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
\[\begin{array}{*{35}{l}}
Middle\text{ }=\text{ }7+\left( \left( 50-36 \right)/40 \right)\text{ }\times \text{ }3 \\
~ \\
\end{array}\]
\[Middle\text{ }=\text{ }7+42/40\]
\[Median=8.05\]
Compute the Mode:
Modular class = 7-10,
Where, l = 7, f1 = 40, f0 = 30, f2 = 16 and h = 3
\[Mode\text{ }=\text{ }7+\left( \left( 40-30 \right)/\left( 2\times 40-30-16 \right) \right)\text{ }\times \text{ }3\]
\[=\text{ }7+\left( 30/34 \right)\]
= 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
\[Mean\text{ }=\text{ }x\text{ }=\text{ }\sum fi\text{ }xi/\sum fi\]
\[\begin{array}{*{35}{l}}
Mean\text{ }=\text{ }825/100\text{ }=\text{ }8.25 \\
~ \\
\end{array}\] Consequently, mean = 8.25