Question

84. Given the following box plot: 10 12 13 Figure 2.41 a. which quarter has the smallest spread of data? What is that spread? b. which quarter has the largest spread of data? What is that spread? C. find the interquartile range (IQR). d. are there more data in the interval 5-10 or in the interval 10-13? How do you know this? e. which interval has the fewest data in it? How do you know this? i. 0-2 ii. 2-4 iii. 10-12 iv. 12-13 V. need more information 148 Chapter 2 Descriptive Statistics 85. The following box plot shows the U.S. Population for 1990, the latest available year. 6 17 33 50 -105 Figure 2.42 a. Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)? How do you know? b. 12.6% are age 65 and over. Approximately what percentage of the population are working age adults (above age 17 to age 65)?

Answer 1

84. The given image is the box and whishker plot of a data set.

a) A spread is the variability of the data set, which says how much variation present in the data set, in other words how data is spread or scattered. The measure of spread are Variances, Interquartile range , Range.

Here to find the minimum spread of the quarter so as we can see that the last quarter 12-13 appears to be smaller in area as can be witnessed by naked eye, so let's check its Range.

Range = Maximum value- Minimum value

Range=13-12

=1

So, we can see that Quarter 12-13 has the least Range and has least spread.

b) A spread is the variability of the data set, which says how much variation present in the data set, in other words how data is spread or scattered. The measure of spread are Variances, Interquartile range , Range.

Here to find the largest spread of the quarter so as we can see that the quarter 02-10 appears to be larges in area as can be witnessed by naked eye, so let's check its Range.

Range = Maximum value- Minimum value

Range=10-2

=8

So, we can see that Quarter 02-10 has the Maximum Range and has maximum spread.

c) IQR is the interquartile range which is caluclated as:

Q3-Q1

where Q1 is the the Quartile 1 which lies at the 25th percentile of the data set expressed by box-plot, and in our case the Q1 is 02.

and Q1 is the the Quartile 3 which lies at the 75th percentile of the data set expressed by box-plot, and in our case the Q1 is 12.

So, IQR= Q3-Q1

=> IQR=12- 02

=> IQR = 10

d) 10-13 area hhas the more data set tha 5-10 because 10 is the 50th percentile and 13 is the maximum value of the data set and 50 % of data lie between 10- 13, but in case of 5-10, 10 is the 50th percentile value and 5 is some where between 02-10, and 02 is the 25th percentile of the data set which means less than 25 % of data lie within 5-10.

e) Again 2 -4 has the fewest data , since all the intervals are having 25 % of data set and 4 is somewhere between interval 2-10 which also constitues 25% od data, so the interval 2-4 has fewest data or less than 25% of data.

85)

a) No, Age 17 or below has more children than of the interval which has senior citizen age over 65 becasue the plot which is provided for calculation is a box and whishker-plot and which suggest that Age below 17 the no of children are 25% of Total no of people, because 0- 17 interval is a quarter of the data set and 25% of values lie within and 65 is some where between interval 50- 105 which is also a quarter and consist of 25 % of people so, 65- 105 will have less than 25% of values.

b) If 12.6 % are over 65 years of age then from the box plot almost 100-12.6= 87.4% are less than 65 years of age .

Also from the box plot we can say that 25% are below age of 17 because 17 is at Q1 which is 25th percentile, so the percentage of population working between 17 and 65 years of age are:

=> 87.4-25

=> 62.4 %.

Note : By the below image the box-plot can be more understood: