Question

Please answer as soon as possible

Compute the Quartile Deviation from the scores given below: (c) 10, 14, 16, 18, 20, 22, 23, 24, 26, 27, 12 (d) Calculate the combined Mean from the data given below: Mean (M) No. of Students (N) Group 25 20 A 15 40 B

Answer 1

(c) First , to arrange the given observations in increasing order.

10,12,14,16,18,20,22,23,24,26,27,

Since , n=11

The first quartile is ,

$Q_1=(\frac{n+1}{4})^{th} Observation$

$=(\frac{11+1}{4})^{th} Observation$

$=(\frac{12}{4})^{th} Observation$

$=14$

The third quartile is ,

$Q_3=(\frac{3(n+1)}{4})^{th} Observation$

$=(\frac{3(11+1)}{4})^{th} Observation$

$=(\frac{36}{4})^{th} Observation$

$=24$

Therefore , the quartile deviation is ,

$Q.D.=\frac{Q_3-Q_1}{2}=\frac{24-14}{2}=5$

(d) The combined mean is ,

$\bar{X}_{c}=\frac{n_{A}\bar{X}_{A}+n_{B}\bar{X}_{B}}{n_{A}+n_{B}}=\frac{20*25+40*15}{20+40}=18.33$