Name: Variance and Standard Deviation for Ungrouped Distribution
Uploaded: 2019-07-19
Duration: 6 min 21 s
Description: In this video, let us learn to find the variance and standard deviation of ungrouped data. We will also learn the formula to find the discrete frequency dist...

Question

Calculate the partition values

Q_{1}, Q_{2}, D_{2}, D_{7}, D_{8}, P_{22}

and

P_{38}

for the following data:

4, 7, 3, 9, 4, 12, 7, 12, 6, 18, 19, 20, 4, 7 . 6, 5, 17, 16 . 19

Accepted Answer

Arranging the given data in ascending order, we have

$3, 4, 4, 4, 5, 6, 6, 7, 7, 7, 9, 12, 12, 16, 17, 18, 19, 19, 20$

Here no. of observations $= n = 19$ (odd)

$Q_{1} = {(\frac{n + 1}{4})}^{th} value = {(\frac{19 + 1}{4})}^{th} value$ i.e $5^{th}$ value $= 5$

$∴ Q_{1} = 5$ $Q_{3} = 3 {(\frac{n + 1}{4})}^{th} value = 3 {(\frac{19 + 1}{4})}^{th} value = 15^{th} value = 17$

$D_{2} = 2 {(\frac{n + 1}{10})}^{th} value = 2 {(\frac{19 + 1}{10})}^{th} value = 4^{th} value = 4$

$D_{7} = 7 {(\frac{n + 1}{10})}^{th} value = 7 {(\frac{19 + 1}{10})}^{th} value = 14^{th} value = 16$

$D_{8} = 8 {(\frac{n + 1}{10})}^{th} value = 8 {(\frac{19 + 1}{10})}^{th} value = 16^{th} value = 18$

$P_{22} = 22 {(\frac{n + 1}{100})}^{th} value = 22 {(\frac{19 + 1}{100})}^{th} value = 4 . 4^{th} value$

$= 4^{th} value + 0.4 (5^{th} - 4^{th})$ value

$= 4 + 0.4 (5 - 4) = 4 + 0.4 = 4.4$

$P_{38} = 38 {(\frac{n + 1}{100})}^{th} value = 38 {(\frac{19 + 1}{100})}^{th} value = 7 . 6^{th} value$

$= 7^{th} value + 0.6 (8^{th} - 7^{th}) value$

$= 7 + 0.6 (7 - 6) = 7 + 0.6 = 7.6$

Hence, the partition values of $Q_{1}, Q_{2}, D_{2}, D_{7}, D_{8}, P_{22}$ and $P_{38}$ are $5, 17, 4, 16, 16, 4.4$ and $7.6$ .

$x_{i}$	$18$	$19$	$20$	$21$	$22$	$23$	$24$	$25$	$26$	$27$
$f_{i}$	$15$	$18$	$25$	$27$	$40$	$25$	$19$	$16$	$8$	$= 7^{th} value + 0.6 (8^{th} - 7^{th}) value$

Marks	Below $10$	$10 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	Above $80$
Number of students	$8$	$10$	$22$	$25$	$10$	$5$

Daily wages (in ₹)	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
No. of workers	$22$	$38$	$46$	$35$	$20$

Height ( in inches)	$58$	$59$	$60$	$61$	$62$	$63$	$64$	$65$	$66$
No. of students	$15$	$20$	$32$	$35$	$35$	$22$	$20$	$10$	$8$

Wages (in ₹)	$15 - 19$	$20 - 24$	$25 - 29$	$30 - 34$	$35 - 39$	$40 - 44$	$45 - 49$	$50 - 54$	$55 - 59$	$60 - 64$
No. of workers	$31$	$47$	$59$	$78$	$104$	$113$	$81$	$60$	$52$	$25$

Calculate the partition values $Q_{1}, Q_{2}, D_{2}, D_{7}, D_{8}, P_{22}$ and $P_{38}$ for the following data: $4, 7, 3, 9, 4, 12, 7, 12, 6, 18, 19, 20, 4, 7 . 6, 5, 17, 16 . 19$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Mass (kg)	$50 - 58$	$59 - 67$	$68 - 76$	$77 - 85$	$86 - 94$	$95 - 103$
Frequency	$15$	$15$	$23$	$20$	$9$	$8$

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50$ and above
No. of students	$3$	$7$	$11$	$12$	$23$	$4$

Calculate the partition values Q1, Q2, D2, D7, D8, P22 and P38 for the following data: 4, 7, 3, 9, 4, 12, 7, 12, 6, 18, 19, 20, 4, 7. 6, 5, 17, 16. 19

Important Questions on Statistics

Learn and Prepare for any exam you want !

Calculate the partition values $Q_{1}, Q_{2}, D_{2}, D_{7}, D_{8}, P_{22}$ and $P_{38}$ for the following data: $4, 7, 3, 9, 4, 12, 7, 12, 6, 18, 19, 20, 4, 7 . 6, 5, 17, 16 . 19$