In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:
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.

Question

In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:
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.

Infinity Learn · Accepted Answer

To calculate median:Class IntervalFrequencyCumulative Frequency1-4664-730367-10407610-13169213-1649616-194100Given:n = 100 &n2 = 50Median class = 7-10Therefore, l = 7, Cf = 36, f = 40 & h = 3Median = 7+(50-3640) × 3Median = 7+4240Median=8.05Calculate the Mode:Modal class = 7-10,Where, l = 7, f1 = 40, f0 = 30, f2 = 16 & h = 3Mode = 7+(40-3080-30-16) × 3= 7+3034= 7.88Therefore mode = 7.88Calculate the Mean:Class Intervalfixifixi1-462.5154-7305.51657-10408.534010-131611.518413-16414.55116-19417.570 Sum fi = 100 Sum fixi = 825Mean = x̄ = ∑ fixi∑ fi Mean = 825100 = 8.25Therefore, mean = 8.25

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Number of letters	1-4	4-7	7-10	10-13	13-16	16-19
Number of surnames	6	30	40	16	4	4

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

Class Interval	f_i	x_i	f_ix_i
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
	Sum f_i = 100		Sum f_ix_i = 825