Question

	Women’s salaries (thousands of pounds)	Men’s salaries (thousands of pounds)
Min	22	26
Median	26.5	30.5
Max	33	36
Mean	27.1	31.7
SD	3.4	3
IQ range	6	3
Range	11	10

a

(ii) Is this an example of continuous or discrete data? (iii) Use the two measures of location to say which gender has the er salary on average (iv) Use all three measures of spread to say which gender has the greater variability in their salary (b) (i) Create boxplots for these two datasets (either drawn by hand or as a printout from Dataplotter). Include all the relevant information required for drawing boxplots as set out in Subsection 1.2 of Unit 11 The summary values can be displayed on the borplots themselves or in a table to the side of the chart, as they appear in Dataplotter (ii) Use the boxplot for women's salaries to say whether the data are symmetric or skewed. If the data are skewed, then state whether they are skewed to the left or skewed to the right. What does this tell you about how the data are spread in the dataset for women? (iii) The HR manager of the company tries to summarise what the boxplots are telling him. Are the following statements true or false? In each case justify your answer (1) About three-quarters of the women are paid less than £24000 (2) There are more men being paid more than £32000 than men being paid less than £32000 New data 5 Min: Q1: Median: 26.5 Q3: 30 Max: 33 Mean: 27.1 SD: IQR: 6 Range: 11 22 24 26 28 30 32 34 3 20 n: Womens Salaries New data 6 Min: 26 Q1: 30.5 Median: 32 33.5 Q3: Max: 36 Mean: 31.7 SD: 2.97 IQR: 3 Range: 10 22 24 26 28 30 32 34 36 20 n: Mens Salaries (c) The company also records the length of service for the two groups. The data are given in Table 2 Men's and women's length of service Table 2 Women (years Men (years) 0 Min Median 21 16 Max 10.3 8.3 Mean 6.3 3.8 SD 12 5.5 IQ range 21 16 The HR manager creates histograms for the length of service data, shown in Figure 1, but forgets to label them. Which histogram represents the women's data? Explain your answer 21 15 10 Years Interval: 2 Start value: 0 0 20 10 Intervat: 2 Start value: 0

Answer 1

a (i) It is an example of conitnuous data.

(ii) Mean and median are 2 of the measures of location. Looking at the mean and median salary, we see that men have a greater salary on an average than women. Measure of location help to summarize the data and arrive at a value that can be used on a general level.

	Women	Men
Median	26.5	30.5
Mean	27.1	31.7

(iii) The 3 measures of spread are range, interquartile range and standard deviation. Looking at the data women have a greater variablility than men. Measure of spread help us to check if the data values are similar and close to each other or vary highly.

	Women	Men
Range	11	10
IQR	6	3
SD	3.4	3

b (i) For a boxplot we need 5 values : Min, Q1, Median, Q3 and Max.

	Women	Men
Min	22	26
Q1	24	30.5
Median	26.5	32
Q3	30	33.5
Max	33	36

There has been an incorrection : In the first set of values median of men is 30.5 and in the second set it is 32. Please look into this.

The question shows the box plot. Description: Starting from left, the 1st point is Min, the 1st side of the box is Q1, the line in the box is the Median, the second side is the Q3 and the last point is Max.

(ii) In a box plot, if the median line is to towards the left of the box then we it is skewed right and vice versa. Looking at the women's plot we see that the space is wider to the right of the median. That means it is skewed right.Mean of women is greater than median.It means that salaries of women receiving more than 26500 are close to each other than those receiving less than 26500.

(iii) (1) It is a false statement.

Q1 = 24 which tells use the 25th percentile or one quarter. Q3 tells us about 75th percentile or 3 quarters. So according to the data one quarter of women are paid less than 24000.

(2) it is a false statement.

Looking at plot, the median line is in the middle of the box. That is it is symmetrical. That means equal number of men getting paid more than 32000 as tha of less than 32000.

c) The first histogram describes woemn's service time and second shows for men. Following are the measures compared to interpret the result:

Max : Max of women is 16 which is smaller than 21 (men). In the 1st plot, it ends at 16.

Sd : SD of women is 3.8 whic is lesser than 6.3. That means data of men will be more spread out than women. Second one is more spread out compartively.