STATISTICS (LECTURE 4)

April 30, 2020

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 👇

take your SET-A Mathematics Note Book
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 !!👍
Make a column on the right hand side, if you need to do any rough work
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😄
Write today's date on the line after that.
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 (f_i)	Class Marks (x_i)	u_i = x_i - 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 (f_i)	Class Marks (x_i)	u_i = x_i - A h	f_iu_i
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 f_iu_{i =}-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 (f_i)
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 (f_i)	Class Marks (x_i)	u_i = x_i - A h	f_iu_i
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			åf_iu_{i =}- 66