| Number of letters | 1-4 | 4-7 | 7-10 | 10-13 | 13-16 | 16-19 |
| Number of surnames | 6 | 30 | 40 | 16 | 4 | 4 |
Determine the number of median letters in the surnames. Find the number of mean letters in the surnames and also, find the size of modal in the surnames.
Solution:
To compute middle:
Class Interval Frequency Cumulative Frequency
1-4 6 6
4-7 30 36
7-10 40 76
10-13 16 92
13-16 4 96
16-19 4 100
Given:
n = 100 &n/2 = 50
Middle class = 7-10
Consequently, l = 7, Cf = 36, f = 40 and h = 3
![\[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> Middle\text{ }=\text{ }7+\left( \left( 50-36 \right)/40 \right)\text{ }\times \text{ }3 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9593ba884e793008ca9600f177bcb562_l3.png "Rendered by QuickLaTeX.com")
![\[Middle\text{ }=\text{ }7+42/40\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dbce067f6ce8b52bc8629856c966cce8_l3.png "Rendered by QuickLaTeX.com")
![\[Median=8.05\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2b3ab48ae1fa73e6d313d4f112079515_l3.png "Rendered by QuickLaTeX.com")
Compute the Mode:
Modular class = 7-10,
Where, l = 7, f1 = 40, f0 = 30, f2 = 16 and h = 3
![\[Mode\text{ }=\text{ }7+\left( \left( 40-30 \right)/\left( 2\times 40-30-16 \right) \right)\text{ }\times \text{ }3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6f3504750a47aca09becdb755bc172ac_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }7+\left( 30/34 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0503c4f4a5860fa074233ba58ce5f1bf_l3.png "Rendered by QuickLaTeX.com")
= 7.88
Consequently mode = 7.88
Compute the Mean:
Class Interval fi xi fixi
1-4 6 2.5 15
4-7 30 5.5 165
7-10 40 8.5 340
10-13 16 11.5 184
13-16 4 14.5 51
16-19 4 17.5 70
Total fi = 100 Sum fixi = 825
![\[Mean\text{ }=\text{ }x\text{ }=\text{ }\sum fi\text{ }xi/\sum fi\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-db6e1fd387938a51b5ead8bcc8fd0a11_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> Mean\text{ }=\text{ }825/100\text{ }=\text{ }8.25 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-aa366f1f97427e77af53999deeab5559_l3.png "Rendered by QuickLaTeX.com")
