Question

Calculate mean by step-deviation method, for the following data.
Marks:
100 - 200
200 – 300
300 – 400
400 - 500
500 - 600
600 – 700

frequency:
24
23
38
23
22
20​

Answer 1

Answer:

hope it would be helpful for u

Step-by-step explanation:

With the given distribution , xi=35,45,55,65,75,85,95

fi=3,7,12,15,8,3,2

∴xifi=105,315,660,975,600,255,190

∴∑fi=50

∑xifi=3100

∴Mean(X¯¯¯)=∑xifi∑fi=310050=62

Now, |xi−x¯|=27,17,7,3,13,23,33

|xi−x¯|2=729,289,49,9,169,529,1089

∴|xi−x¯|2fi=2187,2023,588,135,1352,1587,2178

∴ Variance, (σ)2=∑|xi−x¯|2fi∑fi=1005050=201

Standard deviation, (σ)=201−−−√≅14.177.