In a village, an enumerator has surveyed for $25$ households. The size of the family (number of family members) and the number of families is tabulated as follows:
Size of the family
(No. of members) 1-3 3-5 5-7 7-9 9-11
No. of families $6$ $7$ $9$ $2$ $1$
Find the mode of the data.

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Solution

Mode of a grouped frequency data is given by:
Mode = $l + [\frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}}] h$
where, $l$ = lower limit of modal class = $5$
$f_{m}$ = maximum frequency = $9$
$f_{1}$ = frequency of premodal vlass = $7$
$f_{2}$ = frequency of post class = $2$
$h =$ width of modal class = $3$
Mode $= 5 + [\frac{9 - 7}{2 (9) - 7 - 2}] 3$

$= 5 + [\frac{2}{9}] 3$

$= 5 + \frac{2}{3}$

$= 5 + 0.66$

$= 5.66$

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In a village, an enumerator has surveyed for 25 households. The size of the family (number of family members) and the number of families is tabulated as follows:Size of the family(No. of members)1-33-55-77-99-11No. of families67921Find the mode of the data.

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In a village, an enumerator has surveyed for $25$ households. The size of the family (number of family members) and the number of families is tabulated as follows:
Size of the family
(No. of members) 1-3 3-5 5-7 7-9 9-11
No. of families $6$ $7$ $9$ $2$ $1$
Find the mode of the data.