What is the formula of Combined Standard Deviation? - Vidyadip

Question

What is the formula of Combined Standard Deviation?

✓

Answer

If there are two groups containing $n_1$, and $n_2$, observations, $\bar{\text{X}}_1$ and $\bar{\text{X}}_2,$ as respective arithmetic means and $s_1$, and$ s_2,$ as respective standard deviations, then combined standard deviation is given by$\sigma_{\text{c}}=\sqrt{\frac{\text{n}_1\text{s}^2_1+\text{n}_2\text{s}^2_2+\text{n}_1\text{d}^2_1+\text{n}_2\text{d}^2_2}{\text{n}_1+\text{n}_2}}$
where, $d_1$ and $d_2 $are the differences between individual mean and combined mean of series 1 and series 2 respectively.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Measures of Dispersion→Measures of Dispersion — all question types→Economics STD 11 Commerce question papers→CBSE Board STD 11 Commerce question papers→CBSE Board question paper generator→

Similar questions

Mr. X consumes two commodities X and Y whose prices are ₹4 and ₹2 per unit respectively. What will be the value of marginal rate of substitution if the consumer is in the state of equilibrium?

There are three identical firms in a market. The following table shows the supply schedule of firm 1. Compute the market supply schedule.

Price (₹)	0	1	2	3	4	5	6	7	8
$SS _1$ (Units)	0	0	2	4	6	8	10	12	14

→

How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?

Name the graphic method of measuring dispersion. Write its three demerits.

The inter-quartile range of a distribution is $105$ and the value of lower quartile is $45$. Find the value of upper quartile. Also find the coefficient of quartile deviation.

State any two merits and demerits of quartile deviation.

Certain goods are demanded even when their price is zero. Does it mean that we are demanding even those goods which are not scarce ?

What do you understand by pre-testing of the questionnaire?

There are three kinds of lies: lies, damned lies, and statistics. Explain.
OR
There is a general perception that statistical knowledge is intentionally misused. Explain how.

Draw PPC for an economy, if production possibilities are as under. Also find marginal opportunity cost.

Shirt (Millions)	0	1	2	3	4	5
Computer (Thousands)	15	14	12	9	5	0