Question

# The following frequency table summarizes a set of data. What is the five-number summary? Value Frequency...

The following frequency table summarizes a set of data. What is the five-number summary?

Value Frequency
2 5
3 2
4 1
5 1
12 1
13 1
14 5
15 3
17 1
19 1
20 1
22 1

Min Q1 Median Q3 Max
2 5 6 14 22

Min Q1 Median Q3 Max
2 3 7 15 22

Min Q1 Median Q3 Max
2 8 9 17 22

Min Q1 Median Q3 Max
2 4 18 17 22

Min Q1 Median Q3 Max
2 3 14 15 22

Five point summary

We get the data as:

2,2,2,2,2,3,3,4,5,12,13,14,14,14,14,14,15,15,15,17,19,20,22.

So there are 23 data points in total.

Minimum and maximum are clearly 2 and 22 respectively.

As 23 is odd so [(23+1)/2]= 12th data point is the median which is 14 here. So median =14.

Q1 and Q3 are the middle points of the first and second halves of the data respectively.

Now the first half is 2,2,2,2,2,3,3,4,5,12,13 and the second half is 14,14,14,14,15,15,15,17,19,20,22.

Clearly the middle point of first half is 3 and second half is 15.

Thus Q1= 3 and Q3= 15.

So the last option is correct.

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