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62
62
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0
0
|-
|-
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Finn
Finn
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10.0
10.0
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1
1
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44
44
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1
1
|-
|-
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Dernbach
Dernbach
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10.0
10.0
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0
0
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73
73
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2
2
|-
|-
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Swann
Swann
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9.0
9.0
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0
0
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34
34
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3
3
|-
|-
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S Patel
S Patel
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8.0
8.0
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0
0
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55
55
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0
0
|-
|-
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Bopara
Bopara
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4.0
4.0
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0
0
|
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24
24
|
|
0
0
|}
|}
|}
|}
== Recording Data ==
== Recording Data ==
and wrote the choice of fruit against each name. This list would help
and wrote the choice of fruit against each name. This list would help
the teacher to distribute fruits according to the choice.
the teacher to distribute fruits according to the choice.
{| border="1"
{| border="1"
Rati — Banana
Rati — Banana
|
|
Javed — Banana
Javed — Banana
|}
|}
this information to Maria. Maria does so using a paper and a pencil.
this information to Maria. Maria does so using a paper and a pencil.
After arranging the choices in a column, she puts against a choice of
After arranging the choices in a column, she puts against a choice of
food one ( / ) mark for every student making that choice.
food one ( / ) mark for every student making that choice.
{| border="1"
{| border="1"
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Choice
Choice
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Number of students
Number of students
|-
|-
Both rice and chapati
Both rice and chapati
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////////////////////
////////////////////
|}
|}
Umesh, after seeing the
Umesh, after seeing the
table suggested a better method to count the students. He asked
table suggested a better method to count the students. He asked
Maria to organise the marks ( / ) in a group of ten as shown below :
Maria to organise the marks ( / ) in a group of ten as shown below :
{| border="1"
{| border="1"
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Choice
Choice
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Tally marks
Tally marks
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Number of students
Number of students
|-
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Both rice and chapati
Both rice and chapati
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////////// //////////
////////// //////////
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20
20
|}
|}
shown below :
shown below :
{| border="1"
{| border="1"
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Choice
Choice
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Tally marks
Tally marks
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Number of students
Number of students
|-
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Both rice and chapati
Both rice and chapati
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///// ///// ///// /////
///// ///// ///// /////
|
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20
20
|}
|}
given time period. It is not easy to answer the
given time period. It is not easy to answer the
question looking at the choices written haphazardly. We arrange the
question looking at the choices written haphazardly. We arrange the
data in Table below using tally marks.
data in Table below using tally marks.
{| border="1"
{| border="1"
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Subject
Subject
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Tally Marks
Tally Marks
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Number of Students
Number of Students
|-
|-
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Art
Art
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///// //
///// //
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7
7
|-
|-
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Mathematics
Mathematics
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/////
/////
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5
5
|-
|-
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Science
Science
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///// /
///// /
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6
6
|-
|-
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English
English
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////
////
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4
4
|}
|}
The number of tallies
The number of tallies
Examples - political
Examples - political
affiliation, religious affiliation, blood type etc. Below is Blood
affiliation, religious affiliation, blood type etc. Below is Blood
Type frequency distribution example.
Type frequency distribution example.
{| border="1"
{| border="1"
|
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Class
Class
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Frequency
Frequency
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Percent
Percent
|-
|-
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A
A
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5
5
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20
20
|-
|-
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B
B
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7
7
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28
28
|-
|-
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C
C
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9
9
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36
36
|-
|-
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D
D
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4
4
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16
16
|}
|}
== Activities ==
== Activities ==
The first four columns have headings. Choose headings for the other
The first four columns have headings. Choose headings for the other
columns and collect data from the 10 of your class mates
columns and collect data from the 10 of your class mates
{| border="1"
{| border="1"
|
|
'''Name'''
'''Name'''
|
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'''Age'''
'''Age'''
|
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'''Height'''
'''Height'''
|
|
'''Favourite Colour '''
'''Favourite Colour '''
|
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<Add More Headings>
<Add More Headings>
|
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<Add More Headings>
<Add More Headings>
|
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<Add More Headings>
<Add More Headings>
|
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<Add More Headings>
<Add More Headings>
|-
|-
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-
-
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|}
==== Evaluation ====
==== Evaluation ====
=== What is a histogram? ===
=== What is a histogram? ===
[[Image:KOER-%20Mathematics%20-%20Statistics_html_6201ec25.png]]
[[Image:KOER-%20Mathematics%20-%20Statistics_html_6201ec25.png]]
=== How do you construct a histogram from a continuous variable? ===
=== How do you construct a histogram from a continuous variable? ===
=== Choosing the correct bin width ===
=== Choosing the correct bin width ===
graph or a histogram? Why is this choice better than the other?
graph or a histogram? Why is this choice better than the other?
Using the following data, construct the graph that you choose.
Using the following data, construct the graph that you choose.
{| border="1"
{| border="1"
|
|
Month
Month
|
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Number of Tickets Sold
Number of Tickets Sold
|-
|-
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January
January
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25
25
|-
|-
|
|
February
February
|
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20
20
|-
|-
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March
March
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15
15
|-
|-
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April
April
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20
20
|-
|-
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May
May
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30
30
|-
|-
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June
June
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35
35
|-
|-
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July
July
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40
40
|-
|-
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August
August
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20
20
|-
|-
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September
September
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25
25
|-
|-
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October
October
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15
15
|-
|-
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November
November
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20
20
|-
|-
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December
December
|
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30
30
|}
|}
depth increment size) for the following data. In which case(s) is the
depth increment size) for the following data. In which case(s) is the
histogram the same as the bar graph? How do the other histograms vary
histogram the same as the bar graph? How do the other histograms vary
from the bar graph?
from the bar graph?
{| border="1"
{| border="1"
|-
|-
|
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'''Depth Range'''
'''Depth Range'''
|
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'''Number of Living Creatures '''
'''Number of Living Creatures '''
|-
|-
|
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0 – 1 meters
0 – 1 meters
|
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10
10
|-
|-
|
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1 – 2 meters
1 – 2 meters
|
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93
93
|-
|-
|
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2 – 3 meters
2 – 3 meters
|
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23
23
|-
|-
|
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3 – 4 meters
3 – 4 meters
|
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47
47
|-
|-
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4 – 5 meters
4 – 5 meters
|
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68
68
|-
|-
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5 – 6 meters
5 – 6 meters
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51
51
|-
|-
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6 – 7 meters
6 – 7 meters
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43
43
|-
|-
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7 – 8 meters
7 – 8 meters
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21
21
|-
|-
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8 – 9 meters
8 – 9 meters
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15
15
|-
|-
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9 – 10 meters
9 – 10 meters
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8
8
|}
|}
=== Dependent and Independent Variables ===
=== Dependent and Independent Variables ===
=== Experimental and Non-Experimental Research ===
=== Experimental and Non-Experimental Research ===
=== Categorical and Continuous Variables ===
=== Categorical and Continuous Variables ===
=== Ambiguities in classifying a type of variable ===
=== Ambiguities in classifying a type of variable ===
especially small or large in numerical value. For example, consider
especially small or large in numerical value. For example, consider
the wages of staff at a factory below:
the wages of staff at a factory below:
{| border="1"
{| border="1"
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Staff
Staff
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1
1
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2
2
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3
3
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4
4
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5
5
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6
6
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7
7
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8
8
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9
9
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10
10
|-
|-
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Salary
Salary
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15k
15k
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18k
18k
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16k
16k
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14k
14k
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15k
15k
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15k
15k
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12k
12k
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17k
17k
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90k
90k
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95k
95k
|}
|}
that has been arranged in order of magnitude. The median is less
that has been arranged in order of magnitude. The median is less
affected by outliers and skewed data. In order to calculate the
affected by outliers and skewed data. In order to calculate the
median, suppose we have the data below:
median, suppose we have the data below:
{| border="1"
{| border="1"
|
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65
65
|
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55
55
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89
89
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56
56
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35
35
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14
14
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56
56
|
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55
55
|
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87
87
|
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45
45
|
|
92
92
|}
|}
We first need to rearrange that data into order of
We first need to rearrange that data into order of
magnitude (smallest first):
magnitude (smallest first):
{| border="1"
{| border="1"
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14
14
|
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35
35
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45
45
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55
55
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55
55
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'''56'''
'''56'''
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56
56
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65
65
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87
87
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89
89
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92
92
|}
|}
Our median mark is the middle mark - in this case
Our median mark is the middle mark - in this case
of scores? What if you had only 10 scores? Well, you simply have to
of scores? What if you had only 10 scores? Well, you simply have to
take the middle two scores and average the result. So, if we look at
take the middle two scores and average the result. So, if we look at
the example below:
the example below:
{| border="1"
{| border="1"
|
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65
65
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55
55
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89
89
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56
56
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35
35
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14
14
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56
56
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55
55
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87
87
|
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45
45
|}
|}
We again rearrange that data into order of
We again rearrange that data into order of
magnitude (smallest first):
magnitude (smallest first):
{| border="1"
{| border="1"
|
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14
14
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35
35
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45
45
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55
55
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'''55'''
'''55'''
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'''56'''
'''56'''
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56
56
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65
65
|
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87
87
|
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89
89
|
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92
92
|}
|}
Only now we have to take the 5th and 6th score in
Only now we have to take the 5th and 6th score in
Please use the following summary table to know
Please use the following summary table to know
what the best measure of central tendency is with respect to the
what the best measure of central tendency is with respect to the
different types of variables.
different types of variables.
{| border="1"
{| border="1"
|
|
'''Type of Variable'''
'''Type of Variable'''
|
|
'''Best measure of central tendency'''
'''Best measure of central tendency'''
|-
|-
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|
Nominal
Nominal
|
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Mode
Mode
|-
|-
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|
Ordinal
Ordinal
|
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Median
Median
|-
|-
|
|
Interval/Ratio (not skewed)
Interval/Ratio (not skewed)
|
|
Mean
Mean
|-
|-
|
|
Interval/Ratio (skewed)
Interval/Ratio (skewed)
|
|
Median
Median
|}
|}
== Relative advantages and disadvantages of mean, median and mode ==
== Relative advantages and disadvantages of mean, median and mode ==
==== Pre-requisites/ Instructions ====
==== Pre-requisites/ Instructions ====
A. 27 members of a
A. 27 members of a
class were given a puzzle to solve and the times (in minutes) each
class were given a puzzle to solve and the times (in minutes) each
pupil took to solve it were noted.
pupil took to solve it were noted.
{| border="1"
{| border="1"
|
|
'''the times (in minutes) each pupil took'''
'''the times (in minutes) each pupil took'''
|-
|-
12 2 17 15 14 10 11 10 12
12 2 17 15 14 10 11 10 12
|}
|}
# Which of the three measures do you think is most representative of the average time? In this case it is probably the mean, but this will not always be so.
# Which of the three measures do you think is most representative of the average time? In this case it is probably the mean, but this will not always be so.
# Which of these measures is of most use?
# Which of these measures is of most use?
Dress sizes sold in one week
Dress sizes sold in one week
{| border="1"
{| border="1"
16
16
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18
18
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14
14
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16
16
|
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8
8
|}
|}
==== Evaluation ====
==== Evaluation ====
your study and your range is 7 to 123 years old you know you have
your study and your range is 7 to 123 years old you know you have
made a mistake!
made a mistake!
=== Quartiles and Interquartile Range ===
=== Quartiles and Interquartile Range ===
=== Absolute Deviation and Mean Absolute Deviation ===
=== Absolute Deviation and Mean Absolute Deviation ===
=== Variance ===
=== Variance ===
* When the coefficient of variation is less, the given data is more consistent.
* When the coefficient of variation is less, the given data is more consistent.
