# Barrow Solutions Chapter 1

Michael Barrow

Solutions to End of Chapter Problems – Selected Chapters

Chapter 1 –

Problem number:

1.1a)

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When comparing, you have to taken into consideration the difference in the sample size, which distorts the comparison. Comparing the two graphs, there seems to be more women than men with Other Qualification and more men with Higher Education.

1.1b)

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Comparing the two graphs, there is an indication that there are more inactive women, especially in the Other Qualification and No Qualification groups.

1.1c)

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Outcome is very similar to Figure 1.4, and the reasons are likely to be the same as well.

1.1d)

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Not too dissimilar to Figure 1.5, but comparatively a higher percentage of women with Other Qualifications (54.4% vs. 41%) and lower percentage in the other categories.

1.2a) The data in this exercise show median in each category, whereas exercise 1 showed count. Previous exercise was frequency and this exercise is monetary values.

1.2b)

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Key conclusions from this bar chart are:

• Salary reduces as employees are less qualified

• Male salaries are higher than female salaries in all qualification levels

1.2c)This data is not additive and stacked bar charts should only be used when data is additive, i.e. when you are using frequencies, not medians as in this case. To combine different sets of information like this, normally you would need to take a weighted average, but that would only work for means and you would need to know the number of males and females in the sample. For medians that can not be done.

1.3a)Higher Education with 88%

| |Higher Education |A Levels |Other Qualification |No Qualification | |In Work |87.82% |80.89% |65.57% |35.38% | |Unemployed |5.04% |4.00% |7.73% |12.31% | |Inactive |7.14% |15.11% |26.70% |52.31% |

1.3b)In Work with 20%.

| |Higher Education |A Levels |Other Qualification |No Qualification | |In Work |19.72% |17.17% |54.43% |8.68% | |Unemployed |9.92% |7.44% |56.20% |26.45% | |Inactive |4.03% |8.06% |55.69% |32.23% |

1.4a)156 for men (433 -277) and 145 for women (346 – 201)

1.4b)The mean is more affected by outliers than the median, and as the likelihood is that the range of men’s salaries is greater than the range of women’s salaries, one would expect the difference of the means to be greater than the difference of the medians.

1.5)

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1.6

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1.7a)Note: all answers in 000s

Mean = (Sum mid-point of each class * Number) / Sum of number = 322,157.5 / 19,645 = 16.399

Median – (19.645+1) / 2 = 9.823, which is the position of the median; Median = (9,823 – 7,095 –cumulative frequency up to class 3-) / 3,483 * 5 (class 4 size) + 5 (start of class 4) = 8.916

Mode – by dividing each class by the width (e.g. 1606/1; 2927/2000; 2562/2000, etc), you will find that the class with the highest density is the first, which is were the mode is.

1.7b)Q1 - (19,645+1) / 4 = 4,911, which is the position of Q1; Q1 = (4,911 – 4,533 –cumulative frequency up to class 2-) / 2,562 * 2 + 3 = 3.295 Q3 = 18.34 and IQR = 15.044

Variance = 652.88 (sum of the square of the mid-points times the frequency for all classes -18,108,920- divided by the frequency -19,645- minus the mean squared)

Standard deviation = 25.55

Coefficient of Variation = Standard Deviation / Mean = 1.56

1.7c)Coefficient of skewness = sum of [frequency *...

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