Question

This histogram represents a sampling of recent visitors to the mall on a Friday night, grouped by their ages.


If you knew the exact values of the data points for this data set, which measure of center (the mean or median) would most likely provide a more accurate picture of the data set? Explain your reasoning.

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Answer 1

Solution :-

we know that, when their are few extreme score , median is best measure to provide a more accurate picture of the data set .

so, finding the median we get,

Class interval Fi CF

9 - 19 ----------- 8 ------- 8

19 - 29 ----------5 ------- 13

29 - 39 ----------4 ------- 17

39 - 49 ----------2 ------- 19

49 - 59 -----------1 ------- 20

here,

→ N/2 = 20/2 = 10

Then, Cumulative frequency greater than 10 is 13, corresponds to the class 19 - 29.

Therefore,

→ Class 19 - 29 is the median class.

Now,

• Median = l + [{(n/2) - cf} / f] * h

from data we have :-

• l = lower limit of median class = 19
• n = total frequency = 20
• cf = Cumulative frequency of class before median class = 8 .
• f = frequency of median class = 5 .
• h = size of class = 10 .

Putting all value we get :-

→ Median = 19 + [(10 - 8)/5] * 10

→ Median = 19 + (2/5) * 10

→ Median = 19 + 4

→ Median = 23 .

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