For the data of problem 13, find median calories consumed daily by a day.

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Solution

For the calculation of median, we need to prepare the cumulative frequency distribution (less than type)
table as shown:

Calories Frequency of no. of boys $(f_{i})$ Cumulative frequency (less than type)

1000-1500 5 5

1500-2000 13 18

2000-2500 16 34

2500-3000 18 52

3000-3500 27 79

3500-4000 10 89

4000-4500 4 93

$Total frequency = \sum_{}^{} f_{i} = N = 93 ∴ \frac{N}{2} = \frac{93}{2} = 46.5 So, cumulative frequency should be just greater than or equal to 46.5, i . e . 52 . Therefore, the median class will be 2500 - 3000 . Median = L + (\frac{N}{2} - c . f .) \frac{h}{f} Here, L = lower limit of the median class = 2500 c . f . = cumulative frequency of the class preceeding the median clas s = 34 h = width of the median class = 500 f = frequency of the median class = 18 ∴ Median = 2500 + (46.5 - 34) \frac{500}{18} = 2500 + 12.5 \times 27.78 = 2500 + 347.25 = 2847.25 ∴ Media n calories consumed daily by a boy are 2847.25 .$

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Similar questions

Calories	1000-1500	1500-2000	2000-2500	2500-3000	3000-3500	3500-4000	4000-4500
No. of boys	5	13	16	18	27	10	4

1680

12 %

900

1600

\frac{1}{2}

\frac{1}{4}

25

1, 000

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Calories	Frequency of no. of boys $(f_{i})$	Cumulative frequency (less than type)
1000-1500	5	5
1500-2000	13	18
2000-2500	16	34
2500-3000	18	52
3000-3500	27	79
3500-4000	10	89
4000-4500	4	93