STATISTICS (LECTURE 4)

STATISTICS_CLASS 10

LESSON 4

Good Morning 

We have covered the following learning outcomes so far:

• Recall the different ways in which the data can be written
• Recall the measures of central tendencies
• Defined mode of the given data
• Calculate Mode of the given data
• Interpret Mode of the given data
• Calculate Class Marks of the given class intervals
• Calculate Mean of the given data using "direct method"
• Calculate Mean of the given data using "assumed mean method"

Let us go through the guidelines for the  blog once again:

•              The text in Red, is to be written in your register

•              The text in blue is to be viewed by clicking on it

•              The text in green is to be practiced for home work



TO BEGIN 👇

1. take your SET-A Mathematics Note Book
2. Our handwriting reflects a lot about us. It will be awesome if you use good presentation and cursive hand writing. Hope you are still at it !!👍
3. Make a column on the right hand side, if you need to do any rough work
4. Leave two lines where you finished yesterday’s work and draw a horizontal line. Recall SDG-12 (turn the leaves of your notebooks to read that!) Thank you😄
5. Write today's date on the line after that. 
6. Please write the learning outcomes as mentioned below

I will be able to  :  

• Calculate Mean for the grouped data using the STEP DEVIATION METHOD.
• Calculate Missing Frequencies , when the Mean is given to us.                                                                       

Please click on ➤👇

Q1)  If the class interval are (10 --15), (15--20), (20--25) and so 
        on then the value of "h" is ___

                            { Hint: The class size is "h". How much is (15 -10) and (20-15) and (25-20) ?}

Q2)  Calculate the values of "x" & "u" for each class interval in the following table: (make the table in the notebook)

Class Intervals	Frequency (fi)	Class Marks (xi)	ui  = xi -  A             h
115 - 150	23
150 – 185	52
185 – 225	45
225 - 260	37
260 - 295	15

{ Hint: What is A ? , Recall from the concept of assumed mean , done yesterday}

Now that you have calculated (u_i), you do not even need to look at your class interval column or (x_i) . All the remaining calculations will just involve :

(f_i) & (u_i)  

Please click ➤👇to see how !

Now that you have seen how to calculate the mean using "Step deviation method",

Please use the following formula to 
calculate mean using "step deviation method"  in Q2   👇

Are you going to start over again ? Of course NOT !! 😡

Get back to where you did Q2. 

You already have 4 columns there ?

Make the 5th column with heading as (f_i u_i)

Do the calculations for the 5th column and use the formula for "step deviation method" to calculate the mean 👍

We will practice few questions with "Missing frequencies".
Please write the following Questions as important Questions in your notebook👇

Q3) Find the values of f₁ & f₂ in the following table, 
      if the mean is 62.8

A3)

Substituting the value of f₂ from (i) 
⇒  62.8 = [2060 + 30f₁  + 70(20 - f₁)] / 50
⇒  62.8 × 50 = [2060 + 30f₁  + 70(20 - f₁)] 
⇒  3140 = 2060 + 30f₁  + 1400 - 70f₁
⇒  3140 - 2060 -1400 =  30f₁  - 70f₁
 ⇒  -320 = -40f₁
 ⇒  f₁ = 8   ,  f₂ = 20 - 8  = 12

However if I do the same question using step deviation method👇

Class Intervals	Frequency (fi)	Class Marks (xi)	ui  = xi -  A             h	fiui
0-20	5	10	-3	-15
20-40	f1	30	-2	-2 f1
40-60	10	50	-1	-10
60-80	f2	70	0	0
80-100	7	90	1	7
100-120	8	110	2	16
	åf i = 50			å fiui  =  -2 -2 f1

f₂ = 20 –f₁

Mean = A +   (å f_iu_i / å f _i ) ×  h

Þ   62.8  = 70 + [ (-2 - 2 f₁) / 50] × 20

Þ   [ (2 + 2 f₁) / 50] × 20 = 70 – 62.8

Þ   (1 +  f₁) × 4/5 = 7.2

Þ   (1 +  f₁)  = 7.2 × 5/4

 ⇒  f₁ = 8   ,  f₂ = 20 - 8  = 12

Q4) Find the values of  'f '   in the following table:

Class Intervals	Frequency (fi)
11-13	7
13-15	6
15-17	9
17-19	15
19-21	f
21-23	5
23-25	4

A4)

Class Intervals	Frequency (fi)	Class Marks (xi)	ui  = xi -  A             h	fiui
11-13	7	12	-4	-28
13-15	6	14	-3	-18
15-17	9	16	-2	-18
17-19	15	18	-1	-15
19-21	f	20	0	0
21-23	5	22	1	5
23-25	4	24	2	8
	åf i = f + 44			åfiui  =  - 66

Mean = A +   (å f_iu_i / å f _i ) ×  h

Þ  18  = 20 + [- 66 / (f + 44)] × 2

Þ   18 – 20 = -132 / (f + 44)

Þ   f + 44 = 66

Þ   f = 22

Home Work: NCERT Ex 14.1 (Q3, 7, 8, 9)

That will be all for today !

Good Morning and Thank you boys !  😊

See you in the next class on 9th April 2020 !

Take a good care of yourselves !