a) Find the mean and standard deviation for the following data:

Question

Class interval	Frequency
0 – 10	5
10 – 20	10
20 – 30	14
30 – 40	15
40 – 50	6

b) State Chebychev’s inequality. Hence obtain the lower bound for $P[-1<x<9]$ if the E(x) and $E(x^2)$ of x are 4 and 20 respectively.

12 Mar 2024

Answer :

Word Count : 518

To find the mean (average) and standard deviation for the given data, we first need to find the midpoint of each class interval, then calculate the weighted mean and standard deviation.

Here are the steps:

1. Find the midpoint of each class interval.
2. Calculate the weighted mean.
3. Calculate the variance.
4. Calculate the standard deviation.

Let's proceed with the calculations:

1. Midpoints:
- Midpoint of 0 – 10: (0 + 10) / 2 = 5
- Midpoint of 10 – 20: (10 + 20) / 2 = 15
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$x\rightarrow$	$y\downarrow$	0	1	2
0		$\frac{1}{12}$	$\frac{1}{6}$	$\frac{1}{24}$
1		$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{40}$
2		$\frac{1}{8}$	$\frac{1}{20}$	__
3		$\frac{1}{120}$	__	$\frac{1}{120}$