SaiBook.us Statistics

Lesson Example Discussion Quiz: Class Homework

Example

Title: Bowley’s Coefficient of skewness

Grade: 9-a Lesson: S2-L8

Explanation: The best way to understand statistics is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

The weights of 8 people were recorded in kg as 35, 41, 42, 56, 58, 62, 90, 77. Find the percentile for the weight 58 kg.

$1$

Step 1a

Bulding the cumulative frequencies

Explanation:

Height (in inches) ⇒ No.of females

Cumulative frequency

< 61 ⇒ 9

61-63 ⇒ 20

9+20 = 29

63-65 ⇒ 35

29+35 = 64

65-67 ⇒ 10

64+10 = 74

67-69 ⇒ 6

74+6 = 80

Step 1b

Calculating the quartiles \$Q_1,Q_2,Q_3\$

Explanation:

\$Q_1 = N/4 = 80/4 = 20\$

\$Q_1\$ class is (61-63)

\$l_1 = 61,l_2 = 63\$ ,c.f. = 9,f=20

\$Q_1 = l_1 + ((l_2-l_1)(N/4 - c.f.))/f\$

\$Q_1 = 61 + ((63-61)(20 - 9))/20\$

⇒\$Q_1 = 62.1\$

\$Q_2 = "2N"/4 = 2*80/4 = 160/4 = 40\$

\$Q_2\$ class is (63-65)

\$l_1 = 63,l_2 = 65\$ ,c.f. = 29,f=35

\$Q_2 = l_1 + ((l_2-l_1)(2N/4 - c.f.))/f\$

\$Q_2 = 63 + ((65-63)(40 - 29))/35\$

⇒\$Q_2 = 63.62\$

\$Q_3 = "3N"/4 = 3*80/4 = 240/4 = 60\$

\$Q_3\$ class is (63-65)

\$l_1 = 63,l_2 = 65\$ ,c.f. = 29,f=35

\$Q_3 = l_1 + ((l_2-l_1)(3N/4 - c.f.))/f\$

\$Q_3 = 63 + ((65-63)(60 - 29))/35\$

⇒\$Q_3 = 64.77\$

Step 1c

Calculate skewness

Explanation:

skewness = \$(Q_3+Q_1-2Q_2)/(Q_3-Q_1)\$

substitute \$Q_1 = 62.1,Q_2 = 63.62,Q_3 = 64.77\$ in skewness

\$SK_B = (64.77+62.1-2(63.62))/(64.77-62.1)\$

\$SK_B = -0.144\$

skewness < 0,

i.e,\$Q_3-Q_2 < Q_2-Q_1\$ then the distribution or the curve is negatively skewed.