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The mode of the following data is $3.286$:
Family size
Number of families
1-3
7
3-5
8
5-7
2
7-9
2
9-11
1
Find the mean and median of the above data.
Family size
Number of families
1-3
7
3-5
8
5-7
2
7-9
2
9-11
1
Find the mean and median of the above data.
Show SolutionHide Solution↓
Correct Table: (2 Marks)
Mean = $\frac{84}{20} = 4.2$ (1 + 1/2 Mark)
Median = $3 + \frac{10-7}{8} \times 2$ (1 Mark)
$= 3.75$ (1/2 Mark)
Aliter: $3 \text{median} = 2(\text{4.2}) + 3.286$ or $3(3.75) = 2\text{mean} + 3.286$ (1 Mark)
$\text{median} = 3.895$ or $\text{mean} = 3.982$ (1/2 Mark)
Mean = $\frac{84}{20} = 4.2$ (1 + 1/2 Mark)
Median = $3 + \frac{10-7}{8} \times 2$ (1 Mark)
$= 3.75$ (1/2 Mark)
Aliter: $3 \text{median} = 2(\text{4.2}) + 3.286$ or $3(3.75) = 2\text{mean} + 3.286$ (1 Mark)
$\text{median} = 3.895$ or $\text{mean} = 3.982$ (1/2 Mark)